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-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/Atlas.cpp1519
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/Atlas.h186
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.cpp1320
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.h111
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.cpp1387
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.h63
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.cpp483
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.h15
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.cpp99
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.h15
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.cpp323
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.h56
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.cpp53
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.h18
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/Util.cpp326
-rw-r--r--thirdparty/thekla_atlas/nvmesh/param/Util.h18
16 files changed, 5992 insertions, 0 deletions
diff --git a/thirdparty/thekla_atlas/nvmesh/param/Atlas.cpp b/thirdparty/thekla_atlas/nvmesh/param/Atlas.cpp
new file mode 100644
index 0000000000..98f92cef96
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/Atlas.cpp
@@ -0,0 +1,1519 @@
+// Copyright NVIDIA Corporation 2006 -- Ignacio Castano <icastano@nvidia.com>
+
+#include "nvmesh.h" // pch
+
+#include "Atlas.h"
+#include "Util.h"
+#include "AtlasBuilder.h"
+#include "AtlasPacker.h"
+#include "SingleFaceMap.h"
+#include "OrthogonalProjectionMap.h"
+#include "LeastSquaresConformalMap.h"
+#include "ParameterizationQuality.h"
+
+//#include "nvmesh/export/MeshExportOBJ.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/halfedge/Vertex.h"
+
+#include "nvmesh/MeshBuilder.h"
+#include "nvmesh/MeshTopology.h"
+#include "nvmesh/param/Util.h"
+#include "nvmesh/geometry/Measurements.h"
+
+#include "nvmath/Vector.inl"
+#include "nvmath/Fitting.h"
+#include "nvmath/Box.inl"
+#include "nvmath/ProximityGrid.h"
+#include "nvmath/Morton.h"
+
+#include "nvcore/StrLib.h"
+#include "nvcore/Array.inl"
+#include "nvcore/HashMap.inl"
+
+using namespace nv;
+
+
+/// Ctor.
+Atlas::Atlas()
+{
+ failed=false;
+}
+
+// Dtor.
+Atlas::~Atlas()
+{
+ deleteAll(m_meshChartsArray);
+}
+
+uint Atlas::chartCount() const
+{
+ uint count = 0;
+ foreach(c, m_meshChartsArray) {
+ count += m_meshChartsArray[c]->chartCount();
+ }
+ return count;
+}
+
+const Chart * Atlas::chartAt(uint i) const
+{
+ foreach(c, m_meshChartsArray) {
+ uint count = m_meshChartsArray[c]->chartCount();
+
+ if (i < count) {
+ return m_meshChartsArray[c]->chartAt(i);
+ }
+
+ i -= count;
+ }
+
+ return NULL;
+}
+
+Chart * Atlas::chartAt(uint i)
+{
+ foreach(c, m_meshChartsArray) {
+ uint count = m_meshChartsArray[c]->chartCount();
+
+ if (i < count) {
+ return m_meshChartsArray[c]->chartAt(i);
+ }
+
+ i -= count;
+ }
+
+ return NULL;
+}
+
+// Extract the charts and add to this atlas.
+void Atlas::addMeshCharts(MeshCharts * meshCharts)
+{
+ m_meshChartsArray.append(meshCharts);
+}
+
+void Atlas::extractCharts(const HalfEdge::Mesh * mesh)
+{
+ MeshCharts * meshCharts = new MeshCharts(mesh);
+ meshCharts->extractCharts();
+ addMeshCharts(meshCharts);
+}
+
+void Atlas::computeCharts(const HalfEdge::Mesh * mesh, const SegmentationSettings & settings, const Array<uint> & unchartedMaterialArray)
+{
+ failed=false;
+ MeshCharts * meshCharts = new MeshCharts(mesh);
+ meshCharts->computeCharts(settings, unchartedMaterialArray);
+ addMeshCharts(meshCharts);
+}
+
+
+
+
+#if 0
+
+/// Compute a seamless texture atlas.
+bool Atlas::computeSeamlessTextureAtlas(bool groupFaces/*= true*/, bool scaleTiles/*= false*/, uint w/*= 1024*/, uint h/* = 1024*/)
+{
+ // Implement seamless texture atlas similar to what ZBrush does. See also:
+ // "Meshed Atlases for Real-Time Procedural Solid Texturing"
+ // http://graphics.cs.uiuc.edu/~jch/papers/rtpst.pdf
+
+ // Other methods that we should experiment with:
+ //
+ // Seamless Texture Atlases:
+ // http://www.cs.jhu.edu/~bpurnomo/STA/index.html
+ //
+ // Rectangular Multi-Chart Geometry Images:
+ // http://graphics.cs.uiuc.edu/~jch/papers/rmcgi.pdf
+ //
+ // Discrete differential geometry also provide a way of constructing
+ // seamless quadrangulations as shown in:
+ // http://www.geometry.caltech.edu/pubs/TACD06.pdf
+ //
+
+#pragma message(NV_FILE_LINE "TODO: Implement seamless texture atlas.")
+
+ if (groupFaces)
+ {
+ // @@ TODO.
+ }
+ else
+ {
+ // @@ Create one atlas per face.
+ }
+
+ if (scaleTiles)
+ {
+ // @@ TODO
+ }
+
+ /*
+ if (!isQuadMesh(m_mesh)) {
+ // Only handle quads for now.
+ return false;
+ }
+
+ // Each face is a chart.
+ const uint faceCount = m_mesh->faceCount();
+ m_chartArray.resize(faceCount);
+
+ for(uint f = 0; f < faceCount; f++) {
+ m_chartArray[f].faceArray.clear();
+ m_chartArray[f].faceArray.append(f);
+ }
+
+ // Map each face to a separate square.
+
+ // Determine face layout according to width and height.
+ float aspect = float(m_width) / float(m_height);
+
+ uint i = 2;
+ uint total = (m_width / (i+1)) * (m_height / (i+1));
+ while(total > faceCount) {
+ i *= 2;
+ total = (m_width / (i+1)) * (m_height / (i+1));
+ }
+
+ uint tileSize = i / 2;
+
+ int x = 0;
+ int y = 0;
+
+ m_result = new HalfEdge::Mesh();
+
+ // Once you have that it's just matter of traversing the faces.
+ for(uint f = 0; f < faceCount; f++) {
+ // Compute texture coordinates.
+ Vector2 tex[4];
+ tex[0] = Vector2(float(x), float(y));
+ tex[1] = Vector2(float(x+tileSize), float(y));
+ tex[2] = Vector2(float(x+tileSize), float(y+tileSize));
+ tex[3] = Vector2(float(x), float(y+tileSize));
+
+ Array<uint> indexArray(4);
+
+ const HalfEdge::Face * face = m_mesh->faceAt(f);
+
+ int i = 0;
+ for(HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance(), i++) {
+ const HalfEdge::Edge * edge = it.current();
+ const HalfEdge::Vertex * vertex = edge->from();
+
+ HalfEdge::Vertex * newVertex = m_result->addVertex(vertex->id(), vertex->pos());
+
+ newVertex->setTex(Vector3(tex[i], 0));
+ newVertex->setNor(vertex->nor());
+
+ indexArray.append(m_result->vertexCount() + 1);
+ }
+
+ m_result->addFace(indexArray);
+
+ // Move to the next tile.
+ x += tileSize + 1;
+ if (x + tileSize > m_width) {
+ x = 0;
+ y += tileSize + 1;
+ }
+ }
+ */
+
+ return false;
+}
+
+#endif
+
+
+void Atlas::parameterizeCharts()
+{
+ foreach(i, m_meshChartsArray) {
+ m_meshChartsArray[i]->parameterizeCharts();
+ }
+}
+
+
+float Atlas::packCharts(int quality, float texelsPerUnit, bool blockAlign, bool conservative)
+{
+ AtlasPacker packer(this);
+ packer.packCharts(quality, texelsPerUnit, blockAlign, conservative);
+ if (hasFailed())
+ return 0;
+ return packer.computeAtlasUtilization();
+}
+
+
+
+
+/// Ctor.
+MeshCharts::MeshCharts(const HalfEdge::Mesh * mesh) : m_mesh(mesh)
+{
+}
+
+// Dtor.
+MeshCharts::~MeshCharts()
+{
+ deleteAll(m_chartArray);
+}
+
+
+void MeshCharts::extractCharts()
+{
+ const uint faceCount = m_mesh->faceCount();
+
+ int first = 0;
+ Array<uint> queue(faceCount);
+
+ BitArray bitFlags(faceCount);
+ bitFlags.clearAll();
+
+ for (uint f = 0; f < faceCount; f++)
+ {
+ if (bitFlags.bitAt(f) == false)
+ {
+ // Start new patch. Reset queue.
+ first = 0;
+ queue.clear();
+ queue.append(f);
+ bitFlags.setBitAt(f);
+
+ while (first != queue.count())
+ {
+ const HalfEdge::Face * face = m_mesh->faceAt(queue[first]);
+
+ // Visit face neighbors of queue[first]
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+ nvDebugCheck(edge->pair != NULL);
+
+ if (!edge->isBoundary() && /*!edge->isSeam()*/
+ //!(edge->from()->tex() != edge->pair()->to()->tex() || edge->to()->tex() != edge->pair()->from()->tex()))
+ !(edge->from() != edge->pair->to() || edge->to() != edge->pair->from())) // Preserve existing seams (not just texture seams).
+ {
+ const HalfEdge::Face * neighborFace = edge->pair->face;
+ nvDebugCheck(neighborFace != NULL);
+
+ if (bitFlags.bitAt(neighborFace->id) == false)
+ {
+ queue.append(neighborFace->id);
+ bitFlags.setBitAt(neighborFace->id);
+ }
+ }
+ }
+
+ first++;
+ }
+
+ Chart * chart = new Chart();
+ chart->build(m_mesh, queue);
+
+ m_chartArray.append(chart);
+ }
+ }
+}
+
+
+/*
+LSCM:
+- identify sharp features using local dihedral angles.
+- identify seed faces farthest from sharp features.
+- grow charts from these seeds.
+
+MCGIM:
+- phase 1: chart growth
+ - grow all charts simultaneously using dijkstra search on the dual graph of the mesh.
+ - graph edges are weighted based on planarity metric.
+ - metric uses distance to global chart normal.
+ - terminate when all faces have been assigned.
+- phase 2: seed computation:
+ - place new seed of the chart at the most interior face.
+ - most interior is evaluated using distance metric only.
+
+- method repeates the two phases, until the location of the seeds does not change.
+ - cycles are detected by recording all the previous seeds and chartification terminates.
+
+D-Charts:
+
+- Uniaxial conic metric:
+ - N_c = axis of the generalized cone that best fits the chart. (cone can a be cylinder or a plane).
+ - omega_c = angle between the face normals and the axis.
+ - Fitting error between chart C and tringle t: F(c,t) = (N_c*n_t - cos(omega_c))^2
+
+- Compactness metrics:
+ - Roundness:
+ - C(c,t) = pi * D(S_c,t)^2 / A_c
+ - S_c = chart seed.
+ - D(S_c,t) = length of the shortest path inside the chart betwen S_c and t.
+ - A_c = chart area.
+ - Straightness:
+ - P(c,t) = l_out(c,t) / l_in(c,t)
+ - l_out(c,t) = lenght of the edges not shared between C and t.
+ - l_in(c,t) = lenght of the edges shared between C and t.
+
+- Combined metric:
+ - Cost(c,t) = F(c,t)^alpha + C(c,t)^beta + P(c,t)^gamma
+ - alpha = 1, beta = 0.7, gamma = 0.5
+
+
+
+
+Our basic approach:
+- Just one iteration of k-means?
+- Avoid dijkstra by greedily growing charts until a threshold is met. Increase threshold and repeat until no faces left.
+- If distortion metric is too high, split chart, add two seeds.
+- If chart size is low, try removing chart.
+
+
+Postprocess:
+- If topology is not disk:
+ - Fill holes, if new faces fit proxy.
+ - Find best cut, otherwise.
+- After parameterization:
+ - If boundary self-intersects:
+ - cut chart along the closest two diametral boundary vertices, repeat parametrization.
+ - what if the overlap is on an appendix? How do we find that out and cut appropiately?
+ - emphasize roundness metrics to prevent those cases.
+ - If interior self-overlaps: preserve boundary parameterization and use mean-value map.
+
+*/
+
+
+SegmentationSettings::SegmentationSettings()
+{
+ // Charts have no area or boundary limits right now.
+ maxChartArea = NV_FLOAT_MAX;
+ maxBoundaryLength = NV_FLOAT_MAX;
+
+ proxyFitMetricWeight = 1.0f;
+ roundnessMetricWeight = 0.1f;
+ straightnessMetricWeight = 0.25f;
+ normalSeamMetricWeight = 1.0f;
+ textureSeamMetricWeight = 0.1f;
+}
+
+
+
+void MeshCharts::computeCharts(const SegmentationSettings & settings, const Array<uint> & unchartedMaterialArray)
+{
+ Chart * vertexMap = NULL;
+
+ if (unchartedMaterialArray.count() != 0) {
+ vertexMap = new Chart();
+ vertexMap->buildVertexMap(m_mesh, unchartedMaterialArray);
+
+ if (vertexMap->faceCount() == 0) {
+ delete vertexMap;
+ vertexMap = NULL;
+ }
+ }
+
+
+ AtlasBuilder builder(m_mesh);
+
+ if (vertexMap != NULL) {
+ // Mark faces that do not need to be charted.
+ builder.markUnchartedFaces(vertexMap->faceArray());
+
+ m_chartArray.append(vertexMap);
+ }
+
+ if (builder.facesLeft != 0) {
+
+ // Tweak these values:
+ const float maxThreshold = 2;
+ const uint growFaceCount = 32;
+ const uint maxIterations = 4;
+
+ builder.settings = settings;
+
+ //builder.settings.proxyFitMetricWeight *= 0.75; // relax proxy fit weight during initial seed placement.
+ //builder.settings.roundnessMetricWeight = 0;
+ //builder.settings.straightnessMetricWeight = 0;
+
+ // This seems a reasonable estimate.
+ uint maxSeedCount = max(6U, builder.facesLeft);
+
+ // Create initial charts greedely.
+ nvDebug("### Placing seeds\n");
+ builder.placeSeeds(maxThreshold, maxSeedCount);
+ nvDebug("### Placed %d seeds (max = %d)\n", builder.chartCount(), maxSeedCount);
+
+ builder.updateProxies();
+
+ builder.mergeCharts();
+
+ #if 1
+ nvDebug("### Relocating seeds\n");
+ builder.relocateSeeds();
+
+ nvDebug("### Reset charts\n");
+ builder.resetCharts();
+
+ if (vertexMap != NULL) {
+ builder.markUnchartedFaces(vertexMap->faceArray());
+ }
+
+ builder.settings = settings;
+
+ nvDebug("### Growing charts\n");
+
+ // Restart process growing charts in parallel.
+ uint iteration = 0;
+ while (true)
+ {
+ if (!builder.growCharts(maxThreshold, growFaceCount))
+ {
+ nvDebug("### Can't grow anymore\n");
+
+ // If charts cannot grow more: fill holes, merge charts, relocate seeds and start new iteration.
+
+ nvDebug("### Filling holes\n");
+ builder.fillHoles(maxThreshold);
+ nvDebug("### Using %d charts now\n", builder.chartCount());
+
+ builder.updateProxies();
+
+ nvDebug("### Merging charts\n");
+ builder.mergeCharts();
+ nvDebug("### Using %d charts now\n", builder.chartCount());
+
+ nvDebug("### Reseeding\n");
+ if (!builder.relocateSeeds())
+ {
+ nvDebug("### Cannot relocate seeds anymore\n");
+
+ // Done!
+ break;
+ }
+
+ if (iteration == maxIterations)
+ {
+ nvDebug("### Reached iteration limit\n");
+ break;
+ }
+ iteration++;
+
+ nvDebug("### Reset charts\n");
+ builder.resetCharts();
+
+ if (vertexMap != NULL) {
+ builder.markUnchartedFaces(vertexMap->faceArray());
+ }
+
+ nvDebug("### Growing charts\n");
+ }
+ };
+ #endif
+
+ // Make sure no holes are left!
+ nvDebugCheck(builder.facesLeft == 0);
+
+ const uint chartCount = builder.chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ Chart * chart = new Chart();
+ m_chartArray.append(chart);
+
+ chart->build(m_mesh, builder.chartFaces(i));
+ }
+ }
+
+
+ const uint chartCount = m_chartArray.count();
+
+ // Build face indices.
+ m_faceChart.resize(m_mesh->faceCount());
+ m_faceIndex.resize(m_mesh->faceCount());
+
+ for (uint i = 0; i < chartCount; i++)
+ {
+ const Chart * chart = m_chartArray[i];
+
+ const uint faceCount = chart->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ uint idx = chart->faceAt(f);
+ m_faceChart[idx] = i;
+ m_faceIndex[idx] = f;
+ }
+ }
+
+ // Build an exclusive prefix sum of the chart vertex counts.
+ m_chartVertexCountPrefixSum.resize(chartCount);
+
+ if (chartCount > 0)
+ {
+ m_chartVertexCountPrefixSum[0] = 0;
+
+ for (uint i = 1; i < chartCount; i++)
+ {
+ const Chart * chart = m_chartArray[i-1];
+ m_chartVertexCountPrefixSum[i] = m_chartVertexCountPrefixSum[i-1] + chart->vertexCount();
+ }
+
+ m_totalVertexCount = m_chartVertexCountPrefixSum[chartCount - 1] + m_chartArray[chartCount-1]->vertexCount();
+ }
+ else
+ {
+ m_totalVertexCount = 0;
+ }
+}
+
+
+void MeshCharts::parameterizeCharts()
+{
+ ParameterizationQuality globalParameterizationQuality;
+
+ // Parameterize the charts.
+ uint diskCount = 0;
+ const uint chartCount = m_chartArray.count();
+ for (uint i = 0; i < chartCount; i++)\
+ {
+ Chart * chart = m_chartArray[i];
+
+ bool isValid = false;
+
+ if (chart->isVertexMapped()) {
+ continue;
+ }
+
+ if (chart->isDisk())
+ {
+ diskCount++;
+
+ ParameterizationQuality chartParameterizationQuality;
+
+ if (chart->faceCount() == 1) {
+ computeSingleFaceMap(chart->unifiedMesh());
+
+ chartParameterizationQuality = ParameterizationQuality(chart->unifiedMesh());
+ }
+ else {
+ computeOrthogonalProjectionMap(chart->unifiedMesh());
+ ParameterizationQuality orthogonalQuality(chart->unifiedMesh());
+
+ computeLeastSquaresConformalMap(chart->unifiedMesh());
+ ParameterizationQuality lscmQuality(chart->unifiedMesh());
+
+ // If the orthogonal projection produces better results, just use that.
+ // @@ It may be dangerous to do this, because isValid() does not detect self-overlaps.
+ // @@ Another problem is that with very thin patches with nearly zero parametric area, the results of our metric are not accurate.
+ /*if (orthogonalQuality.isValid() && orthogonalQuality.rmsStretchMetric() < lscmQuality.rmsStretchMetric()) {
+ computeOrthogonalProjectionMap(chart->unifiedMesh());
+ chartParameterizationQuality = orthogonalQuality;
+ }
+ else*/ {
+ chartParameterizationQuality = lscmQuality;
+ }
+
+ // If conformal map failed,
+
+ // @@ Experiment with other parameterization methods.
+ //computeCircularBoundaryMap(chart->unifiedMesh());
+ //computeConformalMap(chart->unifiedMesh());
+ //computeNaturalConformalMap(chart->unifiedMesh());
+ //computeGuidanceGradientMap(chart->unifiedMesh());
+ }
+
+ //ParameterizationQuality chartParameterizationQuality(chart->unifiedMesh());
+
+ isValid = chartParameterizationQuality.isValid();
+
+ if (!isValid)
+ {
+ nvDebug("*** Invalid parameterization.\n");
+#if 0
+ // Dump mesh to inspect problem:
+ static int pieceCount = 0;
+
+ StringBuilder fileName;
+ fileName.format("invalid_chart_%d.obj", pieceCount++);
+ exportMesh(chart->unifiedMesh(), fileName.str());
+#endif
+ }
+
+ // @@ Check that parameterization quality is above a certain threshold.
+
+ // @@ Detect boundary self-intersections.
+
+ globalParameterizationQuality += chartParameterizationQuality;
+ }
+
+ if (!isValid)
+ {
+ //nvDebugBreak();
+ // @@ Run the builder again, but only on this chart.
+ //AtlasBuilder builder(chart->chartMesh());
+ }
+
+ // Transfer parameterization from unified mesh to chart mesh.
+ chart->transferParameterization();
+
+ }
+
+ nvDebug(" Parameterized %d/%d charts.\n", diskCount, chartCount);
+ nvDebug(" RMS stretch metric: %f\n", globalParameterizationQuality.rmsStretchMetric());
+ nvDebug(" MAX stretch metric: %f\n", globalParameterizationQuality.maxStretchMetric());
+ nvDebug(" RMS conformal metric: %f\n", globalParameterizationQuality.rmsConformalMetric());
+ nvDebug(" RMS authalic metric: %f\n", globalParameterizationQuality.maxAuthalicMetric());
+}
+
+
+
+Chart::Chart() : m_chartMesh(NULL), m_unifiedMesh(NULL), m_isDisk(false), m_isVertexMapped(false)
+{
+}
+
+void Chart::build(const HalfEdge::Mesh * originalMesh, const Array<uint> & faceArray)
+{
+ // Copy face indices.
+ m_faceArray = faceArray;
+
+ const uint meshVertexCount = originalMesh->vertexCount();
+
+ m_chartMesh = new HalfEdge::Mesh();
+ m_unifiedMesh = new HalfEdge::Mesh();
+
+ Array<uint> chartMeshIndices;
+ chartMeshIndices.resize(meshVertexCount, ~0);
+
+ Array<uint> unifiedMeshIndices;
+ unifiedMeshIndices.resize(meshVertexCount, ~0);
+
+ // Add vertices.
+ const uint faceCount = faceArray.count();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = originalMesh->faceAt(faceArray[f]);
+ nvDebugCheck(face != NULL);
+
+ for(HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Vertex * vertex = it.current()->vertex;
+ const HalfEdge::Vertex * unifiedVertex = vertex->firstColocal();
+
+ if (unifiedMeshIndices[unifiedVertex->id] == ~0)
+ {
+ unifiedMeshIndices[unifiedVertex->id] = m_unifiedMesh->vertexCount();
+
+ nvDebugCheck(vertex->pos == unifiedVertex->pos);
+ m_unifiedMesh->addVertex(vertex->pos);
+ }
+
+ if (chartMeshIndices[vertex->id] == ~0)
+ {
+ chartMeshIndices[vertex->id] = m_chartMesh->vertexCount();
+ m_chartToOriginalMap.append(vertex->id);
+ m_chartToUnifiedMap.append(unifiedMeshIndices[unifiedVertex->id]);
+
+ HalfEdge::Vertex * v = m_chartMesh->addVertex(vertex->pos);
+ v->nor = vertex->nor;
+ v->tex = vertex->tex;
+ }
+ }
+ }
+
+ // This is ignoring the canonical map:
+ // - Is it really necessary to link colocals?
+
+ m_chartMesh->linkColocals();
+ //m_unifiedMesh->linkColocals(); // Not strictly necessary, no colocals in the unified mesh. # Wrong.
+
+ // This check is not valid anymore, if the original mesh vertices were linked with a canonical map, then it might have
+ // some colocal vertices that were unlinked. So, the unified mesh might have some duplicate vertices, because firstColocal()
+ // is not guaranteed to return the same vertex for two colocal vertices.
+ //nvCheck(m_chartMesh->colocalVertexCount() == m_unifiedMesh->vertexCount());
+
+ // Is that OK? What happens in meshes were that happens? Does anything break? Apparently not...
+
+
+
+ Array<uint> faceIndices(7);
+
+ // Add faces.
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = originalMesh->faceAt(faceArray[f]);
+ nvDebugCheck(face != NULL);
+
+ faceIndices.clear();
+
+ for(HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Vertex * vertex = it.current()->vertex;
+ nvDebugCheck(vertex != NULL);
+
+ faceIndices.append(chartMeshIndices[vertex->id]);
+ }
+
+ m_chartMesh->addFace(faceIndices);
+
+ faceIndices.clear();
+
+ for(HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Vertex * vertex = it.current()->vertex;
+ nvDebugCheck(vertex != NULL);
+
+ vertex = vertex->firstColocal();
+
+ faceIndices.append(unifiedMeshIndices[vertex->id]);
+ }
+
+ m_unifiedMesh->addFace(faceIndices);
+ }
+
+ m_chartMesh->linkBoundary();
+ m_unifiedMesh->linkBoundary();
+
+ //exportMesh(m_unifiedMesh.ptr(), "debug_input.obj");
+
+ if (m_unifiedMesh->splitBoundaryEdges()) {
+ m_unifiedMesh = unifyVertices(m_unifiedMesh.ptr());
+ }
+
+ //exportMesh(m_unifiedMesh.ptr(), "debug_split.obj");
+
+ // Closing the holes is not always the best solution and does not fix all the problems.
+ // We need to do some analysis of the holes and the genus to:
+ // - Find cuts that reduce genus.
+ // - Find cuts to connect holes.
+ // - Use minimal spanning trees or seamster.
+ if (!closeHoles()) {
+ /*static int pieceCount = 0;
+ StringBuilder fileName;
+ fileName.format("debug_hole_%d.obj", pieceCount++);
+ exportMesh(m_unifiedMesh.ptr(), fileName.str());*/
+ }
+
+ m_unifiedMesh = triangulate(m_unifiedMesh.ptr());
+
+ //exportMesh(m_unifiedMesh.ptr(), "debug_triangulated.obj");
+
+
+ // Analyze chart topology.
+ MeshTopology topology(m_unifiedMesh.ptr());
+ m_isDisk = topology.isDisk();
+
+ // This is sometimes failing, when triangulate fails to add a triangle, it generates a hole in the mesh.
+ //nvDebugCheck(m_isDisk);
+
+ /*if (!m_isDisk) {
+ static int pieceCount = 0;
+ StringBuilder fileName;
+ fileName.format("debug_hole_%d.obj", pieceCount++);
+ exportMesh(m_unifiedMesh.ptr(), fileName.str());
+ }*/
+
+
+#if 0
+ if (!m_isDisk) {
+ nvDebugBreak();
+
+ static int pieceCount = 0;
+
+ StringBuilder fileName;
+ fileName.format("debug_nodisk_%d.obj", pieceCount++);
+ exportMesh(m_chartMesh.ptr(), fileName.str());
+ }
+#endif
+
+}
+
+
+void Chart::buildVertexMap(const HalfEdge::Mesh * originalMesh, const Array<uint> & unchartedMaterialArray)
+{
+ nvCheck(m_chartMesh == NULL && m_unifiedMesh == NULL);
+
+ m_isVertexMapped = true;
+
+ // Build face indices.
+ m_faceArray.clear();
+
+ const uint meshFaceCount = originalMesh->faceCount();
+ for (uint f = 0; f < meshFaceCount; f++) {
+ const HalfEdge::Face * face = originalMesh->faceAt(f);
+
+ if (unchartedMaterialArray.contains(face->material)) {
+ m_faceArray.append(f);
+ }
+ }
+
+ const uint faceCount = m_faceArray.count();
+
+ if (faceCount == 0) {
+ return;
+ }
+
+
+ // @@ The chartMesh construction is basically the same as with regular charts, don't duplicate!
+
+ const uint meshVertexCount = originalMesh->vertexCount();
+
+ m_chartMesh = new HalfEdge::Mesh();
+
+ Array<uint> chartMeshIndices;
+ chartMeshIndices.resize(meshVertexCount, ~0);
+
+ // Vertex map mesh only has disconnected vertices.
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = originalMesh->faceAt(m_faceArray[f]);
+ nvDebugCheck(face != NULL);
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Vertex * vertex = it.current()->vertex;
+
+ if (chartMeshIndices[vertex->id] == ~0)
+ {
+ chartMeshIndices[vertex->id] = m_chartMesh->vertexCount();
+ m_chartToOriginalMap.append(vertex->id);
+
+ HalfEdge::Vertex * v = m_chartMesh->addVertex(vertex->pos);
+ v->nor = vertex->nor;
+ v->tex = vertex->tex; // @@ Not necessary.
+ }
+ }
+ }
+
+ // @@ Link colocals using the original mesh canonical map? Build canonical map on the fly? Do we need to link colocals at all for this?
+ //m_chartMesh->linkColocals();
+
+ Array<uint> faceIndices(7);
+
+ // Add faces.
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = originalMesh->faceAt(m_faceArray[f]);
+ nvDebugCheck(face != NULL);
+
+ faceIndices.clear();
+
+ for(HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Vertex * vertex = it.current()->vertex;
+ nvDebugCheck(vertex != NULL);
+ nvDebugCheck(chartMeshIndices[vertex->id] != ~0);
+
+ faceIndices.append(chartMeshIndices[vertex->id]);
+ }
+
+ HalfEdge::Face * new_face = m_chartMesh->addFace(faceIndices);
+ nvDebugCheck(new_face != NULL);
+ }
+
+ m_chartMesh->linkBoundary();
+
+
+ const uint chartVertexCount = m_chartMesh->vertexCount();
+
+ Box bounds;
+ bounds.clearBounds();
+
+ for (uint i = 0; i < chartVertexCount; i++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(i);
+ bounds.addPointToBounds(vertex->pos);
+ }
+
+ ProximityGrid grid;
+ grid.init(bounds, chartVertexCount);
+
+ for (uint i = 0; i < chartVertexCount; i++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(i);
+ grid.add(vertex->pos, i);
+ }
+
+
+#if 0
+ // Arrange vertices in a rectangle.
+ vertexMapWidth = ftoi_ceil(sqrtf(float(chartVertexCount)));
+ vertexMapHeight = (chartVertexCount + vertexMapWidth - 1) / vertexMapWidth;
+ nvDebugCheck(vertexMapWidth >= vertexMapHeight);
+
+ int x = 0, y = 0;
+ for (uint i = 0; i < chartVertexCount; i++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(i);
+
+ vertex->tex.x = float(x);
+ vertex->tex.y = float(y);
+
+ x++;
+ if (x == vertexMapWidth) {
+ x = 0;
+ y++;
+ nvCheck(y < vertexMapHeight);
+ }
+ }
+
+#elif 0
+ // Arrange vertices in a rectangle, traversing grid in 3D morton order and laying them down in 2D morton order.
+ vertexMapWidth = ftoi_ceil(sqrtf(float(chartVertexCount)));
+ vertexMapHeight = (chartVertexCount + vertexMapWidth - 1) / vertexMapWidth;
+ nvDebugCheck(vertexMapWidth >= vertexMapHeight);
+
+ int n = 0;
+ uint32 texelCode = 0;
+
+ uint cellsVisited = 0;
+
+ const uint32 cellCodeCount = grid.mortonCount();
+ for (uint32 cellCode = 0; cellCode < cellCodeCount; cellCode++) {
+ int cell = grid.mortonIndex(cellCode);
+ if (cell < 0) continue;
+
+ cellsVisited++;
+
+ const Array<uint> & indexArray = grid.cellArray[cell].indexArray;
+
+ foreach(i, indexArray) {
+ uint idx = indexArray[i];
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(idx);
+
+ //vertex->tex.x = float(n % rectangleWidth) + 0.5f;
+ //vertex->tex.y = float(n / rectangleWidth) + 0.5f;
+
+ // Lay down the points in z order too.
+ uint x, y;
+ do {
+ x = decodeMorton2X(texelCode);
+ y = decodeMorton2Y(texelCode);
+ texelCode++;
+ } while (x >= U32(vertexMapWidth) || y >= U32(vertexMapHeight));
+
+ vertex->tex.x = float(x);
+ vertex->tex.y = float(y);
+
+ n++;
+ }
+ }
+
+ nvDebugCheck(cellsVisited == grid.cellArray.count());
+ nvDebugCheck(n == chartVertexCount);
+
+#else
+
+ uint texelCount = 0;
+
+ const float positionThreshold = 0.01f;
+ const float normalThreshold = 0.01f;
+
+ uint verticesVisited = 0;
+ uint cellsVisited = 0;
+
+ Array<int> vertexIndexArray;
+ vertexIndexArray.resize(chartVertexCount, -1); // Init all indices to -1.
+
+ // Traverse vertices in morton order. @@ It may be more interesting to sort them based on orientation.
+ const uint cellCodeCount = grid.mortonCount();
+ for (uint cellCode = 0; cellCode < cellCodeCount; cellCode++) {
+ int cell = grid.mortonIndex(cellCode);
+ if (cell < 0) continue;
+
+ cellsVisited++;
+
+ const Array<uint> & indexArray = grid.cellArray[cell].indexArray;
+
+ foreach(i, indexArray) {
+ uint idx = indexArray[i];
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(idx);
+
+ nvDebugCheck(vertexIndexArray[idx] == -1);
+
+ Array<uint> neighbors;
+ grid.gather(vertex->pos, positionThreshold, /*ref*/neighbors);
+
+ // Compare against all nearby vertices, cluster greedily.
+ foreach(j, neighbors) {
+ uint otherIdx = neighbors[j];
+
+ if (vertexIndexArray[otherIdx] != -1) {
+ HalfEdge::Vertex * otherVertex = m_chartMesh->vertexAt(otherIdx);
+
+ if (distance(vertex->pos, otherVertex->pos) < positionThreshold &&
+ distance(vertex->nor, otherVertex->nor) < normalThreshold)
+ {
+ vertexIndexArray[idx] = vertexIndexArray[otherIdx];
+ break;
+ }
+ }
+ }
+
+ // If index not assigned, assign new one.
+ if (vertexIndexArray[idx] == -1) {
+ vertexIndexArray[idx] = texelCount++;
+ }
+
+ verticesVisited++;
+ }
+ }
+
+ nvDebugCheck(cellsVisited == grid.cellArray.count());
+ nvDebugCheck(verticesVisited == chartVertexCount);
+
+ vertexMapWidth = ftoi_ceil(sqrtf(float(texelCount)));
+ vertexMapWidth = (vertexMapWidth + 3) & ~3; // Width aligned to 4.
+ vertexMapHeight = vertexMapWidth == 0 ? 0 : (texelCount + vertexMapWidth - 1) / vertexMapWidth;
+ //vertexMapHeight = (vertexMapHeight + 3) & ~3; // Height aligned to 4.
+ nvDebugCheck(vertexMapWidth >= vertexMapHeight);
+
+ nvDebug("Reduced vertex count from %d to %d.\n", chartVertexCount, texelCount);
+
+#if 0
+ // This lays down the clustered vertices linearly.
+ for (uint i = 0; i < chartVertexCount; i++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(i);
+
+ int idx = vertexIndexArray[i];
+
+ vertex->tex.x = float(idx % vertexMapWidth);
+ vertex->tex.y = float(idx / vertexMapWidth);
+ }
+#else
+ // Lay down the clustered vertices in morton order.
+
+ Array<uint> texelCodes;
+ texelCodes.resize(texelCount);
+
+ // For each texel, assign one morton code.
+ uint texelCode = 0;
+ for (uint i = 0; i < texelCount; i++) {
+ uint x, y;
+ do {
+ x = decodeMorton2X(texelCode);
+ y = decodeMorton2Y(texelCode);
+ texelCode++;
+ } while (x >= U32(vertexMapWidth) || y >= U32(vertexMapHeight));
+
+ texelCodes[i] = texelCode - 1;
+ }
+
+ for (uint i = 0; i < chartVertexCount; i++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(i);
+
+ int idx = vertexIndexArray[i];
+ if (idx != -1) {
+ uint texelCode = texelCodes[idx];
+ uint x = decodeMorton2X(texelCode);
+ uint y = decodeMorton2Y(texelCode);
+
+ vertex->tex.x = float(x);
+ vertex->tex.y = float(y);
+ }
+ }
+
+#endif
+
+#endif
+
+}
+
+
+
+static void getBoundaryEdges(HalfEdge::Mesh * mesh, Array<HalfEdge::Edge *> & boundaryEdges)
+{
+ nvDebugCheck(mesh != NULL);
+
+ const uint edgeCount = mesh->edgeCount();
+
+ BitArray bitFlags(edgeCount);
+ bitFlags.clearAll();
+
+ boundaryEdges.clear();
+
+ // Search for boundary edges. Mark all the edges that belong to the same boundary.
+ for (uint e = 0; e < edgeCount; e++)
+ {
+ HalfEdge::Edge * startEdge = mesh->edgeAt(e);
+
+ if (startEdge != NULL && startEdge->isBoundary() && bitFlags.bitAt(e) == false)
+ {
+ nvDebugCheck(startEdge->face != NULL);
+ nvDebugCheck(startEdge->pair->face == NULL);
+
+ startEdge = startEdge->pair;
+
+ const HalfEdge::Edge * edge = startEdge;
+ do {
+ nvDebugCheck(edge->face == NULL);
+ nvDebugCheck(bitFlags.bitAt(edge->id/2) == false);
+
+ bitFlags.setBitAt(edge->id / 2);
+ edge = edge->next;
+ } while(startEdge != edge);
+
+ boundaryEdges.append(startEdge);
+ }
+ }
+}
+
+
+bool Chart::closeLoop(uint start, const Array<HalfEdge::Edge *> & loop)
+{
+ const uint vertexCount = loop.count() - start;
+
+ nvDebugCheck(vertexCount >= 3);
+ if (vertexCount < 3) return false;
+
+ nvDebugCheck(loop[start]->vertex->isColocal(loop[start+vertexCount-1]->to()));
+
+ // If the hole is planar, then we add a single face that will be properly triangulated later.
+ // If the hole is not planar, we add a triangle fan with a vertex at the hole centroid.
+ // This is still a bit of a hack. There surely are better hole filling algorithms out there.
+
+ Array<Vector3> points;
+ points.resize(vertexCount);
+ for (uint i = 0; i < vertexCount; i++) {
+ points[i] = loop[start+i]->vertex->pos;
+ }
+
+ bool isPlanar = Fit::isPlanar(vertexCount, points.buffer());
+
+ if (isPlanar) {
+ // Add face and connect edges.
+ HalfEdge::Face * face = m_unifiedMesh->addFace();
+ for (uint i = 0; i < vertexCount; i++) {
+ HalfEdge::Edge * edge = loop[start + i];
+
+ edge->face = face;
+ edge->setNext(loop[start + (i + 1) % vertexCount]);
+ }
+ face->edge = loop[start];
+
+ nvDebugCheck(face->isValid());
+ }
+ else {
+ // If the polygon is not planar, we just cross our fingers, and hope this will work:
+
+ // Compute boundary centroid:
+ Vector3 centroidPos(0);
+
+ for (uint i = 0; i < vertexCount; i++) {
+ centroidPos += points[i];
+ }
+
+ centroidPos *= (1.0f / vertexCount);
+
+ HalfEdge::Vertex * centroid = m_unifiedMesh->addVertex(centroidPos);
+
+ // Add one pair of edges for each boundary vertex.
+ for (uint j = vertexCount-1, i = 0; i < vertexCount; j = i++) {
+ HalfEdge::Face * face = m_unifiedMesh->addFace(centroid->id, loop[start+j]->vertex->id, loop[start+i]->vertex->id);
+ nvDebugCheck(face != NULL);
+ }
+ }
+
+ return true;
+}
+
+
+bool Chart::closeHoles()
+{
+ nvDebugCheck(!m_isVertexMapped);
+
+ Array<HalfEdge::Edge *> boundaryEdges;
+ getBoundaryEdges(m_unifiedMesh.ptr(), boundaryEdges);
+
+ uint boundaryCount = boundaryEdges.count();
+ if (boundaryCount <= 1)
+ {
+ // Nothing to close.
+ return true;
+ }
+
+ // Compute lengths and areas.
+ Array<float> boundaryLengths;
+ //Array<Vector3> boundaryCentroids;
+
+ for (uint i = 0; i < boundaryCount; i++)
+ {
+ const HalfEdge::Edge * startEdge = boundaryEdges[i];
+ nvCheck(startEdge->face == NULL);
+
+ //float boundaryEdgeCount = 0;
+ float boundaryLength = 0.0f;
+ //Vector3 boundaryCentroid(zero);
+
+ const HalfEdge::Edge * edge = startEdge;
+ do {
+ Vector3 t0 = edge->from()->pos;
+ Vector3 t1 = edge->to()->pos;
+
+ //boundaryEdgeCount++;
+ boundaryLength += length(t1 - t0);
+ //boundaryCentroid += edge->vertex()->pos;
+
+ edge = edge->next;
+ } while(edge != startEdge);
+
+ boundaryLengths.append(boundaryLength);
+ //boundaryCentroids.append(boundaryCentroid / boundaryEdgeCount);
+ }
+
+
+ // Find disk boundary.
+ uint diskBoundary = 0;
+ float maxLength = boundaryLengths[0];
+
+ for (uint i = 1; i < boundaryCount; i++)
+ {
+ if (boundaryLengths[i] > maxLength)
+ {
+ maxLength = boundaryLengths[i];
+ diskBoundary = i;
+ }
+ }
+
+
+ // Sew holes.
+ /*for (uint i = 0; i < boundaryCount; i++)
+ {
+ if (diskBoundary == i)
+ {
+ // Skip disk boundary.
+ continue;
+ }
+
+ HalfEdge::Edge * startEdge = boundaryEdges[i];
+ nvCheck(startEdge->face() == NULL);
+
+ boundaryEdges[i] = m_unifiedMesh->sewBoundary(startEdge);
+ }
+
+ exportMesh(m_unifiedMesh.ptr(), "debug_sewn.obj");*/
+
+ //bool hasNewHoles = false;
+
+ // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+ // @@ Close loop is wrong, after closing a loop, we do not only have to add the face, but make sure that every edge in he loop is pointing to the right place.
+
+ // Close holes.
+ for (uint i = 0; i < boundaryCount; i++)
+ {
+ if (diskBoundary == i)
+ {
+ // Skip disk boundary.
+ continue;
+ }
+
+ HalfEdge::Edge * startEdge = boundaryEdges[i];
+ nvDebugCheck(startEdge != NULL);
+ nvDebugCheck(startEdge->face == NULL);
+
+#if 1
+ Array<HalfEdge::Vertex *> vertexLoop;
+ Array<HalfEdge::Edge *> edgeLoop;
+
+ HalfEdge::Edge * edge = startEdge;
+ do {
+ HalfEdge::Vertex * vertex = edge->next->vertex; // edge->to()
+
+ uint i;
+ for (i = 0; i < vertexLoop.count(); i++) {
+ if (vertex->isColocal(vertexLoop[i])) {
+ break;
+ }
+ }
+
+ bool isCrossing = (i != vertexLoop.count());
+
+ if (isCrossing) {
+
+ HalfEdge::Edge * prev = edgeLoop[i]; // Previous edge before the loop.
+ HalfEdge::Edge * next = edge->next; // Next edge after the loop.
+
+ nvDebugCheck(prev->to()->isColocal(next->from()));
+
+ // Close loop.
+ edgeLoop.append(edge);
+ closeLoop(i+1, edgeLoop);
+
+ // Link boundary loop.
+ prev->setNext(next);
+ vertex->setEdge(next);
+
+ // Start over again.
+ vertexLoop.clear();
+ edgeLoop.clear();
+
+ edge = startEdge;
+ vertex = edge->to();
+ }
+
+ vertexLoop.append(vertex);
+ edgeLoop.append(edge);
+
+ edge = edge->next;
+ } while(edge != startEdge);
+
+ closeLoop(0, edgeLoop);
+#endif
+
+ /*
+
+ // Add face and connect boundary edges.
+ HalfEdge::Face * face = m_unifiedMesh->addFace();
+ face->setEdge(startEdge);
+
+ HalfEdge::Edge * edge = startEdge;
+ do {
+ edge->setFace(face);
+
+ edge = edge->next();
+ } while(edge != startEdge);
+
+ */
+
+
+ /*
+ uint edgeCount = 0;
+ HalfEdge::Edge * edge = startEdge;
+ do {
+ edgeCount++;
+ edge = edge->next();
+ } while(edge != startEdge);
+
+
+
+ // Count edges in this boundary.
+ uint edgeCount = 0;
+ HalfEdge::Edge * edge = startEdge;
+ do {
+ edgeCount++;
+ edge = edge->next();
+ } while(edge != startEdge);
+
+ // Trivial hole, fill with one triangle. This actually works for all convex boundaries with non colinear vertices.
+ if (edgeCount == 3) {
+ // Add face and connect boundary edges.
+ HalfEdge::Face * face = m_unifiedMesh->addFace();
+ face->setEdge(startEdge);
+
+ edge = startEdge;
+ do {
+ edge->setFace(face);
+
+ edge = edge->next();
+ } while(edge != startEdge);
+
+ // @@ Implement the above using addFace, it should now work with existing edges, as long as their face pointers is zero.
+
+ }
+ else {
+ // Ideally we should:
+ // - compute best fit plane of boundary vertices.
+ // - project boundary polygon onto plane.
+ // - triangulate boundary polygon.
+ // - add faces of the resulting triangulation.
+
+ // I don't have a good triangulator available. A more simple solution that works in more (but not all) cases:
+ // - compute boundary centroid.
+ // - add vertex centroid.
+ // - connect centroid vertex with boundary vertices.
+ // - connect radial edges with boundary edges.
+
+ // This should work for non-convex boundaries with colinear vertices as long as the kernel of the polygon is not empty.
+
+ // Compute boundary centroid:
+ Vector3 centroid_pos(0);
+ Vector2 centroid_tex(0);
+
+ HalfEdge::Edge * edge = startEdge;
+ do {
+ centroid_pos += edge->vertex()->pos;
+ centroid_tex += edge->vertex()->tex;
+ edge = edge->next();
+ } while(edge != startEdge);
+
+ centroid_pos *= (1.0f / edgeCount);
+ centroid_tex *= (1.0f / edgeCount);
+
+ HalfEdge::Vertex * centroid = m_unifiedMesh->addVertex(centroid_pos);
+ centroid->tex = centroid_tex;
+
+ // Add one pair of edges for each boundary vertex.
+ edge = startEdge;
+ do {
+ HalfEdge::Edge * next = edge->next();
+
+ nvCheck(edge->face() == NULL);
+ HalfEdge::Face * face = m_unifiedMesh->addFace(centroid->id(), edge->from()->id(), edge->to()->id());
+
+ if (face != NULL) {
+ nvCheck(edge->face() == face);
+ }
+ else {
+ hasNewHoles = true;
+ }
+
+ edge = next;
+ } while(edge != startEdge);
+ }
+ */
+ }
+
+ /*nvDebugCheck(!hasNewHoles);
+
+ if (hasNewHoles) {
+ // Link boundary again, in case closeHoles created new holes!
+ m_unifiedMesh->linkBoundary();
+ }*/
+
+ // Because some algorithms do not expect sparse edge buffers.
+ //m_unifiedMesh->compactEdges();
+
+ // In case we messed up:
+ //m_unifiedMesh->linkBoundary();
+
+ getBoundaryEdges(m_unifiedMesh.ptr(), boundaryEdges);
+
+ boundaryCount = boundaryEdges.count();
+ nvDebugCheck(boundaryCount == 1);
+
+ //exportMesh(m_unifiedMesh.ptr(), "debug_hole_filled.obj");
+
+ return boundaryCount == 1;
+}
+
+
+// Transfer parameterization from unified mesh to chart mesh.
+void Chart::transferParameterization() {
+ nvDebugCheck(!m_isVertexMapped);
+
+ uint vertexCount = m_chartMesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(v);
+ HalfEdge::Vertex * unifiedVertex = m_unifiedMesh->vertexAt(mapChartVertexToUnifiedVertex(v));
+ vertex->tex = unifiedVertex->tex;
+ }
+}
+
+float Chart::computeSurfaceArea() const {
+ return nv::computeSurfaceArea(m_chartMesh.ptr()) * scale;
+}
+
+float Chart::computeParametricArea() const {
+ // This only makes sense in parameterized meshes.
+ nvDebugCheck(m_isDisk);
+ nvDebugCheck(!m_isVertexMapped);
+
+ return nv::computeParametricArea(m_chartMesh.ptr());
+}
+
+Vector2 Chart::computeParametricBounds() const {
+ // This only makes sense in parameterized meshes.
+ nvDebugCheck(m_isDisk);
+ nvDebugCheck(!m_isVertexMapped);
+
+ Box bounds;
+ bounds.clearBounds();
+
+ uint vertexCount = m_chartMesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++) {
+ HalfEdge::Vertex * vertex = m_chartMesh->vertexAt(v);
+ bounds.addPointToBounds(Vector3(vertex->tex, 0));
+ }
+
+ return bounds.extents().xy();
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/Atlas.h b/thirdparty/thekla_atlas/nvmesh/param/Atlas.h
new file mode 100644
index 0000000000..41cfaea9cb
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/Atlas.h
@@ -0,0 +1,186 @@
+// Copyright NVIDIA Corporation 2006 -- Ignacio Castano <icastano@nvidia.com>
+
+#pragma once
+#ifndef NV_MESH_ATLAS_H
+#define NV_MESH_ATLAS_H
+
+#include "nvcore/Array.h"
+#include "nvcore/Ptr.h"
+#include "nvmath/Vector.h"
+#include "nvmesh/nvmesh.h"
+#include "nvmesh/halfedge/Mesh.h"
+
+
+namespace nv
+{
+ namespace HalfEdge { class Mesh; }
+
+ class Chart;
+ class MeshCharts;
+ class VertexMap;
+
+ struct SegmentationSettings
+ {
+ SegmentationSettings();
+
+ float maxChartArea;
+ float maxBoundaryLength;
+
+ float proxyFitMetricWeight;
+ float roundnessMetricWeight;
+ float straightnessMetricWeight;
+ float normalSeamMetricWeight;
+ float textureSeamMetricWeight;
+ };
+
+
+ /// An atlas is a set of charts.
+ class Atlas
+ {
+ public:
+
+ Atlas();
+ ~Atlas();
+
+ uint meshCount() const { return m_meshChartsArray.count(); }
+ const MeshCharts * meshAt(uint i) const { return m_meshChartsArray[i]; }
+ MeshCharts * meshAt(uint i) { return m_meshChartsArray[i]; }
+
+ uint chartCount() const;
+ const Chart * chartAt(uint i) const;
+ Chart * chartAt(uint i);
+
+ // Add mesh charts and takes ownership.
+ void addMeshCharts(MeshCharts * meshCharts);
+
+ void extractCharts(const HalfEdge::Mesh * mesh);
+ void computeCharts(const HalfEdge::Mesh * mesh, const SegmentationSettings & settings, const Array<uint> & unchartedMaterialArray);
+
+
+ // Compute a trivial seamless texture similar to ZBrush.
+ //bool computeSeamlessTextureAtlas(bool groupFaces = true, bool scaleTiles = false, uint w = 1024, uint h = 1024);
+
+ void parameterizeCharts();
+
+ // Pack charts in the smallest possible rectangle.
+ float packCharts(int quality, float texelArea, bool blockAlign, bool conservative);
+ void setFailed() { failed = true; }
+ bool hasFailed() const { return failed; }
+
+ private:
+
+ bool failed;
+ Array<MeshCharts *> m_meshChartsArray;
+
+ };
+
+
+ // Set of charts corresponding to a single mesh.
+ class MeshCharts
+ {
+ public:
+ MeshCharts(const HalfEdge::Mesh * mesh);
+ ~MeshCharts();
+
+ uint chartCount() const { return m_chartArray.count(); }
+ uint vertexCount () const { return m_totalVertexCount; }
+
+ const Chart * chartAt(uint i) const { return m_chartArray[i]; }
+ Chart * chartAt(uint i) { return m_chartArray[i]; }
+
+ void computeVertexMap(const Array<uint> & unchartedMaterialArray);
+
+ // Extract the charts of the input mesh.
+ void extractCharts();
+
+ // Compute charts using a simple segmentation algorithm.
+ void computeCharts(const SegmentationSettings & settings, const Array<uint> & unchartedMaterialArray);
+
+ void parameterizeCharts();
+
+ uint faceChartAt(uint i) const { return m_faceChart[i]; }
+ uint faceIndexWithinChartAt(uint i) const { return m_faceIndex[i]; }
+
+ uint vertexCountBeforeChartAt(uint i) const { return m_chartVertexCountPrefixSum[i]; }
+
+ private:
+
+ const HalfEdge::Mesh * m_mesh;
+
+ Array<Chart *> m_chartArray;
+
+ Array<uint> m_chartVertexCountPrefixSum;
+ uint m_totalVertexCount;
+
+ Array<uint> m_faceChart; // the chart of every face of the input mesh.
+ Array<uint> m_faceIndex; // the index within the chart for every face of the input mesh.
+ };
+
+
+ /// A chart is a connected set of faces with a certain topology (usually a disk).
+ class Chart
+ {
+ public:
+
+ Chart();
+
+ void build(const HalfEdge::Mesh * originalMesh, const Array<uint> & faceArray);
+ void buildVertexMap(const HalfEdge::Mesh * originalMesh, const Array<uint> & unchartedMaterialArray);
+
+ bool closeHoles();
+
+ bool isDisk() const { return m_isDisk; }
+ bool isVertexMapped() const { return m_isVertexMapped; }
+
+ uint vertexCount() const { return m_chartMesh->vertexCount(); }
+ uint colocalVertexCount() const { return m_unifiedMesh->vertexCount(); }
+
+ uint faceCount() const { return m_faceArray.count(); }
+ uint faceAt(uint i) const { return m_faceArray[i]; }
+
+ const HalfEdge::Mesh * chartMesh() const { return m_chartMesh.ptr(); }
+ HalfEdge::Mesh * chartMesh() { return m_chartMesh.ptr(); }
+ const HalfEdge::Mesh * unifiedMesh() const { return m_unifiedMesh.ptr(); }
+ HalfEdge::Mesh * unifiedMesh() { return m_unifiedMesh.ptr(); }
+
+ //uint vertexIndex(uint i) const { return m_vertexIndexArray[i]; }
+
+ uint mapChartVertexToOriginalVertex(uint i) const { return m_chartToOriginalMap[i]; }
+ uint mapChartVertexToUnifiedVertex(uint i) const { return m_chartToUnifiedMap[i]; }
+
+ const Array<uint> & faceArray() const { return m_faceArray; }
+
+ void transferParameterization();
+
+ float computeSurfaceArea() const;
+ float computeParametricArea() const;
+ Vector2 computeParametricBounds() const;
+
+
+ float scale = 1.0f;
+ uint vertexMapWidth;
+ uint vertexMapHeight;
+
+ private:
+
+ bool closeLoop(uint start, const Array<HalfEdge::Edge *> & loop);
+
+ // Chart mesh.
+ AutoPtr<HalfEdge::Mesh> m_chartMesh;
+ AutoPtr<HalfEdge::Mesh> m_unifiedMesh;
+
+ bool m_isDisk;
+ bool m_isVertexMapped;
+
+ // List of faces of the original mesh that belong to this chart.
+ Array<uint> m_faceArray;
+
+ // Map vertices of the chart mesh to vertices of the original mesh.
+ Array<uint> m_chartToOriginalMap;
+
+ Array<uint> m_chartToUnifiedMap;
+ };
+
+} // nv namespace
+
+#endif // NV_MESH_ATLAS_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.cpp b/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.cpp
new file mode 100644
index 0000000000..bd2140c2f3
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.cpp
@@ -0,0 +1,1320 @@
+// This code is in the public domain -- castano@gmail.com
+
+#include "nvmesh.h" // pch
+
+#include "AtlasBuilder.h"
+#include "Util.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/halfedge/Vertex.h"
+
+#include "nvmath/Matrix.inl"
+#include "nvmath/Vector.inl"
+
+//#include "nvcore/IntroSort.h"
+#include "nvcore/Array.inl"
+
+#include <algorithm> // std::sort
+
+#include <float.h> // FLT_MAX
+#include <limits.h> // UINT_MAX
+
+using namespace nv;
+
+namespace
+{
+
+ // Dummy implementation of a priority queue using sort at insertion.
+ // - Insertion is o(n)
+ // - Smallest element goes at the end, so that popping it is o(1).
+ // - Resorting is n*log(n)
+ // @@ Number of elements in the queue is usually small, and we'd have to rebalance often. I'm not sure it's worth implementing a heap.
+ // @@ Searcing at removal would remove the need for sorting when priorities change.
+ struct PriorityQueue
+ {
+ PriorityQueue(uint size = UINT_MAX) : maxSize(size) {}
+
+ void push(float priority, uint face) {
+ uint i = 0;
+ const uint count = pairs.count();
+ for (; i < count; i++) {
+ if (pairs[i].priority > priority) break;
+ }
+
+ Pair p = { priority, face };
+ pairs.insertAt(i, p);
+
+ if (pairs.count() > maxSize) {
+ pairs.removeAt(0);
+ }
+ }
+
+ // push face out of order, to be sorted later.
+ void push(uint face) {
+ Pair p = { 0.0f, face };
+ pairs.append(p);
+ }
+
+ uint pop() {
+ uint f = pairs.back().face;
+ pairs.pop_back();
+ return f;
+ }
+
+ void sort() {
+ //nv::sort(pairs); // @@ My intro sort appears to be much slower than it should!
+ std::sort(pairs.buffer(), pairs.buffer() + pairs.count());
+ }
+
+ void clear() {
+ pairs.clear();
+ }
+
+ uint count() const { return pairs.count(); }
+
+ float firstPriority() const { return pairs.back().priority; }
+
+
+ const uint maxSize;
+
+ struct Pair {
+ bool operator <(const Pair & p) const { return priority > p.priority; } // !! Sort in inverse priority order!
+ float priority;
+ uint face;
+ };
+
+
+ Array<Pair> pairs;
+ };
+
+ static bool isNormalSeam(const HalfEdge::Edge * edge) {
+ return (edge->vertex->nor != edge->pair->next->vertex->nor || edge->next->vertex->nor != edge->pair->vertex->nor);
+ }
+
+ static bool isTextureSeam(const HalfEdge::Edge * edge) {
+ return (edge->vertex->tex != edge->pair->next->vertex->tex || edge->next->vertex->tex != edge->pair->vertex->tex);
+ }
+
+} // namespace
+
+
+struct nv::ChartBuildData
+{
+ ChartBuildData(int id) : id(id) {
+ planeNormal = Vector3(0);
+ centroid = Vector3(0);
+ coneAxis = Vector3(0);
+ coneAngle = 0;
+ area = 0;
+ boundaryLength = 0;
+ normalSum = Vector3(0);
+ centroidSum = Vector3(0);
+ }
+
+ int id;
+
+ // Proxy info:
+ Vector3 planeNormal;
+ Vector3 centroid;
+ Vector3 coneAxis;
+ float coneAngle;
+
+ float area;
+ float boundaryLength;
+ Vector3 normalSum;
+ Vector3 centroidSum;
+
+ Array<uint> seeds; // @@ These could be a pointers to the HalfEdge faces directly.
+ Array<uint> faces;
+ PriorityQueue candidates;
+};
+
+
+
+AtlasBuilder::AtlasBuilder(const HalfEdge::Mesh * m) : mesh(m), facesLeft(m->faceCount())
+{
+ const uint faceCount = m->faceCount();
+ faceChartArray.resize(faceCount, -1);
+ faceCandidateArray.resize(faceCount, -1);
+
+ // @@ Floyd for the whole mesh is too slow. We could compute floyd progressively per patch as the patch grows. We need a better solution to compute most central faces.
+ //computeShortestPaths();
+
+ // Precompute edge lengths and face areas.
+ uint edgeCount = m->edgeCount();
+ edgeLengths.resize(edgeCount);
+
+ for (uint i = 0; i < edgeCount; i++) {
+ uint id = m->edgeAt(i)->id;
+ nvDebugCheck(id / 2 == i);
+
+ edgeLengths[i] = m->edgeAt(i)->length();
+ }
+
+ faceAreas.resize(faceCount);
+ for (uint i = 0; i < faceCount; i++) {
+ faceAreas[i] = m->faceAt(i)->area();
+ }
+}
+
+AtlasBuilder::~AtlasBuilder()
+{
+ const uint chartCount = chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ delete chartArray[i];
+ }
+}
+
+
+void AtlasBuilder::markUnchartedFaces(const Array<uint> & unchartedFaces)
+{
+ const uint unchartedFaceCount = unchartedFaces.count();
+ for (uint i = 0; i < unchartedFaceCount; i++){
+ uint f = unchartedFaces[i];
+ faceChartArray[f] = -2;
+ //faceCandidateArray[f] = -2; // @@ ?
+
+ removeCandidate(f);
+ }
+
+ nvDebugCheck(facesLeft >= unchartedFaceCount);
+ facesLeft -= unchartedFaceCount;
+}
+
+
+void AtlasBuilder::computeShortestPaths()
+{
+ const uint faceCount = mesh->faceCount();
+ shortestPaths.resize(faceCount*faceCount, FLT_MAX);
+
+ // Fill edges:
+ for (uint i = 0; i < faceCount; i++)
+ {
+ shortestPaths[i*faceCount + i] = 0.0f;
+
+ const HalfEdge::Face * face_i = mesh->faceAt(i);
+ Vector3 centroid_i = face_i->centroid();
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face_i->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ if (!edge->isBoundary())
+ {
+ const HalfEdge::Face * face_j = edge->pair->face;
+
+ uint j = face_j->id;
+ Vector3 centroid_j = face_j->centroid();
+
+ shortestPaths[i*faceCount + j] = shortestPaths[j*faceCount + i] = length(centroid_i - centroid_j);
+ }
+ }
+ }
+
+ // Use Floyd-Warshall algorithm to compute all paths:
+ for (uint k = 0; k < faceCount; k++)
+ {
+ for (uint i = 0; i < faceCount; i++)
+ {
+ for (uint j = 0; j < faceCount; j++)
+ {
+ shortestPaths[i*faceCount + j] = min(shortestPaths[i*faceCount + j], shortestPaths[i*faceCount + k]+shortestPaths[k*faceCount + j]);
+ }
+ }
+ }
+}
+
+
+void AtlasBuilder::placeSeeds(float threshold, uint maxSeedCount)
+{
+ // Instead of using a predefiened number of seeds:
+ // - Add seeds one by one, growing chart until a certain treshold.
+ // - Undo charts and restart growing process.
+
+ // @@ How can we give preference to faces far from sharp features as in the LSCM paper?
+ // - those points can be found using a simple flood filling algorithm.
+ // - how do we weight the probabilities?
+
+ for (uint i = 0; i < maxSeedCount; i++)
+ {
+ if (facesLeft == 0) {
+ // No faces left, stop creating seeds.
+ break;
+ }
+
+ createRandomChart(threshold);
+ }
+}
+
+
+void AtlasBuilder::createRandomChart(float threshold)
+{
+ ChartBuildData * chart = new ChartBuildData(chartArray.count());
+ chartArray.append(chart);
+
+ // Pick random face that is not used by any chart yet.
+ uint randomFaceIdx = rand.getRange(facesLeft - 1);
+ uint i = 0;
+ for (uint f = 0; f != randomFaceIdx; f++, i++)
+ {
+ while (faceChartArray[i] != -1) i++;
+ }
+ while (faceChartArray[i] != -1) i++;
+
+ chart->seeds.append(i);
+
+ addFaceToChart(chart, i, true);
+
+ // Grow the chart as much as possible within the given threshold.
+ growChart(chart, threshold * 0.5f, facesLeft);
+ //growCharts(threshold - threshold * 0.75f / chartCount(), facesLeft);
+}
+
+void AtlasBuilder::addFaceToChart(ChartBuildData * chart, uint f, bool recomputeProxy)
+{
+ // Add face to chart.
+ chart->faces.append(f);
+
+ nvDebugCheck(faceChartArray[f] == -1);
+ faceChartArray[f] = chart->id;
+
+ facesLeft--;
+
+ // Update area and boundary length.
+ chart->area = evaluateChartArea(chart, f);
+ chart->boundaryLength = evaluateBoundaryLength(chart, f);
+ chart->normalSum = evaluateChartNormalSum(chart, f);
+ chart->centroidSum = evaluateChartCentroidSum(chart, f);
+
+ if (recomputeProxy) {
+ // Update proxy and candidate's priorities.
+ updateProxy(chart);
+ }
+
+ // Update candidates.
+ removeCandidate(f);
+ updateCandidates(chart, f);
+ updatePriorities(chart);
+}
+
+// @@ Get N best candidates in one pass.
+const AtlasBuilder::Candidate & AtlasBuilder::getBestCandidate() const
+{
+ uint best = 0;
+ float bestCandidateMetric = FLT_MAX;
+
+ const uint candidateCount = candidateArray.count();
+ nvCheck(candidateCount > 0);
+
+ for (uint i = 0; i < candidateCount; i++)
+ {
+ const Candidate & candidate = candidateArray[i];
+
+ if (candidate.metric < bestCandidateMetric) {
+ bestCandidateMetric = candidate.metric;
+ best = i;
+ }
+ }
+
+ return candidateArray[best];
+}
+
+
+// Returns true if any of the charts can grow more.
+bool AtlasBuilder::growCharts(float threshold, uint faceCount)
+{
+#if 1 // Using one global list.
+
+ faceCount = min(faceCount, facesLeft);
+
+ for (uint i = 0; i < faceCount; i++)
+ {
+ const Candidate & candidate = getBestCandidate();
+
+ if (candidate.metric > threshold) {
+ return false; // Can't grow more.
+ }
+
+ addFaceToChart(candidate.chart, candidate.face);
+ }
+
+ return facesLeft != 0; // Can continue growing.
+
+#else // Using one list per chart.
+ bool canGrowMore = false;
+
+ const uint chartCount = chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ if (growChart(chartArray[i], threshold, faceCount))
+ {
+ canGrowMore = true;
+ }
+ }
+
+ return canGrowMore;
+#endif
+}
+
+bool AtlasBuilder::growChart(ChartBuildData * chart, float threshold, uint faceCount)
+{
+ // Try to add faceCount faces within threshold to chart.
+ for (uint i = 0; i < faceCount; )
+ {
+ if (chart->candidates.count() == 0 || chart->candidates.firstPriority() > threshold)
+ {
+ return false;
+ }
+
+ uint f = chart->candidates.pop();
+ if (faceChartArray[f] == -1)
+ {
+ addFaceToChart(chart, f);
+ i++;
+ }
+ }
+
+ if (chart->candidates.count() == 0 || chart->candidates.firstPriority() > threshold)
+ {
+ return false;
+ }
+
+ return true;
+}
+
+
+void AtlasBuilder::resetCharts()
+{
+ const uint faceCount = mesh->faceCount();
+ for (uint i = 0; i < faceCount; i++)
+ {
+ faceChartArray[i] = -1;
+ faceCandidateArray[i] = -1;
+ }
+
+ facesLeft = faceCount;
+
+ candidateArray.clear();
+
+ const uint chartCount = chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ ChartBuildData * chart = chartArray[i];
+
+ const uint seed = chart->seeds.back();
+
+ chart->area = 0.0f;
+ chart->boundaryLength = 0.0f;
+ chart->normalSum = Vector3(0);
+ chart->centroidSum = Vector3(0);
+
+ chart->faces.clear();
+ chart->candidates.clear();
+
+ addFaceToChart(chart, seed);
+ }
+}
+
+
+void AtlasBuilder::updateCandidates(ChartBuildData * chart, uint f)
+{
+ const HalfEdge::Face * face = mesh->faceAt(f);
+
+ // Traverse neighboring faces, add the ones that do not belong to any chart yet.
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current()->pair;
+
+ if (!edge->isBoundary())
+ {
+ uint f = edge->face->id;
+
+ if (faceChartArray[f] == -1)
+ {
+ chart->candidates.push(f);
+ }
+ }
+ }
+}
+
+
+void AtlasBuilder::updateProxies()
+{
+ const uint chartCount = chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ updateProxy(chartArray[i]);
+ }
+}
+
+
+namespace {
+
+ float absoluteSum(Vector4::Arg v)
+ {
+ return fabs(v.x) + fabs(v.y) + fabs(v.z) + fabs(v.w);
+ }
+
+ //#pragma message(NV_FILE_LINE "FIXME: Using the c=cos(teta) substitution, the equation system becomes linear and we can avoid the newton solver.")
+
+ struct ConeFitting
+ {
+ ConeFitting(const HalfEdge::Mesh * m, float g, float tf, float tx) : mesh(m), gamma(g), tolf(tf), tolx(tx), F(0), D(0), H(0) {
+ }
+
+ void addTerm(Vector3 N, float A)
+ {
+ const float c = cosf(X.w);
+ const float s = sinf(X.w);
+ const float tmp = dot(X.xyz(), N) - c;
+
+ F += tmp * tmp;
+
+ D.x += 2 * X.x * tmp;
+ D.y += 2 * X.y * tmp;
+ D.z += 2 * X.z * tmp;
+ D.w += 2 * s * tmp;
+
+ H(0,0) = 2 * X.x * N.x + 2 * tmp;
+ H(0,1) = 2 * X.x * N.y;
+ H(0,2) = 2 * X.x * N.z;
+ H(0,3) = 2 * X.x * s;
+
+ H(1,0) = 2 * X.y * N.x;
+ H(1,1) = 2 * X.y * N.y + 2 * tmp;
+ H(1,2) = 2 * X.y * N.z;
+ H(1,3) = 2 * X.y * s;
+
+ H(2,0) = 2 * X.z * N.x;
+ H(2,1) = 2 * X.z * N.y;
+ H(2,2) = 2 * X.z * N.z + 2 * tmp;
+ H(2,3) = 2 * X.z * s;
+
+ H(3,0) = 2 * s * N.x;
+ H(3,1) = 2 * s * N.y;
+ H(3,2) = 2 * s * N.z;
+ H(3,3) = 2 * s * s + 2 * c * tmp;
+ }
+
+ Vector4 solve(ChartBuildData * chart, Vector4 start)
+ {
+ const uint faceCount = chart->faces.count();
+
+ X = start;
+
+ Vector4 dX;
+
+ do {
+ for (uint i = 0; i < faceCount; i++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(chart->faces[i]);
+
+ addTerm(face->normal(), face->area());
+ }
+
+ Vector4 dX;
+ //solveKramer(H, D, &dX);
+ solveLU(H, D, &dX);
+
+ // @@ Do a full newton step and reduce by half if F doesn't decrease.
+ X -= gamma * dX;
+
+ // Constrain normal to be normalized.
+ X = Vector4(normalize(X.xyz()), X.w);
+
+ } while(absoluteSum(D) > tolf || absoluteSum(dX) > tolx);
+
+ return X;
+ }
+
+ HalfEdge::Mesh const * const mesh;
+ const float gamma;
+ const float tolf;
+ const float tolx;
+
+ Vector4 X;
+
+ float F;
+ Vector4 D;
+ Matrix H;
+ };
+
+ // Unnormalized face normal assuming it's a triangle.
+ static Vector3 triangleNormal(const HalfEdge::Face * face)
+ {
+ Vector3 p0 = face->edge->vertex->pos;
+ Vector3 p1 = face->edge->next->vertex->pos;
+ Vector3 p2 = face->edge->next->next->vertex->pos;
+
+ Vector3 e0 = p2 - p0;
+ Vector3 e1 = p1 - p0;
+
+ return normalizeSafe(cross(e0, e1), Vector3(0), 0.0f);
+ }
+
+ static Vector3 triangleNormalAreaScaled(const HalfEdge::Face * face)
+ {
+ Vector3 p0 = face->edge->vertex->pos;
+ Vector3 p1 = face->edge->next->vertex->pos;
+ Vector3 p2 = face->edge->next->next->vertex->pos;
+
+ Vector3 e0 = p2 - p0;
+ Vector3 e1 = p1 - p0;
+
+ return cross(e0, e1);
+ }
+
+ // Average of the edge midpoints weighted by the edge length.
+ // I want a point inside the triangle, but closer to the cirumcenter.
+ static Vector3 triangleCenter(const HalfEdge::Face * face)
+ {
+ Vector3 p0 = face->edge->vertex->pos;
+ Vector3 p1 = face->edge->next->vertex->pos;
+ Vector3 p2 = face->edge->next->next->vertex->pos;
+
+ float l0 = length(p1 - p0);
+ float l1 = length(p2 - p1);
+ float l2 = length(p0 - p2);
+
+ Vector3 m0 = (p0 + p1) * l0 / (l0 + l1 + l2);
+ Vector3 m1 = (p1 + p2) * l1 / (l0 + l1 + l2);
+ Vector3 m2 = (p2 + p0) * l2 / (l0 + l1 + l2);
+
+ return m0 + m1 + m2;
+ }
+
+} // namespace
+
+void AtlasBuilder::updateProxy(ChartBuildData * chart)
+{
+ //#pragma message(NV_FILE_LINE "TODO: Use best fit plane instead of average normal.")
+
+ chart->planeNormal = normalizeSafe(chart->normalSum, Vector3(0), 0.0f);
+ chart->centroid = chart->centroidSum / float(chart->faces.count());
+
+ //#pragma message(NV_FILE_LINE "TODO: Experiment with conic fitting.")
+
+ // F = (Nc*Nt - cos Oc)^2 = (x*Nt_x + y*Nt_y + z*Nt_z - cos w)^2
+ // dF/dx = 2 * x * (x*Nt_x + y*Nt_y + z*Nt_z - cos w)
+ // dF/dy = 2 * y * (x*Nt_x + y*Nt_y + z*Nt_z - cos w)
+ // dF/dz = 2 * z * (x*Nt_x + y*Nt_y + z*Nt_z - cos w)
+ // dF/dw = 2 * sin w * (x*Nt_x + y*Nt_y + z*Nt_z - cos w)
+
+ // JacobianMatrix({
+ // 2 * x * (x*Nt_x + y*Nt_y + z*Nt_z - Cos(w)),
+ // 2 * y * (x*Nt_x + y*Nt_y + z*Nt_z - Cos(w)),
+ // 2 * z * (x*Nt_x + y*Nt_y + z*Nt_z - Cos(w)),
+ // 2 * Sin(w) * (x*Nt_x + y*Nt_y + z*Nt_z - Cos(w))}, {x,y,z,w})
+
+ // H[0,0] = 2 * x * Nt_x + 2 * (x*Nt_x + y*Nt_y + z*Nt_z - cos(w));
+ // H[0,1] = 2 * x * Nt_y;
+ // H[0,2] = 2 * x * Nt_z;
+ // H[0,3] = 2 * x * sin(w);
+
+ // H[1,0] = 2 * y * Nt_x;
+ // H[1,1] = 2 * y * Nt_y + 2 * (x*Nt_x + y*Nt_y + z*Nt_z - cos(w));
+ // H[1,2] = 2 * y * Nt_z;
+ // H[1,3] = 2 * y * sin(w);
+
+ // H[2,0] = 2 * z * Nt_x;
+ // H[2,1] = 2 * z * Nt_y;
+ // H[2,2] = 2 * z * Nt_z + 2 * (x*Nt_x + y*Nt_y + z*Nt_z - cos(w));
+ // H[2,3] = 2 * z * sin(w);
+
+ // H[3,0] = 2 * sin(w) * Nt_x;
+ // H[3,1] = 2 * sin(w) * Nt_y;
+ // H[3,2] = 2 * sin(w) * Nt_z;
+ // H[3,3] = 2 * sin(w) * sin(w) + 2 * cos(w) * (x*Nt_x + y*Nt_y + z*Nt_z - cos(w));
+
+ // @@ Cone fitting might be quite slow.
+
+ /*ConeFitting coneFitting(mesh, 0.1f, 0.001f, 0.001f);
+
+ Vector4 start = Vector4(chart->coneAxis, chart->coneAngle);
+ Vector4 solution = coneFitting.solve(chart, start);
+
+ chart->coneAxis = solution.xyz();
+ chart->coneAngle = solution.w;*/
+}
+
+
+
+bool AtlasBuilder::relocateSeeds()
+{
+ bool anySeedChanged = false;
+
+ const uint chartCount = chartArray.count();
+ for (uint i = 0; i < chartCount; i++)
+ {
+ if (relocateSeed(chartArray[i]))
+ {
+ anySeedChanged = true;
+ }
+ }
+
+ return anySeedChanged;
+}
+
+
+bool AtlasBuilder::relocateSeed(ChartBuildData * chart)
+{
+ Vector3 centroid = computeChartCentroid(chart);
+
+ const uint N = 10; // @@ Hardcoded to 10?
+ PriorityQueue bestTriangles(N);
+
+ // Find the first N triangles that fit the proxy best.
+ const uint faceCount = chart->faces.count();
+ for (uint i = 0; i < faceCount; i++)
+ {
+ float priority = evaluateProxyFitMetric(chart, chart->faces[i]);
+ bestTriangles.push(priority, chart->faces[i]);
+ }
+
+ // Of those, choose the most central triangle.
+ uint mostCentral;
+ float maxDistance = -1;
+
+ const uint bestCount = bestTriangles.count();
+ for (uint i = 0; i < bestCount; i++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(bestTriangles.pairs[i].face);
+ Vector3 faceCentroid = triangleCenter(face);
+
+ float distance = length(centroid - faceCentroid);
+
+ /*#pragma message(NV_FILE_LINE "TODO: Implement evaluateDistanceToBoundary.")
+ float distance = evaluateDistanceToBoundary(chart, bestTriangles.pairs[i].face);*/
+
+ if (distance > maxDistance)
+ {
+ maxDistance = distance;
+ mostCentral = bestTriangles.pairs[i].face;
+ }
+ }
+ nvDebugCheck(maxDistance >= 0);
+
+ // In order to prevent k-means cyles we record all the previously chosen seeds.
+ uint index;
+ if (chart->seeds.find(mostCentral, &index))
+ {
+ // Move new seed to the end of the seed array.
+ uint last = chart->seeds.count() - 1;
+ swap(chart->seeds[index], chart->seeds[last]);
+ return false;
+ }
+ else
+ {
+ // Append new seed.
+ chart->seeds.append(mostCentral);
+ return true;
+ }
+}
+
+void AtlasBuilder::removeCandidate(uint f)
+{
+ int c = faceCandidateArray[f];
+ if (c != -1) {
+ faceCandidateArray[f] = -1;
+
+ if (c == candidateArray.count() - 1) {
+ candidateArray.popBack();
+ }
+ else {
+ candidateArray.replaceWithLast(c);
+ faceCandidateArray[candidateArray[c].face] = c;
+ }
+ }
+}
+
+void AtlasBuilder::updateCandidate(ChartBuildData * chart, uint f, float metric)
+{
+ if (faceCandidateArray[f] == -1) {
+ const uint index = candidateArray.count();
+ faceCandidateArray[f] = index;
+ candidateArray.resize(index + 1);
+ candidateArray[index].face = f;
+ candidateArray[index].chart = chart;
+ candidateArray[index].metric = metric;
+ }
+ else {
+ int c = faceCandidateArray[f];
+ nvDebugCheck(c != -1);
+
+ Candidate & candidate = candidateArray[c];
+ nvDebugCheck(candidate.face == f);
+
+ if (metric < candidate.metric || chart == candidate.chart) {
+ candidate.metric = metric;
+ candidate.chart = chart;
+ }
+ }
+
+}
+
+
+void AtlasBuilder::updatePriorities(ChartBuildData * chart)
+{
+ // Re-evaluate candidate priorities.
+ uint candidateCount = chart->candidates.count();
+ for (uint i = 0; i < candidateCount; i++)
+ {
+ chart->candidates.pairs[i].priority = evaluatePriority(chart, chart->candidates.pairs[i].face);
+
+ if (faceChartArray[chart->candidates.pairs[i].face] == -1)
+ {
+ updateCandidate(chart, chart->candidates.pairs[i].face, chart->candidates.pairs[i].priority);
+ }
+ }
+
+ // Sort candidates.
+ chart->candidates.sort();
+}
+
+
+// Evaluate combined metric.
+float AtlasBuilder::evaluatePriority(ChartBuildData * chart, uint face)
+{
+ // Estimate boundary length and area:
+ float newBoundaryLength = evaluateBoundaryLength(chart, face);
+ float newChartArea = evaluateChartArea(chart, face);
+
+ float F = evaluateProxyFitMetric(chart, face);
+ float C = evaluateRoundnessMetric(chart, face, newBoundaryLength, newChartArea);
+ float P = evaluateStraightnessMetric(chart, face);
+
+ // Penalize faces that cross seams, reward faces that close seams or reach boundaries.
+ float N = evaluateNormalSeamMetric(chart, face);
+ float T = evaluateTextureSeamMetric(chart, face);
+
+ //float R = evaluateCompletenessMetric(chart, face);
+
+ //float D = evaluateDihedralAngleMetric(chart, face);
+ // @@ Add a metric based on local dihedral angle.
+
+ // @@ Tweaking the normal and texture seam metrics.
+ // - Cause more impedance. Never cross 90 degree edges.
+ // -
+
+ float cost = float(
+ settings.proxyFitMetricWeight * F +
+ settings.roundnessMetricWeight * C +
+ settings.straightnessMetricWeight * P +
+ settings.normalSeamMetricWeight * N +
+ settings.textureSeamMetricWeight * T);
+
+ /*cost = settings.proxyFitMetricWeight * powf(F, settings.proxyFitMetricExponent);
+ cost = max(cost, settings.roundnessMetricWeight * powf(C, settings.roundnessMetricExponent));
+ cost = max(cost, settings.straightnessMetricWeight * pow(P, settings.straightnessMetricExponent));
+ cost = max(cost, settings.normalSeamMetricWeight * N);
+ cost = max(cost, settings.textureSeamMetricWeight * T);*/
+
+ // Enforce limits strictly:
+ if (newChartArea > settings.maxChartArea) cost = FLT_MAX;
+ if (newBoundaryLength > settings.maxBoundaryLength) cost = FLT_MAX;
+
+ // Make sure normal seams are fully respected:
+ if (settings.normalSeamMetricWeight >= 1000 && N != 0) cost = FLT_MAX;
+
+ nvCheck(isFinite(cost));
+ return cost;
+}
+
+
+// Returns a value in [0-1].
+float AtlasBuilder::evaluateProxyFitMetric(ChartBuildData * chart, uint f)
+{
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ Vector3 faceNormal = triangleNormal(face);
+ //return square(dot(chart->coneAxis, faceNormal) - cosf(chart->coneAngle));
+
+ // Use plane fitting metric for now:
+ //return square(1 - dot(faceNormal, chart->planeNormal)); // @@ normal deviations should be weighted by face area
+ return 1 - dot(faceNormal, chart->planeNormal); // @@ normal deviations should be weighted by face area
+
+ // Find distance to chart.
+ /*Vector3 faceCentroid = face->centroid();
+
+ float dist = 0;
+ int count = 0;
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ if (!edge->isBoundary()) {
+ const HalfEdge::Face * neighborFace = edge->pair()->face();
+ if (faceChartArray[neighborFace->id()] == chart->id) {
+ dist += length(neighborFace->centroid() - faceCentroid);
+ count++;
+ }
+ }
+ }
+
+ dist /= (count * count);
+
+ return (1 - dot(faceNormal, chart->planeNormal)) * dist;*/
+
+ //return (1 - dot(faceNormal, chart->planeNormal));
+}
+
+float AtlasBuilder::evaluateDistanceToBoundary(ChartBuildData * chart, uint face)
+{
+//#pragma message(NV_FILE_LINE "TODO: Evaluate distance to boundary metric.")
+
+ // @@ This is needed for the seed relocation code.
+ // @@ This could provide a better roundness metric.
+
+ return 0.0f;
+}
+
+float AtlasBuilder::evaluateDistanceToSeed(ChartBuildData * chart, uint f)
+{
+ //const uint seed = chart->seeds.back();
+ //const uint faceCount = mesh->faceCount();
+ //return shortestPaths[seed * faceCount + f];
+
+ const HalfEdge::Face * seed = mesh->faceAt(chart->seeds.back());
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ return length(triangleCenter(seed) - triangleCenter(face));
+}
+
+
+float AtlasBuilder::evaluateRoundnessMetric(ChartBuildData * chart, uint face, float newBoundaryLength, float newChartArea)
+{
+ // @@ D-charts use distance to seed.
+ // C(c,t) = pi * D(S_c,t)^2 / A_c
+ //return PI * square(evaluateDistanceToSeed(chart, face)) / chart->area;
+ //return PI * square(evaluateDistanceToSeed(chart, face)) / chart->area;
+ //return 2 * PI * evaluateDistanceToSeed(chart, face) / chart->boundaryLength;
+
+ // Garland's Hierarchical Face Clustering paper uses ratio between boundary and area, which is easier to compute and might work as well:
+ // roundness = D^2/4*pi*A -> circle = 1, non circle greater than 1
+
+ //return square(newBoundaryLength) / (newChartArea * 4 * PI);
+ float roundness = square(chart->boundaryLength) / chart->area;
+ float newRoundness = square(newBoundaryLength) / newChartArea;
+ if (newRoundness > roundness) {
+ return square(newBoundaryLength) / (newChartArea * 4 * PI);
+ }
+ else {
+ // Offer no impedance to faces that improve roundness.
+ return 0;
+ }
+
+ //return square(newBoundaryLength) / (4 * PI * newChartArea);
+ //return clamp(1 - (4 * PI * newChartArea) / square(newBoundaryLength), 0.0f, 1.0f);
+
+ // Use the ratio between the new roundness vs. the previous roundness.
+ // - If we use the absolute metric, when the initial face is very long, then it's hard to make any progress.
+ //return (square(newBoundaryLength) * chart->area) / (square(chart->boundaryLength) * newChartArea);
+ //return (4 * PI * newChartArea) / square(newBoundaryLength) - (4 * PI * chart->area) / square(chart->boundaryLength);
+
+ //if (square(newBoundaryLength) * chart->area) / (square(chart->boundaryLength) * newChartArea);
+
+}
+
+float AtlasBuilder::evaluateStraightnessMetric(ChartBuildData * chart, uint f)
+{
+ float l_out = 0.0f;
+ float l_in = 0.0f;
+
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ //float l = edge->length();
+ float l = edgeLengths[edge->id/2];
+
+ if (edge->isBoundary())
+ {
+ l_out += l;
+ }
+ else
+ {
+ uint neighborFaceId = edge->pair->face->id;
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ l_out += l;
+ }
+ else {
+ l_in += l;
+ }
+ }
+ }
+ nvDebugCheck(l_in != 0.0f); // Candidate face must be adjacent to chart. @@ This is not true if the input mesh has zero-length edges.
+
+ //return l_out / l_in;
+ float ratio = (l_out - l_in) / (l_out + l_in);
+ //if (ratio < 0) ratio *= 10; // Encourage closing gaps.
+ return min(ratio, 0.0f); // Only use the straightness metric to close gaps.
+ //return ratio;
+}
+
+
+float AtlasBuilder::evaluateNormalSeamMetric(ChartBuildData * chart, uint f)
+{
+ float seamFactor = 0.0f;
+ float totalLength = 0.0f;
+
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ if (edge->isBoundary()) {
+ continue;
+ }
+
+ const uint neighborFaceId = edge->pair->face->id;
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ continue;
+ }
+
+ //float l = edge->length();
+ float l = edgeLengths[edge->id/2];
+
+ totalLength += l;
+
+ if (!edge->isSeam()) {
+ continue;
+ }
+
+ // Make sure it's a normal seam.
+ if (isNormalSeam(edge))
+ {
+ float d0 = clamp(dot(edge->vertex->nor, edge->pair->next->vertex->nor), 0.0f, 1.0f);
+ float d1 = clamp(dot(edge->next->vertex->nor, edge->pair->vertex->nor), 0.0f, 1.0f);
+ //float a0 = clamp(acosf(d0) / (PI/2), 0.0f, 1.0f);
+ //float a1 = clamp(acosf(d1) / (PI/2), 0.0f, 1.0f);
+ //l *= (a0 + a1) * 0.5f;
+
+ l *= 1 - (d0 + d1) * 0.5f;
+
+ seamFactor += l;
+ }
+ }
+
+ if (seamFactor == 0) return 0.0f;
+ return seamFactor / totalLength;
+}
+
+
+float AtlasBuilder::evaluateTextureSeamMetric(ChartBuildData * chart, uint f)
+{
+ float seamLength = 0.0f;
+ //float newSeamLength = 0.0f;
+ //float oldSeamLength = 0.0f;
+ float totalLength = 0.0f;
+
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ /*float l = edge->length();
+ totalLength += l;
+
+ if (edge->isBoundary() || !edge->isSeam()) {
+ continue;
+ }
+
+ // Make sure it's a texture seam.
+ if (isTextureSeam(edge))
+ {
+ uint neighborFaceId = edge->pair()->face()->id();
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ newSeamLength += l;
+ }
+ else {
+ oldSeamLength += l;
+ }
+ }*/
+
+ if (edge->isBoundary()) {
+ continue;
+ }
+
+ const uint neighborFaceId = edge->pair->face->id;
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ continue;
+ }
+
+ //float l = edge->length();
+ float l = edgeLengths[edge->id/2];
+ totalLength += l;
+
+ if (!edge->isSeam()) {
+ continue;
+ }
+
+ // Make sure it's a texture seam.
+ if (isTextureSeam(edge))
+ {
+ seamLength += l;
+ }
+ }
+
+ if (seamLength == 0.0f) {
+ return 0.0f; // Avoid division by zero.
+ }
+
+ return seamLength / totalLength;
+}
+
+
+float AtlasBuilder::evaluateSeamMetric(ChartBuildData * chart, uint f)
+{
+ float newSeamLength = 0.0f;
+ float oldSeamLength = 0.0f;
+ float totalLength = 0.0f;
+
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ //float l = edge->length();
+ float l = edgeLengths[edge->id/2];
+
+ if (edge->isBoundary())
+ {
+ newSeamLength += l;
+ }
+ else
+ {
+ if (edge->isSeam())
+ {
+ uint neighborFaceId = edge->pair->face->id;
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ newSeamLength += l;
+ }
+ else {
+ oldSeamLength += l;
+ }
+ }
+ }
+
+ totalLength += l;
+ }
+
+ return (newSeamLength - oldSeamLength) / totalLength;
+}
+
+
+float AtlasBuilder::evaluateChartArea(ChartBuildData * chart, uint f)
+{
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ //return chart->area + face->area();
+ return chart->area + faceAreas[face->id];
+}
+
+
+float AtlasBuilder::evaluateBoundaryLength(ChartBuildData * chart, uint f)
+{
+ float boundaryLength = chart->boundaryLength;
+
+ // Add new edges, subtract edges shared with the chart.
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+ //float edgeLength = edge->length();
+ float edgeLength = edgeLengths[edge->id/2];
+
+ if (edge->isBoundary())
+ {
+ boundaryLength += edgeLength;
+ }
+ else
+ {
+ uint neighborFaceId = edge->pair->face->id;
+ if (faceChartArray[neighborFaceId] != chart->id) {
+ boundaryLength += edgeLength;
+ }
+ else {
+ boundaryLength -= edgeLength;
+ }
+ }
+ }
+ //nvDebugCheck(boundaryLength >= 0);
+
+ return max(0.0f, boundaryLength); // @@ Hack!
+}
+
+Vector3 AtlasBuilder::evaluateChartNormalSum(ChartBuildData * chart, uint f)
+{
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ return chart->normalSum + triangleNormalAreaScaled(face);
+}
+
+Vector3 AtlasBuilder::evaluateChartCentroidSum(ChartBuildData * chart, uint f)
+{
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ return chart->centroidSum + face->centroid();
+}
+
+
+Vector3 AtlasBuilder::computeChartCentroid(const ChartBuildData * chart)
+{
+ Vector3 centroid(0);
+
+ const uint faceCount = chart->faces.count();
+ for (uint i = 0; i < faceCount; i++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(chart->faces[i]);
+ centroid += triangleCenter(face);
+ }
+
+ return centroid / float(faceCount);
+}
+
+
+void AtlasBuilder::fillHoles(float threshold)
+{
+ while (facesLeft > 0)
+ {
+ createRandomChart(threshold);
+ }
+}
+
+
+void AtlasBuilder::mergeChart(ChartBuildData * owner, ChartBuildData * chart, float sharedBoundaryLength)
+{
+ const uint faceCount = chart->faces.count();
+ for (uint i = 0; i < faceCount; i++)
+ {
+ uint f = chart->faces[i];
+
+ nvDebugCheck(faceChartArray[f] == chart->id);
+ faceChartArray[f] = owner->id;
+
+ owner->faces.append(f);
+ }
+
+ // Update adjacencies?
+
+ owner->area += chart->area;
+ owner->boundaryLength += chart->boundaryLength - sharedBoundaryLength;
+
+ owner->normalSum += chart->normalSum;
+ owner->centroidSum += chart->centroidSum;
+
+ updateProxy(owner);
+}
+
+void AtlasBuilder::mergeCharts()
+{
+ Array<float> sharedBoundaryLengths;
+
+ const uint chartCount = chartArray.count();
+ for (int c = chartCount-1; c >= 0; c--)
+ {
+ sharedBoundaryLengths.clear();
+ sharedBoundaryLengths.resize(chartCount, 0.0f);
+
+ ChartBuildData * chart = chartArray[c];
+
+ float externalBoundary = 0.0f;
+
+ const uint faceCount = chart->faces.count();
+ for (uint i = 0; i < faceCount; i++)
+ {
+ uint f = chart->faces[i];
+ const HalfEdge::Face * face = mesh->faceAt(f);
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ //float l = edge->length();
+ float l = edgeLengths[edge->id/2];
+
+ if (edge->isBoundary()) {
+ externalBoundary += l;
+ }
+ else {
+ uint neighborFace = edge->pair->face->id;
+ uint neighborChart = faceChartArray[neighborFace];
+
+ if (neighborChart != c) {
+ if ((edge->isSeam() && (isNormalSeam(edge) || isTextureSeam(edge))) || neighborChart == -2) {
+ externalBoundary += l;
+ }
+ else {
+ sharedBoundaryLengths[neighborChart] += l;
+ }
+ }
+ }
+ }
+ }
+
+ for (int cc = chartCount-1; cc >= 0; cc--)
+ {
+ if (cc == c)
+ continue;
+
+ ChartBuildData * chart2 = chartArray[cc];
+ if (chart2 == NULL)
+ continue;
+
+ if (sharedBoundaryLengths[cc] > 0.8 * max(0.0f, chart->boundaryLength - externalBoundary)) {
+
+ // Try to avoid degenerate configurations.
+ if (chart2->boundaryLength > sharedBoundaryLengths[cc])
+ {
+ if (dot(chart2->planeNormal, chart->planeNormal) > -0.25) {
+ mergeChart(chart2, chart, sharedBoundaryLengths[cc]);
+ delete chart;
+ chartArray[c] = NULL;
+ break;
+ }
+ }
+ }
+
+ if (sharedBoundaryLengths[cc] > 0.20 * max(0.0f, chart->boundaryLength - externalBoundary)) {
+
+ // Compare proxies.
+ if (dot(chart2->planeNormal, chart->planeNormal) > 0) {
+ mergeChart(chart2, chart, sharedBoundaryLengths[cc]);
+ delete chart;
+ chartArray[c] = NULL;
+ break;
+ }
+ }
+ }
+ }
+
+ // Remove deleted charts.
+ for (int c = 0; c < I32(chartArray.count()); /*do not increment if removed*/)
+ {
+ if (chartArray[c] == NULL) {
+ chartArray.removeAt(c);
+
+ // Update faceChartArray.
+ const uint faceCount = faceChartArray.count();
+ for (uint i = 0; i < faceCount; i++) {
+ nvDebugCheck (faceChartArray[i] != -1);
+ nvDebugCheck (faceChartArray[i] != c);
+ nvDebugCheck (faceChartArray[i] <= I32(chartArray.count()));
+
+ if (faceChartArray[i] > c) {
+ faceChartArray[i]--;
+ }
+ }
+ }
+ else {
+ chartArray[c]->id = c;
+ c++;
+ }
+ }
+}
+
+
+
+const Array<uint> & AtlasBuilder::chartFaces(uint i) const
+{
+ return chartArray[i]->faces;
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.h b/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.h
new file mode 100644
index 0000000000..f25c724f7e
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/AtlasBuilder.h
@@ -0,0 +1,111 @@
+// This code is in the public domain -- castano@gmail.com
+
+#pragma once
+#ifndef NV_MESH_ATLASBUILDER_H
+#define NV_MESH_ATLASBUILDER_H
+
+#include "Atlas.h"
+
+#include "nvmath/Vector.h"
+#include "nvmath/Random.h"
+#include "nvmesh/nvmesh.h"
+
+#include "nvcore/Array.h"
+#include "nvcore/BitArray.h"
+
+
+
+namespace nv
+{
+ namespace HalfEdge { class Mesh; }
+
+ struct ChartBuildData;
+
+ struct AtlasBuilder
+ {
+ AtlasBuilder(const HalfEdge::Mesh * m);
+ ~AtlasBuilder();
+
+ void markUnchartedFaces(const Array<uint> & unchartedFaces);
+
+ void computeShortestPaths();
+
+ void placeSeeds(float threshold, uint maxSeedCount);
+ void createRandomChart(float threshold);
+
+ void addFaceToChart(ChartBuildData * chart, uint f, bool recomputeProxy=false);
+
+ bool growCharts(float threshold, uint faceCount);
+ bool growChart(ChartBuildData * chart, float threshold, uint faceCount);
+
+ void resetCharts();
+
+ void updateCandidates(ChartBuildData * chart, uint face);
+
+ void updateProxies();
+ void updateProxy(ChartBuildData * chart);
+
+ bool relocateSeeds();
+ bool relocateSeed(ChartBuildData * chart);
+
+ void updatePriorities(ChartBuildData * chart);
+
+ float evaluatePriority(ChartBuildData * chart, uint face);
+ float evaluateProxyFitMetric(ChartBuildData * chart, uint face);
+ float evaluateDistanceToBoundary(ChartBuildData * chart, uint face);
+ float evaluateDistanceToSeed(ChartBuildData * chart, uint face);
+ float evaluateRoundnessMetric(ChartBuildData * chart, uint face, float newBoundaryLength, float newChartArea);
+ float evaluateStraightnessMetric(ChartBuildData * chart, uint face);
+
+ float evaluateNormalSeamMetric(ChartBuildData * chart, uint f);
+ float evaluateTextureSeamMetric(ChartBuildData * chart, uint f);
+ float evaluateSeamMetric(ChartBuildData * chart, uint f);
+
+ float evaluateChartArea(ChartBuildData * chart, uint f);
+ float evaluateBoundaryLength(ChartBuildData * chart, uint f);
+ Vector3 evaluateChartNormalSum(ChartBuildData * chart, uint f);
+ Vector3 evaluateChartCentroidSum(ChartBuildData * chart, uint f);
+
+ Vector3 computeChartCentroid(const ChartBuildData * chart);
+
+
+ void fillHoles(float threshold);
+ void mergeCharts();
+
+ // @@ Cleanup.
+ struct Candidate {
+ uint face;
+ ChartBuildData * chart;
+ float metric;
+ };
+
+ const Candidate & getBestCandidate() const;
+ void removeCandidate(uint f);
+ void updateCandidate(ChartBuildData * chart, uint f, float metric);
+
+ void mergeChart(ChartBuildData * owner, ChartBuildData * chart, float sharedBoundaryLength);
+
+
+ uint chartCount() const { return chartArray.count(); }
+ const Array<uint> & chartFaces(uint i) const;
+
+ const HalfEdge::Mesh * mesh;
+ uint facesLeft;
+ Array<int> faceChartArray;
+ Array<ChartBuildData *> chartArray;
+ Array<float> shortestPaths;
+
+ Array<float> edgeLengths;
+ Array<float> faceAreas;
+
+ Array<Candidate> candidateArray; //
+ Array<uint> faceCandidateArray; // Map face index to candidate index.
+
+ MTRand rand;
+
+ SegmentationSettings settings;
+ };
+
+} // nv namespace
+
+#endif // NV_MESH_ATLASBUILDER_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.cpp b/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.cpp
new file mode 100644
index 0000000000..5ce452cb9e
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.cpp
@@ -0,0 +1,1387 @@
+// This code is in the public domain -- castano@gmail.com
+
+#include "nvmesh.h" // pch
+
+#include "AtlasPacker.h"
+#include "nvmesh/halfedge/Vertex.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/param/Atlas.h"
+#include "nvmesh/param/Util.h"
+#include "nvmesh/raster/Raster.h"
+
+#include "nvmath/Vector.inl"
+#include "nvmath/ConvexHull.h"
+#include "nvmath/Color.h"
+#include "nvmath/ftoi.h"
+
+#include "nvcore/StrLib.h" // debug
+#include "nvcore/StdStream.h" // fileOpen
+
+#include <float.h> // FLT_MAX
+#include <limits.h> // UINT_MAX
+
+using namespace nv;
+
+#define DEBUG_OUTPUT 0
+
+#if DEBUG_OUTPUT
+
+#include "nvimage/ImageIO.h"
+
+namespace
+{
+ const uint TGA_TYPE_GREY = 3;
+ const uint TGA_TYPE_RGB = 2;
+ const uint TGA_ORIGIN_UPPER = 0x20;
+
+#pragma pack(push, 1)
+ struct TgaHeader {
+ uint8 id_length;
+ uint8 colormap_type;
+ uint8 image_type;
+ uint16 colormap_index;
+ uint16 colormap_length;
+ uint8 colormap_size;
+ uint16 x_origin;
+ uint16 y_origin;
+ uint16 width;
+ uint16 height;
+ uint8 pixel_size;
+ uint8 flags;
+
+ enum { Size = 18 }; //const static int SIZE = 18;
+ };
+#pragma pack(pop)
+
+ static void outputDebugBitmap(const char * fileName, const BitMap & bitmap, int w, int h)
+ {
+ FILE * fp = fileOpen(fileName, "wb");
+ if (fp == NULL) return;
+
+ nvStaticCheck(sizeof(TgaHeader) == TgaHeader::Size);
+ TgaHeader tga;
+ tga.id_length = 0;
+ tga.colormap_type = 0;
+ tga.image_type = TGA_TYPE_GREY;
+
+ tga.colormap_index = 0;
+ tga.colormap_length = 0;
+ tga.colormap_size = 0;
+
+ tga.x_origin = 0;
+ tga.y_origin = 0;
+ tga.width = w;
+ tga.height = h;
+ tga.pixel_size = 8;
+ tga.flags = TGA_ORIGIN_UPPER;
+
+ fwrite(&tga, sizeof(TgaHeader), 1, fp);
+
+ for (int j = 0; j < h; j++) {
+ for (int i = 0; i < w; i++) {
+ uint8 color = bitmap.bitAt(i, j) ? 0xFF : 0x0;
+ fwrite(&color, 1, 1, fp);
+ }
+ }
+
+ fclose(fp);
+ }
+
+ static void outputDebugImage(const char * fileName, const Image & bitmap, int w, int h)
+ {
+ FILE * fp = fileOpen(fileName, "wb");
+ if (fp == NULL) return;
+
+ nvStaticCheck(sizeof(TgaHeader) == TgaHeader::Size);
+ TgaHeader tga;
+ tga.id_length = 0;
+ tga.colormap_type = 0;
+ tga.image_type = TGA_TYPE_RGB;
+
+ tga.colormap_index = 0;
+ tga.colormap_length = 0;
+ tga.colormap_size = 0;
+
+ tga.x_origin = 0;
+ tga.y_origin = 0;
+ tga.width = w;
+ tga.height = h;
+ tga.pixel_size = 24;
+ tga.flags = TGA_ORIGIN_UPPER;
+
+ fwrite(&tga, sizeof(TgaHeader), 1, fp);
+
+ for (int j = 0; j < h; j++) {
+ for (int i = 0; i < w; i++) {
+ Color32 color = bitmap.pixel(i, j);
+ fwrite(&color.r, 1, 1, fp);
+ fwrite(&color.g, 1, 1, fp);
+ fwrite(&color.b, 1, 1, fp);
+ }
+ }
+
+ fclose(fp);
+ }
+}
+
+#endif // DEBUG_OUTPUT
+
+inline int align(int x, int a) {
+ //return a * ((x + a - 1) / a);
+ //return (x + a - 1) & -a;
+ return (x + a - 1) & ~(a - 1);
+}
+
+inline bool isAligned(int x, int a) {
+ return (x & (a - 1)) == 0;
+}
+
+
+
+AtlasPacker::AtlasPacker(Atlas * atlas) : m_atlas(atlas), m_bitmap(256, 256)
+{
+ m_width = 0;
+ m_height = 0;
+
+ m_debug_bitmap.allocate(256, 256);
+ m_debug_bitmap.fill(Color32(0,0,0,0));
+}
+
+AtlasPacker::~AtlasPacker()
+{
+}
+
+// This should compute convex hull and use rotating calipers to find the best box. Currently it uses a brute force method.
+static bool computeBoundingBox(Chart * chart, Vector2 * majorAxis, Vector2 * minorAxis, Vector2 * minCorner, Vector2 * maxCorner)
+{
+ // Compute list of boundary points.
+ Array<Vector2> points(16);
+
+ HalfEdge::Mesh * mesh = chart->chartMesh();
+ const uint vertexCount = mesh->vertexCount();
+
+ for (uint i = 0; i < vertexCount; i++) {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(i);
+ if (vertex->isBoundary()) {
+ points.append(vertex->tex);
+ }
+ }
+
+ // This is not valid anymore. The chart mesh may have multiple boundaries!
+ /*const HalfEdge::Vertex * vertex = findBoundaryVertex(chart->chartMesh());
+
+ // Traverse boundary.
+ const HalfEdge::Edge * const firstEdge = vertex->edge();
+ const HalfEdge::Edge * edge = firstEdge;
+ do {
+ vertex = edge->vertex();
+
+ nvDebugCheck (vertex->isBoundary());
+ points.append(vertex->tex);
+
+ edge = edge->next();
+ } while (edge != firstEdge);*/
+
+#if 1
+ Array<Vector2> hull;
+ if (points.size()==0) {
+ return false;
+ }
+
+ convexHull(points, hull, 0.00001f);
+
+ // @@ Ideally I should use rotating calipers to find the best box. Using brute force for now.
+
+ float best_area = FLT_MAX;
+ Vector2 best_min;
+ Vector2 best_max;
+ Vector2 best_axis;
+
+ const uint hullCount = hull.count();
+ for (uint i = 0, j = hullCount-1; i < hullCount; j = i, i++) {
+
+ if (equal(hull[i], hull[j])) {
+ continue;
+ }
+
+ Vector2 axis = normalize(hull[i] - hull[j], 0.0f);
+ nvDebugCheck(isFinite(axis));
+
+ // Compute bounding box.
+ Vector2 box_min(FLT_MAX, FLT_MAX);
+ Vector2 box_max(-FLT_MAX, -FLT_MAX);
+
+ for (uint v = 0; v < hullCount; v++) {
+
+ Vector2 point = hull[v];
+
+ float x = dot(axis, point);
+ if (x < box_min.x) box_min.x = x;
+ if (x > box_max.x) box_max.x = x;
+
+ float y = dot(Vector2(-axis.y, axis.x), point);
+ if (y < box_min.y) box_min.y = y;
+ if (y > box_max.y) box_max.y = y;
+ }
+
+ // Compute box area.
+ float area = (box_max.x - box_min.x) * (box_max.y - box_min.y);
+
+ if (area < best_area) {
+ best_area = area;
+ best_min = box_min;
+ best_max = box_max;
+ best_axis = axis;
+ }
+ }
+
+ // Make sure the box contains all the input points since the convex hull is not 100% accurate.
+ /*const uint pointCount = points.count();
+ for (uint v = 0; v < pointCount; v++) {
+
+ Vector2 point = points[v];
+
+ float x = dot(best_axis, point);
+ if (x < best_min.x) best_min.x = x;
+
+ float y = dot(Vector2(-best_axis.y, best_axis.x), point);
+ if (y < best_min.y) best_min.y = y;
+ }*/
+
+ // Consider all points, not only boundary points, in case the input chart is malformed.
+ for (uint i = 0; i < vertexCount; i++) {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(i);
+ Vector2 point = vertex->tex;
+
+ float x = dot(best_axis, point);
+ if (x < best_min.x) best_min.x = x;
+ if (x > best_max.x) best_max.x = x;
+
+ float y = dot(Vector2(-best_axis.y, best_axis.x), point);
+ if (y < best_min.y) best_min.y = y;
+ if (y > best_max.y) best_max.y = y;
+ }
+
+ *majorAxis = best_axis;
+ *minorAxis = Vector2(-best_axis.y, best_axis.x);
+ *minCorner = best_min;
+ *maxCorner = best_max;
+
+#else
+ // Approximate implementation: try 16 different directions and keep the best.
+
+ const uint N = 16;
+ Vector2 axis[N];
+
+ float minAngle = 0;
+ float maxAngle = PI / 2;
+
+ int best;
+ Vector2 mins[N];
+ Vector2 maxs[N];
+
+ const int iterationCount = 1;
+ for (int j = 0; j < iterationCount; j++)
+ {
+ // Init predefined directions.
+ for (int i = 0; i < N; i++)
+ {
+ float angle = lerp(minAngle, maxAngle, float(i)/N);
+ axis[i].set(cosf(angle), sinf(angle));
+ }
+
+ // Compute box for each direction.
+ for (int i = 0; i < N; i++)
+ {
+ mins[i].set(FLT_MAX, FLT_MAX);
+ maxs[i].set(-FLT_MAX, -FLT_MAX);
+ }
+
+ for (uint p = 0; p < points.count(); p++)
+ {
+ Vector2 point = points[p];
+
+ for (int i = 0; i < N; i++)
+ {
+ float x = dot(axis[i], point);
+ if (x < mins[i].x) mins[i].x = x;
+ if (x > maxs[i].x) maxs[i].x = x;
+
+ float y = dot(Vector2(-axis[i].y, axis[i].x), point);
+ if (y < mins[i].y) mins[i].y = y;
+ if (y > maxs[i].y) maxs[i].y = y;
+ }
+ }
+
+ // Find box with minimum area.
+ best = -1;
+ int second_best = -1;
+ float best_area = FLT_MAX;
+ float second_best_area = FLT_MAX;
+
+ for (int i = 0; i < N; i++)
+ {
+ float area = (maxs[i].x - mins[i].x) * (maxs[i].y - mins[i].y);
+
+ if (area < best_area)
+ {
+ second_best_area = best_area;
+ second_best = best;
+
+ best_area = area;
+ best = i;
+ }
+ else if (area < second_best_area)
+ {
+ second_best_area = area;
+ second_best = i;
+ }
+ }
+ nvDebugCheck(best != -1);
+ nvDebugCheck(second_best != -1);
+ nvDebugCheck(best != second_best);
+
+ if (j != iterationCount-1)
+ {
+ // Handle wrap-around during the first iteration.
+ if (j == 0) {
+ if (best == 0 && second_best == N-1) best = N;
+ if (best == N-1 && second_best == 0) second_best = N;
+ }
+
+ if (best < second_best) swap(best, second_best);
+
+ // Update angles.
+ float deltaAngle = (maxAngle - minAngle) / N;
+ maxAngle = minAngle + (best - 0.5f) * deltaAngle;
+ minAngle = minAngle + (second_best + 0.5f) * deltaAngle;
+ }
+ }
+
+ // Compute major and minor axis, and origin.
+ *majorAxis = axis[best];
+ *minorAxis = Vector2(-axis[best].y, axis[best].x);
+ *origin = mins[best];
+
+ // @@ If the parameterization is invalid, we could have an interior vertex outside the boundary.
+ // @@ In that case the returned bounding box would be incorrect. Compute updated bounds here.
+ /*for (uint p = 0; p < points.count(); p++)
+ {
+ Vector2 point = points[p];
+
+ for (int i = 0; i < N; i++)
+ {
+ float x = dot(*majorAxis, point);
+ float y = dot(*minorAxis, point);
+ }
+ }*/
+#endif
+
+ return true;
+}
+
+
+void AtlasPacker::packCharts(int quality, float texelsPerUnit, bool blockAligned, bool conservative)
+{
+ const uint chartCount = m_atlas->chartCount();
+ if (chartCount == 0) return;
+
+ Array<float> chartOrderArray;
+ chartOrderArray.resize(chartCount);
+
+ Array<Vector2> chartExtents;
+ chartExtents.resize(chartCount);
+
+ float meshArea = 0;
+ for (uint c = 0; c < chartCount; c++)
+ {
+ Chart * chart = m_atlas->chartAt(c);
+
+ if (!chart->isVertexMapped() && !chart->isDisk()) {
+ chartOrderArray[c] = 0;
+
+ // Skip non-disks.
+ continue;
+ }
+
+ Vector2 extents(0.0f);
+
+ if (chart->isVertexMapped()) {
+ // Let's assume vertex maps are arranged in a rectangle.
+ //HalfEdge::Mesh * mesh = chart->chartMesh();
+
+ // Arrange vertices in a rectangle.
+ extents.x = float(chart->vertexMapWidth);
+ extents.y = float(chart->vertexMapHeight);
+ }
+ else {
+ // Compute surface area to sort charts.
+ float chartArea = chart->computeSurfaceArea();
+ meshArea += chartArea;
+ //chartOrderArray[c] = chartArea;
+
+ // Compute chart scale
+ float parametricArea = fabs(chart->computeParametricArea()); // @@ There doesn't seem to be anything preventing parametric area to be negative.
+ if (parametricArea < NV_EPSILON) {
+ // When the parametric area is too small we use a rough approximation to prevent divisions by very small numbers.
+ Vector2 bounds = chart->computeParametricBounds();
+ parametricArea = bounds.x * bounds.y;
+ }
+ float scale = (chartArea / parametricArea) * texelsPerUnit;
+ if (parametricArea == 0) // < NV_EPSILON)
+ {
+ scale = 0;
+ }
+ nvCheck(isFinite(scale));
+
+ // Compute bounding box of chart.
+ Vector2 majorAxis, minorAxis, origin, end;
+ if (!computeBoundingBox(chart, &majorAxis, &minorAxis, &origin, &end)) {
+ m_atlas->setFailed();
+ return;
+ }
+
+ nvCheck(isFinite(majorAxis) && isFinite(minorAxis) && isFinite(origin));
+
+ // Sort charts by perimeter. @@ This is sometimes producing somewhat unexpected results. Is this right?
+ //chartOrderArray[c] = ((end.x - origin.x) + (end.y - origin.y)) * scale;
+
+ // Translate, rotate and scale vertices. Compute extents.
+ HalfEdge::Mesh * mesh = chart->chartMesh();
+ const uint vertexCount = mesh->vertexCount();
+ for (uint i = 0; i < vertexCount; i++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(i);
+
+ //Vector2 t = vertex->tex - origin;
+ Vector2 tmp;
+ tmp.x = dot(vertex->tex, majorAxis);
+ tmp.y = dot(vertex->tex, minorAxis);
+ tmp -= origin;
+ tmp *= scale;
+ if (tmp.x < 0 || tmp.y < 0) {
+ nvDebug("tmp: %f %f\n", tmp.x, tmp.y);
+ nvDebug("scale: %f\n", scale);
+ nvDebug("origin: %f %f\n", origin.x, origin.y);
+ nvDebug("majorAxis: %f %f\n", majorAxis.x, majorAxis.y);
+ nvDebug("minorAxis: %f %f\n", minorAxis.x, minorAxis.y);
+ nvDebugBreak();
+ }
+ //nvCheck(tmp.x >= 0 && tmp.y >= 0);
+
+ vertex->tex = tmp;
+
+ nvCheck(isFinite(vertex->tex.x) && isFinite(vertex->tex.y));
+
+ extents = max(extents, tmp);
+ }
+ nvDebugCheck(extents.x >= 0 && extents.y >= 0);
+
+ // Limit chart size.
+ if (extents.x > 1024 || extents.y > 1024) {
+ float limit = max(extents.x, extents.y);
+
+ scale = 1024 / (limit + 1);
+
+ for (uint i = 0; i < vertexCount; i++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(i);
+ vertex->tex *= scale;
+ }
+
+ extents *= scale;
+
+ nvDebugCheck(extents.x <= 1024 && extents.y <= 1024);
+ }
+
+
+ // Scale the charts to use the entire texel area available. So, if the width is 0.1 we could scale it to 1 without increasing the lightmap usage and making a better
+ // use of it. In many cases this also improves the look of the seams, since vertices on the chart boundaries have more chances of being aligned with the texel centers.
+
+ float scale_x = 1.0f;
+ float scale_y = 1.0f;
+
+ float divide_x = 1.0f;
+ float divide_y = 1.0f;
+
+ if (extents.x > 0) {
+ int cw = ftoi_ceil(extents.x);
+
+ if (blockAligned) {
+ // Align all chart extents to 4x4 blocks, but taking padding into account.
+ if (conservative) {
+ cw = align(cw + 2, 4) - 2;
+ }
+ else {
+ cw = align(cw + 1, 4) - 1;
+ }
+ }
+
+ scale_x = (float(cw) - NV_EPSILON);
+ divide_x = extents.x;
+ extents.x = float(cw);
+ }
+
+ if (extents.y > 0) {
+ int ch = ftoi_ceil(extents.y);
+
+ if (blockAligned) {
+ // Align all chart extents to 4x4 blocks, but taking padding into account.
+ if (conservative) {
+ ch = align(ch + 2, 4) - 2;
+ }
+ else {
+ ch = align(ch + 1, 4) - 1;
+ }
+ }
+
+ scale_y = (float(ch) - NV_EPSILON);
+ divide_y = extents.y;
+ extents.y = float(ch);
+ }
+
+ for (uint v = 0; v < vertexCount; v++) {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+
+ vertex->tex.x /= divide_x;
+ vertex->tex.y /= divide_y;
+ vertex->tex.x *= scale_x;
+ vertex->tex.y *= scale_y;
+
+ nvCheck(isFinite(vertex->tex.x) && isFinite(vertex->tex.y));
+ }
+ }
+
+ chartExtents[c] = extents;
+
+ // Sort charts by perimeter.
+ chartOrderArray[c] = extents.x + extents.y;
+ }
+
+ // @@ We can try to improve compression of small charts by sorting them by proximity like we do with vertex samples.
+ // @@ How to do that? One idea: compute chart centroid, insert into grid, compute morton index of the cell, sort based on morton index.
+ // @@ We would sort by morton index, first, then quantize the chart sizes, so that all small charts have the same size, and sort by size preserving the morton order.
+
+ //nvDebug("Sorting charts.\n");
+
+ // Sort charts by area.
+ m_radix.sort(chartOrderArray);
+ const uint32 * ranks = m_radix.ranks();
+
+ // Estimate size of the map based on the mesh surface area and given texel scale.
+ float texelCount = meshArea * square(texelsPerUnit) / 0.75f; // Assume 75% utilization.
+ if (texelCount < 1) texelCount = 1;
+ uint approximateExtent = nextPowerOfTwo(uint(sqrtf(texelCount)));
+
+ //nvDebug("Init bitmap.\n");
+
+ // @@ Pack all charts smaller than a texel into a compact rectangle.
+ // @@ Start considering only 1x1 charts. Extend to 1xn charts later.
+
+ /*for (uint i = 0; i < chartCount; i++)
+ {
+ uint c = ranks[chartCount - i - 1]; // largest chart first
+
+ Chart * chart = m_atlas->chartAt(c);
+
+ if (!chart->isDisk()) continue;
+
+ if (iceil(chartExtents[c].x) == 1 && iceil(chartExtents[c].x) == 1) {
+ // @@ Add to
+ }
+ }*/
+
+
+
+ // Init bit map.
+ m_bitmap.clearAll();
+ if (approximateExtent > m_bitmap.width()) {
+ m_bitmap.resize(approximateExtent, approximateExtent, false);
+ m_debug_bitmap.resize(approximateExtent, approximateExtent);
+ m_debug_bitmap.fill(Color32(0,0,0,0));
+ }
+
+
+ int w = 0;
+ int h = 0;
+
+#if 1
+ // Add sorted charts to bitmap.
+ for (uint i = 0; i < chartCount; i++)
+ {
+ uint c = ranks[chartCount - i - 1]; // largest chart first
+
+ Chart * chart = m_atlas->chartAt(c);
+
+ if (!chart->isVertexMapped() && !chart->isDisk()) continue;
+
+ //float scale_x = 1;
+ //float scale_y = 1;
+
+ BitMap chart_bitmap;
+
+ if (chart->isVertexMapped()) {
+ // Init all bits to 1.
+ chart_bitmap.resize(ftoi_ceil(chartExtents[c].x), ftoi_ceil(chartExtents[c].y), /*initValue=*/true);
+
+ // @@ Another alternative would be to try to map each vertex to a different texel trying to fill all the available unused texels.
+ }
+ else {
+ // @@ Add special cases for dot and line charts. @@ Lightmap rasterizer also needs to handle these special cases.
+ // @@ We could also have a special case for chart quads. If the quad surface <= 4 texels, align vertices with texel centers and do not add padding. May be very useful for foliage.
+
+ // @@ In general we could reduce the padding of all charts by one texel by using a rasterizer that takes into account the 2-texel footprint of the tent bilinear filter. For example,
+ // if we have a chart that is less than 1 texel wide currently we add one texel to the left and one texel to the right creating a 3-texel-wide bitmap. However, if we know that the
+ // chart is only 1 texel wide we could align it so that it only touches the footprint of two texels:
+
+ // | | <- Touches texels 0, 1 and 2.
+ // | | <- Only touches texels 0 and 1.
+ // \ \ / \ / /
+ // \ X X /
+ // \ / \ / \ /
+ // V V V
+ // 0 1 2
+
+ if (conservative) {
+ // Init all bits to 0.
+ chart_bitmap.resize(ftoi_ceil(chartExtents[c].x) + 2, ftoi_ceil(chartExtents[c].y) + 2, /*initValue=*/false); // + 2 to add padding on both sides.
+
+ // Rasterize chart and dilate.
+ drawChartBitmapDilate(chart, &chart_bitmap, /*padding=*/1);
+ }
+ else {
+ // Init all bits to 0.
+ chart_bitmap.resize(ftoi_ceil(chartExtents[c].x) + 1, ftoi_ceil(chartExtents[c].y) + 1, /*initValue=*/false); // Add half a texels on each side.
+
+ // Rasterize chart and dilate.
+ drawChartBitmap(chart, &chart_bitmap, Vector2(1), Vector2(0.5));
+ }
+ }
+
+ int best_x, best_y;
+ int best_cw, best_ch; // Includes padding now.
+ int best_r;
+ findChartLocation(quality, &chart_bitmap, chartExtents[c], w, h, &best_x, &best_y, &best_cw, &best_ch, &best_r);
+
+ /*if (w < best_x + best_cw || h < best_y + best_ch)
+ {
+ nvDebug("Resize extents to (%d, %d).\n", best_x + best_cw, best_y + best_ch);
+ }*/
+
+ // Update parametric extents.
+ w = max(w, best_x + best_cw);
+ h = max(h, best_y + best_ch);
+
+ w = align(w, 4);
+ h = align(h, 4);
+
+ // Resize bitmap if necessary.
+ if (uint(w) > m_bitmap.width() || uint(h) > m_bitmap.height())
+ {
+ //nvDebug("Resize bitmap (%d, %d).\n", nextPowerOfTwo(w), nextPowerOfTwo(h));
+ m_bitmap.resize(nextPowerOfTwo(U32(w)), nextPowerOfTwo(U32(h)), false);
+ m_debug_bitmap.resize(nextPowerOfTwo(U32(w)), nextPowerOfTwo(U32(h)));
+ }
+
+ //nvDebug("Add chart at (%d, %d).\n", best_x, best_y);
+
+ addChart(&chart_bitmap, w, h, best_x, best_y, best_r, /*debugOutput=*/NULL);
+
+ // IC: Output chart again to debug bitmap.
+ if (chart->isVertexMapped()) {
+ addChart(&chart_bitmap, w, h, best_x, best_y, best_r, &m_debug_bitmap);
+ }
+ else {
+ addChart(chart, w, h, best_x, best_y, best_r, &m_debug_bitmap);
+ }
+
+ //float best_angle = 2 * PI * best_r;
+
+ // Translate and rotate chart texture coordinates.
+ HalfEdge::Mesh * mesh = chart->chartMesh();
+ const uint vertexCount = mesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+
+ Vector2 t = vertex->tex;
+ if (best_r) swap(t.x, t.y);
+ //vertex->tex.x = best_x + t.x * cosf(best_angle) - t.y * sinf(best_angle);
+ //vertex->tex.y = best_y + t.x * sinf(best_angle) + t.y * cosf(best_angle);
+
+ vertex->tex.x = best_x + t.x + 0.5f;
+ vertex->tex.y = best_y + t.y + 0.5f;
+
+ nvCheck(vertex->tex.x >= 0 && vertex->tex.y >= 0);
+ nvCheck(isFinite(vertex->tex.x) && isFinite(vertex->tex.y));
+ }
+
+#if DEBUG_OUTPUT && 0
+ StringBuilder fileName;
+ fileName.format("debug_packer_%d.tga", i);
+ //outputDebugBitmap(fileName.str(), m_bitmap, w, h);
+ outputDebugImage(fileName.str(), m_debug_bitmap, w, h);
+#endif
+ }
+
+#else // 0
+
+ // Add sorted charts to bitmap.
+ for (uint i = 0; i < chartCount; i++)
+ {
+ uint c = ranks[chartCount - i - 1]; // largest chart first
+
+ Chart * chart = m_atlas->chartAt(c);
+
+ if (!chart->isDisk()) continue;
+
+ Vector2 scale(1, 1);
+
+#if 0 // old method.
+ //m_padding_x = 2*padding;
+ //m_padding_y = 2*padding;
+#else
+ //m_padding_x = 0; //padding;
+ //m_padding_y = 0; //padding;
+#endif
+
+ int bw = ftoi_ceil(chartExtents[c].x + 1);
+ int bh = ftoi_ceil(chartExtents[c].y + 1);
+
+ if (chartExtents[c].x < 1.0f) {
+ scale.x = 0.01f; // @@ Ideally we would like to scale it to 0, but then our rasterizer would not touch any pixels.
+ bw = 1;
+ }
+ if (chartExtents[c].y < 1.0f) {
+ scale.y = 0.01f;
+ bh = 1;
+ }
+
+ //BitMap chart_bitmap(iceil(chartExtents[c].x) + 1 + m_padding_x * 2, iceil(chartExtents[c].y) + 1 + m_padding_y * 2);
+ //BitMap chart_bitmap(ftoi_ceil(chartExtents[c].x/2)*2, ftoi_ceil(chartExtents[c].y/2)*2);
+ BitMap chart_bitmap(bw, bh);
+ chart_bitmap.clearAll();
+
+ Vector2 offset;
+ offset.x = 0; // (chart_bitmap.width() - chartExtents[c].x) * 0.5f;
+ offset.y = 0; // (chart_bitmap.height() - chartExtents[c].y) * 0.5f;
+
+ drawChartBitmap(chart, &chart_bitmap, scale, offset);
+
+ int best_x, best_y;
+ int best_cw, best_ch;
+ int best_r;
+ findChartLocation(quality, &chart_bitmap, chartExtents[c], w, h, &best_x, &best_y, &best_cw, &best_ch, &best_r);
+
+ /*if (w < best_x + best_cw || h < best_y + best_ch)
+ {
+ nvDebug("Resize extents to (%d, %d).\n", best_x + best_cw, best_y + best_ch);
+ }*/
+
+ // Update parametric extents.
+ w = max(w, best_x + best_cw);
+ h = max(h, best_y + best_ch);
+
+ // Resize bitmap if necessary.
+ if (uint(w) > m_bitmap.width() || uint(h) > m_bitmap.height())
+ {
+ //nvDebug("Resize bitmap (%d, %d).\n", nextPowerOfTwo(w), nextPowerOfTwo(h));
+ m_bitmap.resize(nextPowerOfTwo(w), nextPowerOfTwo(h), false);
+ m_debug_bitmap.resize(nextPowerOfTwo(w), nextPowerOfTwo(h));
+ }
+
+ //nvDebug("Add chart at (%d, %d).\n", best_x, best_y);
+
+#if 0 // old method.
+#if _DEBUG
+ checkCanAddChart(chart, w, h, best_x, best_y, best_r);
+#endif
+
+ // Add chart.
+ addChart(chart, w, h, best_x, best_y, best_r);
+#else
+ // Add chart reusing its bitmap.
+ addChart(&chart_bitmap, w, h, best_x, best_y, best_r);
+#endif
+
+ //float best_angle = 2 * PI * best_r;
+
+ // Translate and rotate chart texture coordinates.
+ HalfEdge::Mesh * mesh = chart->chartMesh();
+ const uint vertexCount = mesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+
+ Vector2 t = vertex->tex * scale + offset;
+ if (best_r) swap(t.x, t.y);
+ //vertex->tex.x = best_x + t.x * cosf(best_angle) - t.y * sinf(best_angle);
+ //vertex->tex.y = best_y + t.x * sinf(best_angle) + t.y * cosf(best_angle);
+ vertex->tex.x = best_x + t.x + 0.5f;
+ vertex->tex.y = best_y + t.y + 0.5f;
+
+ nvCheck(vertex->tex.x >= 0 && vertex->tex.y >= 0);
+ }
+
+#if DEBUG_OUTPUT && 0
+ StringBuilder fileName;
+ fileName.format("debug_packer_%d.tga", i);
+ //outputDebugBitmap(fileName.str(), m_bitmap, w, h);
+ outputDebugImage(fileName.str(), m_debug_bitmap, w, h);
+#endif
+ }
+
+#endif // 0
+
+ //w -= padding - 1; // Leave one pixel border!
+ //h -= padding - 1;
+
+ m_width = max(0, w);
+ m_height = max(0, h);
+
+ nvCheck(isAligned(m_width, 4));
+ nvCheck(isAligned(m_height, 4));
+
+ m_debug_bitmap.resize(m_width, m_height);
+ m_debug_bitmap.setFormat(Image::Format_ARGB);
+
+#if DEBUG_OUTPUT
+ //outputDebugBitmap("debug_packer_final.tga", m_bitmap, w, h);
+ //outputDebugImage("debug_packer_final.tga", m_debug_bitmap, w, h);
+ ImageIO::save("debug_packer_final.tga", &m_debug_bitmap);
+#endif
+}
+
+
+// IC: Brute force is slow, and random may take too much time to converge. We start inserting large charts in a small atlas. Using brute force is lame, because most of the space
+// is occupied at this point. At the end we have many small charts and a large atlas with sparse holes. Finding those holes randomly is slow. A better approach would be to
+// start stacking large charts as if they were tetris pieces. Once charts get small try to place them randomly. It may be interesting to try a intermediate strategy, first try
+// along one axis and then try exhaustively along that axis.
+void AtlasPacker::findChartLocation(int quality, const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r)
+{
+ int attempts = 256;
+ if (quality == 1) attempts = 4096;
+ if (quality == 2) attempts = 2048;
+ if (quality == 3) attempts = 1024;
+ if (quality == 4) attempts = 512;
+
+ if (quality == 0 || w*h < attempts)
+ {
+ findChartLocation_bruteForce(bitmap, extents, w, h, best_x, best_y, best_w, best_h, best_r);
+ }
+ else
+ {
+ findChartLocation_random(bitmap, extents, w, h, best_x, best_y, best_w, best_h, best_r, attempts);
+ }
+}
+
+#define BLOCK_SIZE 4
+
+void AtlasPacker::findChartLocation_bruteForce(const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r)
+{
+ int best_metric = INT_MAX;
+
+ // Try two different orientations.
+ for (int r = 0; r < 2; r++)
+ {
+ int cw = bitmap->width();
+ int ch = bitmap->height();
+ if (r & 1) swap(cw, ch);
+
+ for (int y = 0; y <= h + 1; y += BLOCK_SIZE) // + 1 to extend atlas in case atlas full.
+ {
+ for (int x = 0; x <= w + 1; x += BLOCK_SIZE) // + 1 not really necessary here.
+ {
+ // Early out.
+ int area = max(w, x+cw) * max(h, y+ch);
+ //int perimeter = max(w, x+cw) + max(h, y+ch);
+ int extents = max(max(w, x+cw), max(h, y+ch));
+
+ int metric = extents*extents + area;
+
+ if (metric > best_metric) {
+ continue;
+ }
+ if (metric == best_metric && max(x, y) >= max(*best_x, *best_y)) {
+ // If metric is the same, pick the one closest to the origin.
+ continue;
+ }
+
+ if (canAddChart(bitmap, w, h, x, y, r))
+ {
+ best_metric = metric;
+ *best_x = x;
+ *best_y = y;
+ *best_w = cw;
+ *best_h = ch;
+ *best_r = r;
+
+ if (area == w*h)
+ {
+ // Chart is completely inside, do not look at any other location.
+ goto done;
+ }
+ }
+ }
+ }
+ }
+
+done:
+ nvDebugCheck (best_metric != INT_MAX);
+}
+
+
+void AtlasPacker::findChartLocation_random(const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r, int minTrialCount)
+{
+ int best_metric = INT_MAX;
+
+ for (int i = 0; i < minTrialCount || best_metric == INT_MAX; i++)
+ {
+ int r = m_rand.getRange(1);
+ int x = m_rand.getRange(w + 1); // + 1 to extend atlas in case atlas full. We may want to use a higher number to increase probability of extending atlas.
+ int y = m_rand.getRange(h + 1); // + 1 to extend atlas in case atlas full.
+
+ x = align(x, BLOCK_SIZE);
+ y = align(y, BLOCK_SIZE);
+
+ int cw = bitmap->width();
+ int ch = bitmap->height();
+ if (r & 1) swap(cw, ch);
+
+ // Early out.
+ int area = max(w, x+cw) * max(h, y+ch);
+ //int perimeter = max(w, x+cw) + max(h, y+ch);
+ int extents = max(max(w, x+cw), max(h, y+ch));
+
+ int metric = extents*extents + area;
+
+ if (metric > best_metric) {
+ continue;
+ }
+ if (metric == best_metric && min(x, y) > min(*best_x, *best_y)) {
+ // If metric is the same, pick the one closest to the origin.
+ continue;
+ }
+
+ if (canAddChart(bitmap, w, h, x, y, r))
+ {
+ best_metric = metric;
+ *best_x = x;
+ *best_y = y;
+ *best_w = cw;
+ *best_h = ch;
+ *best_r = r;
+
+ if (area == w*h)
+ {
+ // Chart is completely inside, do not look at any other location.
+ break;
+ }
+ }
+ }
+}
+
+
+void AtlasPacker::drawChartBitmapDilate(const Chart * chart, BitMap * bitmap, int padding)
+{
+ const int w = bitmap->width();
+ const int h = bitmap->height();
+ const Vector2 extents = Vector2(float(w), float(h));
+
+ // Rasterize chart faces, check that all bits are not set.
+ const uint faceCount = chart->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = chart->chartMesh()->faceAt(f);
+
+ Vector2 vertices[4];
+
+ uint edgeCount = 0;
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ if (edgeCount < 4)
+ {
+ vertices[edgeCount] = it.vertex()->tex + Vector2(0.5) + Vector2(float(padding), float(padding));
+ }
+ edgeCount++;
+ }
+
+ if (edgeCount == 3)
+ {
+ Raster::drawTriangle(Raster::Mode_Antialiased, extents, true, vertices, AtlasPacker::setBitsCallback, bitmap);
+ }
+ else
+ {
+ Raster::drawQuad(Raster::Mode_Antialiased, extents, true, vertices, AtlasPacker::setBitsCallback, bitmap);
+ }
+ }
+
+ // Expand chart by padding pixels. (dilation)
+ BitMap tmp(w, h);
+ for (int i = 0; i < padding; i++) {
+ tmp.clearAll();
+
+ for (int y = 0; y < h; y++) {
+ for (int x = 0; x < w; x++) {
+ bool b = bitmap->bitAt(x, y);
+ if (!b) {
+ if (x > 0) {
+ b |= bitmap->bitAt(x - 1, y);
+ if (y > 0) b |= bitmap->bitAt(x - 1, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x - 1, y + 1);
+ }
+ if (y > 0) b |= bitmap->bitAt(x, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x, y + 1);
+ if (x < w-1) {
+ b |= bitmap->bitAt(x + 1, y);
+ if (y > 0) b |= bitmap->bitAt(x + 1, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x + 1, y + 1);
+ }
+ }
+ if (b) tmp.setBitAt(x, y);
+ }
+ }
+
+ swap(tmp, *bitmap);
+ }
+}
+
+
+void AtlasPacker::drawChartBitmap(const Chart * chart, BitMap * bitmap, const Vector2 & scale, const Vector2 & offset)
+{
+ const int w = bitmap->width();
+ const int h = bitmap->height();
+ const Vector2 extents = Vector2(float(w), float(h));
+
+ static const Vector2 pad[4] = {
+ Vector2(-0.5, -0.5),
+ Vector2(0.5, -0.5),
+ Vector2(-0.5, 0.5),
+ Vector2(0.5, 0.5)
+ };
+ /*static const Vector2 pad[4] = {
+ Vector2(-1, -1),
+ Vector2(1, -1),
+ Vector2(-1, 1),
+ Vector2(1, 1)
+ };*/
+
+ // Rasterize 4 times to add proper padding.
+ for (int i = 0; i < 4; i++) {
+
+ // Rasterize chart faces, check that all bits are not set.
+ const uint faceCount = chart->chartMesh()->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = chart->chartMesh()->faceAt(f);
+
+ Vector2 vertices[4];
+
+ uint edgeCount = 0;
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ if (edgeCount < 4)
+ {
+ vertices[edgeCount] = it.vertex()->tex * scale + offset + pad[i];
+ nvCheck(ftoi_ceil(vertices[edgeCount].x) >= 0);
+ nvCheck(ftoi_ceil(vertices[edgeCount].y) >= 0);
+ nvCheck(ftoi_ceil(vertices[edgeCount].x) <= w);
+ nvCheck(ftoi_ceil(vertices[edgeCount].y) <= h);
+ }
+ edgeCount++;
+ }
+
+ if (edgeCount == 3)
+ {
+ Raster::drawTriangle(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::setBitsCallback, bitmap);
+ }
+ else
+ {
+ Raster::drawQuad(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::setBitsCallback, bitmap);
+ }
+ }
+ }
+
+ // @@ This only allows us to expand the size in texel intervals.
+ /*if (m_padding_x != 0 && m_padding_y != 0)*/ {
+
+ // Expand chart by padding pixels. (dilation)
+ BitMap tmp(w, h);
+ //for (int i = 0; i < 1; i++) {
+ tmp.clearAll();
+
+ for (int y = 0; y < h; y++) {
+ for (int x = 0; x < w; x++) {
+ bool b = bitmap->bitAt(x, y);
+ if (!b) {
+ if (x > 0) {
+ b |= bitmap->bitAt(x - 1, y);
+ if (y > 0) b |= bitmap->bitAt(x - 1, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x - 1, y + 1);
+ }
+ if (y > 0) b |= bitmap->bitAt(x, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x, y + 1);
+ if (x < w-1) {
+ b |= bitmap->bitAt(x + 1, y);
+ if (y > 0) b |= bitmap->bitAt(x + 1, y - 1);
+ if (y < h-1) b |= bitmap->bitAt(x + 1, y + 1);
+ }
+ }
+ if (b) tmp.setBitAt(x, y);
+ }
+ }
+
+ swap(tmp, *bitmap);
+ //}
+ }
+}
+
+bool AtlasPacker::canAddChart(const BitMap * bitmap, int atlas_w, int atlas_h, int offset_x, int offset_y, int r)
+{
+ nvDebugCheck(r == 0 || r == 1);
+
+ // Check whether the two bitmaps overlap.
+
+ const int w = bitmap->width();
+ const int h = bitmap->height();
+
+ if (r == 0) {
+ for (int y = 0; y < h; y++) {
+ int yy = y + offset_y;
+ if (yy >= 0) {
+ for (int x = 0; x < w; x++) {
+ int xx = x + offset_x;
+ if (xx >= 0) {
+ if (bitmap->bitAt(x, y)) {
+ if (xx < atlas_w && yy < atlas_h) {
+ if (m_bitmap.bitAt(xx, yy)) return false;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ else if (r == 1) {
+ for (int y = 0; y < h; y++) {
+ int xx = y + offset_x;
+ if (xx >= 0) {
+ for (int x = 0; x < w; x++) {
+ int yy = x + offset_y;
+ if (yy >= 0) {
+ if (bitmap->bitAt(x, y)) {
+ if (xx < atlas_w && yy < atlas_h) {
+ if (m_bitmap.bitAt(xx, yy)) return false;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ return true;
+}
+
+#if 0
+void AtlasPacker::checkCanAddChart(const Chart * chart, int w, int h, int x, int y, int r)
+{
+ nvDebugCheck(r == 0 || r == 1);
+ Vector2 extents = Vector2(float(w), float(h));
+ Vector2 offset = Vector2(float(x), float(y));
+
+ // Rasterize chart faces, set bits.
+ const uint faceCount = chart->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = chart->chartMesh()->faceAt(f);
+
+ Vector2 vertices[4];
+
+ uint edgeCount = 0;
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ if (edgeCount < 4)
+ {
+ Vector2 t = it.vertex()->tex;
+ if (r == 1) swap(t.x, t.y);
+ vertices[edgeCount] = t + offset;
+ }
+ edgeCount++;
+ }
+
+ if (edgeCount == 3)
+ {
+ Raster::drawTriangle(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::checkBitsCallback, &m_bitmap);
+ }
+ else
+ {
+ Raster::drawQuad(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::checkBitsCallback, &m_bitmap);
+ }
+ }
+}
+#endif // 0
+
+
+static Color32 chartColor = Color32(0);
+static void selectRandomColor(MTRand & rand) {
+ // Pick random color for this chart. @@ Select random hue, but fixed saturation/luminance?
+ chartColor.r = 128 + rand.getRange(127);
+ chartColor.g = 128 + rand.getRange(127);
+ chartColor.b = 128 + rand.getRange(127);
+ chartColor.a = 255;
+}
+static bool debugDrawCallback(void * param, int x, int y, Vector3::Arg, Vector3::Arg, Vector3::Arg, float area)
+{
+ Image * image = (Image *)param;
+
+ if (area > 0.0) {
+ Color32 c = image->pixel(x, y);
+ c.r = chartColor.r;
+ c.g = chartColor.g;
+ c.b = chartColor.b;
+ c.a += U8(ftoi_round(0.5f * area * 255));
+ image->pixel(x, y) = c;
+ }
+
+ return true;
+}
+
+void AtlasPacker::addChart(const Chart * chart, int w, int h, int x, int y, int r, Image * debugOutput)
+{
+ nvDebugCheck(r == 0 || r == 1);
+
+ nvDebugCheck(debugOutput != NULL);
+ selectRandomColor(m_rand);
+
+ Vector2 extents = Vector2(float(w), float(h));
+ Vector2 offset = Vector2(float(x), float(y)) + Vector2(0.5);
+
+ // Rasterize chart faces, set bits.
+ const uint faceCount = chart->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = chart->chartMesh()->faceAt(f);
+
+ Vector2 vertices[4];
+
+ uint edgeCount = 0;
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ if (edgeCount < 4)
+ {
+ Vector2 t = it.vertex()->tex;
+ if (r == 1) swap(t.x, t.y);
+ vertices[edgeCount] = t + offset;
+ }
+ edgeCount++;
+ }
+
+ if (edgeCount == 3)
+ {
+ Raster::drawTriangle(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, debugDrawCallback, debugOutput);
+ }
+ else
+ {
+ Raster::drawQuad(Raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, debugDrawCallback, debugOutput);
+ }
+ }
+}
+
+
+void AtlasPacker::addChart(const BitMap * bitmap, int atlas_w, int atlas_h, int offset_x, int offset_y, int r, Image * debugOutput)
+{
+ nvDebugCheck(r == 0 || r == 1);
+
+ // Check whether the two bitmaps overlap.
+
+ const int w = bitmap->width();
+ const int h = bitmap->height();
+
+ if (debugOutput != NULL) {
+ selectRandomColor(m_rand);
+ }
+
+ if (r == 0) {
+ for (int y = 0; y < h; y++) {
+ int yy = y + offset_y;
+ if (yy >= 0) {
+ for (int x = 0; x < w; x++) {
+ int xx = x + offset_x;
+ if (xx >= 0) {
+ if (bitmap->bitAt(x, y)) {
+ if (xx < atlas_w && yy < atlas_h) {
+ if (debugOutput) debugOutput->pixel(xx, yy) = chartColor;
+ else {
+ nvDebugCheck(m_bitmap.bitAt(xx, yy) == false);
+ m_bitmap.setBitAt(xx, yy);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ else if (r == 1) {
+ for (int y = 0; y < h; y++) {
+ int xx = y + offset_x;
+ if (xx >= 0) {
+ for (int x = 0; x < w; x++) {
+ int yy = x + offset_y;
+ if (yy >= 0) {
+ if (bitmap->bitAt(x, y)) {
+ if (xx < atlas_w && yy < atlas_h) {
+ if (debugOutput) debugOutput->pixel(xx, yy) = chartColor;
+ else {
+ nvDebugCheck(m_bitmap.bitAt(xx, yy) == false);
+ m_bitmap.setBitAt(xx, yy);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+
+
+/*static*/ bool AtlasPacker::checkBitsCallback(void * param, int x, int y, Vector3::Arg, Vector3::Arg, Vector3::Arg, float)
+{
+ BitMap * bitmap = (BitMap * )param;
+
+ nvDebugCheck(bitmap->bitAt(x, y) == false);
+
+ return true;
+}
+
+/*static*/ bool AtlasPacker::setBitsCallback(void * param, int x, int y, Vector3::Arg, Vector3::Arg, Vector3::Arg, float area)
+{
+ BitMap * bitmap = (BitMap * )param;
+
+ if (area > 0.0) {
+ bitmap->setBitAt(x, y);
+ }
+
+ return true;
+}
+
+
+
+float AtlasPacker::computeAtlasUtilization() const {
+ const uint w = m_width;
+ const uint h = m_height;
+ nvDebugCheck(w <= m_bitmap.width());
+ nvDebugCheck(h <= m_bitmap.height());
+
+ uint count = 0;
+ for (uint y = 0; y < h; y++) {
+ for (uint x = 0; x < w; x++) {
+ count += m_bitmap.bitAt(x, y);
+ }
+ }
+
+ return float(count) / (w * h);
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.h b/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.h
new file mode 100644
index 0000000000..2d305f38cd
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/AtlasPacker.h
@@ -0,0 +1,63 @@
+// This code is in the public domain -- castano@gmail.com
+
+#pragma once
+#ifndef NV_MESH_ATLASPACKER_H
+#define NV_MESH_ATLASPACKER_H
+
+#include "nvcore/RadixSort.h"
+#include "nvmath/Vector.h"
+#include "nvmath/Random.h"
+#include "nvimage/BitMap.h"
+#include "nvimage/Image.h"
+
+#include "nvmesh/nvmesh.h"
+
+
+namespace nv
+{
+ class Atlas;
+ class Chart;
+
+ struct AtlasPacker
+ {
+ AtlasPacker(Atlas * atlas);
+ ~AtlasPacker();
+
+ void packCharts(int quality, float texelArea, bool blockAligned, bool conservative);
+ float computeAtlasUtilization() const;
+
+ private:
+
+ void findChartLocation(int quality, const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r);
+ void findChartLocation_bruteForce(const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r);
+ void findChartLocation_random(const BitMap * bitmap, Vector2::Arg extents, int w, int h, int * best_x, int * best_y, int * best_w, int * best_h, int * best_r, int minTrialCount);
+
+ void drawChartBitmapDilate(const Chart * chart, BitMap * bitmap, int padding);
+ void drawChartBitmap(const Chart * chart, BitMap * bitmap, const Vector2 & scale, const Vector2 & offset);
+
+ bool canAddChart(const BitMap * bitmap, int w, int h, int x, int y, int r);
+ void addChart(const BitMap * bitmap, int w, int h, int x, int y, int r, Image * debugOutput);
+ //void checkCanAddChart(const Chart * chart, int w, int h, int x, int y, int r);
+ void addChart(const Chart * chart, int w, int h, int x, int y, int r, Image * debugOutput);
+
+
+ static bool checkBitsCallback(void * param, int x, int y, Vector3::Arg bar, Vector3::Arg dx, Vector3::Arg dy, float coverage);
+ static bool setBitsCallback(void * param, int x, int y, Vector3::Arg bar, Vector3::Arg dx, Vector3::Arg dy, float coverage);
+
+ private:
+
+ Atlas * m_atlas;
+ BitMap m_bitmap;
+ Image m_debug_bitmap;
+ RadixSort m_radix;
+
+ uint m_width;
+ uint m_height;
+
+ MTRand m_rand;
+
+ };
+
+} // nv namespace
+
+#endif // NV_MESH_ATLASPACKER_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.cpp b/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.cpp
new file mode 100644
index 0000000000..cd1e8bbb7b
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.cpp
@@ -0,0 +1,483 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#include "nvmesh.h" // pch
+
+#include "LeastSquaresConformalMap.h"
+#include "ParameterizationQuality.h"
+#include "Util.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Vertex.h"
+#include "nvmesh/halfedge/Face.h"
+
+#include "nvmath/Sparse.h"
+#include "nvmath/Solver.h"
+#include "nvmath/Vector.inl"
+
+#include "nvcore/Array.inl"
+
+
+using namespace nv;
+using namespace HalfEdge;
+
+namespace
+{
+
+ // Test all pairs of vertices in the boundary and check distance.
+ static void findDiameterVertices(HalfEdge::Mesh * mesh, HalfEdge::Vertex ** a, HalfEdge::Vertex ** b)
+ {
+ nvDebugCheck(mesh != NULL);
+ nvDebugCheck(a != NULL);
+ nvDebugCheck(b != NULL);
+
+ const uint vertexCount = mesh->vertexCount();
+
+ float maxLength = 0.0f;
+
+ for (uint v0 = 1; v0 < vertexCount; v0++)
+ {
+ HalfEdge::Vertex * vertex0 = mesh->vertexAt(v0);
+ nvDebugCheck(vertex0 != NULL);
+
+ if (!vertex0->isBoundary()) continue;
+
+ for (uint v1 = 0; v1 < v0; v1++)
+ {
+ HalfEdge::Vertex * vertex1 = mesh->vertexAt(v1);
+ nvDebugCheck(vertex1 != NULL);
+
+ if (!vertex1->isBoundary()) continue;
+
+ float len = length(vertex0->pos - vertex1->pos);
+
+ if (len > maxLength)
+ {
+ maxLength = len;
+
+ *a = vertex0;
+ *b = vertex1;
+ }
+ }
+ }
+
+ nvDebugCheck(*a != NULL && *b != NULL);
+ }
+
+ // Fast sweep in 3 directions
+ static bool findApproximateDiameterVertices(HalfEdge::Mesh * mesh, HalfEdge::Vertex ** a, HalfEdge::Vertex ** b)
+ {
+ nvDebugCheck(mesh != NULL);
+ nvDebugCheck(a != NULL);
+ nvDebugCheck(b != NULL);
+
+ const uint vertexCount = mesh->vertexCount();
+
+ HalfEdge::Vertex * minVertex[3];
+ HalfEdge::Vertex * maxVertex[3];
+
+ minVertex[0] = minVertex[1] = minVertex[2] = NULL;
+ maxVertex[0] = maxVertex[1] = maxVertex[2] = NULL;
+
+ for (uint v = 1; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+ nvDebugCheck(vertex != NULL);
+
+ if (vertex->isBoundary())
+ {
+ minVertex[0] = minVertex[1] = minVertex[2] = vertex;
+ maxVertex[0] = maxVertex[1] = maxVertex[2] = vertex;
+ break;
+ }
+ }
+
+ if (minVertex[0] == NULL)
+ {
+ // Input mesh has not boundaries.
+ return false;
+ }
+
+ for (uint v = 1; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+ nvDebugCheck(vertex != NULL);
+
+ if (!vertex->isBoundary())
+ {
+ // Skip interior vertices.
+ continue;
+ }
+
+ if (vertex->pos.x < minVertex[0]->pos.x) minVertex[0] = vertex;
+ else if (vertex->pos.x > maxVertex[0]->pos.x) maxVertex[0] = vertex;
+
+ if (vertex->pos.y < minVertex[1]->pos.y) minVertex[1] = vertex;
+ else if (vertex->pos.y > maxVertex[1]->pos.y) maxVertex[1] = vertex;
+
+ if (vertex->pos.z < minVertex[2]->pos.z) minVertex[2] = vertex;
+ else if (vertex->pos.z > maxVertex[2]->pos.z) maxVertex[2] = vertex;
+ }
+
+ float lengths[3];
+ for (int i = 0; i < 3; i++)
+ {
+ lengths[i] = length(minVertex[i]->pos - maxVertex[i]->pos);
+ }
+
+ if (lengths[0] > lengths[1] && lengths[0] > lengths[2])
+ {
+ *a = minVertex[0];
+ *b = maxVertex[0];
+ }
+ else if (lengths[1] > lengths[2])
+ {
+ *a = minVertex[1];
+ *b = maxVertex[1];
+ }
+ else
+ {
+ *a = minVertex[2];
+ *b = maxVertex[2];
+ }
+
+ return true;
+ }
+
+ // Conformal relations from Bruno Levy:
+
+ // Computes the coordinates of the vertices of a triangle
+ // in a local 2D orthonormal basis of the triangle's plane.
+ static void project_triangle(Vector3::Arg p0, Vector3::Arg p1, Vector3::Arg p2, Vector2 * z0, Vector2 * z1, Vector2 * z2)
+ {
+ Vector3 X = normalize(p1 - p0, 0.0f);
+ Vector3 Z = normalize(cross(X, (p2 - p0)), 0.0f);
+ Vector3 Y = normalize(cross(Z, X), 0.0f);
+
+ float x0 = 0.0f;
+ float y0 = 0.0f;
+ float x1 = length(p1 - p0);
+ float y1 = 0.0f;
+ float x2 = dot((p2 - p0), X);
+ float y2 = dot((p2 - p0), Y);
+
+ *z0 = Vector2(x0, y0);
+ *z1 = Vector2(x1, y1);
+ *z2 = Vector2(x2, y2);
+ }
+
+ // LSCM equation, geometric form :
+ // (Z1 - Z0)(U2 - U0) = (Z2 - Z0)(U1 - U0)
+ // Where Uk = uk + i.vk is the complex number
+ // corresponding to (u,v) coords
+ // Zk = xk + i.yk is the complex number
+ // corresponding to local (x,y) coords
+ // cool: no divide with this expression,
+ // makes it more numerically stable in
+ // the presence of degenerate triangles.
+
+ static void setup_conformal_map_relations(SparseMatrix & A, int row, const HalfEdge::Vertex * v0, const HalfEdge::Vertex * v1, const HalfEdge::Vertex * v2)
+ {
+ int id0 = v0->id;
+ int id1 = v1->id;
+ int id2 = v2->id;
+
+ Vector3 p0 = v0->pos;
+ Vector3 p1 = v1->pos;
+ Vector3 p2 = v2->pos;
+
+ Vector2 z0, z1, z2;
+ project_triangle(p0, p1, p2, &z0, &z1, &z2);
+
+ Vector2 z01 = z1 - z0;
+ Vector2 z02 = z2 - z0;
+
+ float a = z01.x;
+ float b = z01.y;
+ float c = z02.x;
+ float d = z02.y;
+ nvCheck(b == 0.0f);
+
+ // Note : 2*id + 0 --> u
+ // 2*id + 1 --> v
+ int u0_id = 2 * id0 + 0;
+ int v0_id = 2 * id0 + 1;
+ int u1_id = 2 * id1 + 0;
+ int v1_id = 2 * id1 + 1;
+ int u2_id = 2 * id2 + 0;
+ int v2_id = 2 * id2 + 1;
+
+ // Note : b = 0
+
+ // Real part
+ A.setCoefficient(u0_id, 2 * row + 0, -a+c);
+ A.setCoefficient(v0_id, 2 * row + 0, b-d);
+ A.setCoefficient(u1_id, 2 * row + 0, -c);
+ A.setCoefficient(v1_id, 2 * row + 0, d);
+ A.setCoefficient(u2_id, 2 * row + 0, a);
+
+ // Imaginary part
+ A.setCoefficient(u0_id, 2 * row + 1, -b+d);
+ A.setCoefficient(v0_id, 2 * row + 1, -a+c);
+ A.setCoefficient(u1_id, 2 * row + 1, -d);
+ A.setCoefficient(v1_id, 2 * row + 1, -c);
+ A.setCoefficient(v2_id, 2 * row + 1, a);
+ }
+
+
+ // Conformal relations from Brecht Van Lommel (based on ABF):
+
+ static float vec_angle_cos(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3)
+ {
+ Vector3 d1 = v1 - v2;
+ Vector3 d2 = v3 - v2;
+ return clamp(dot(d1, d2) / (length(d1) * length(d2)), -1.0f, 1.0f);
+ }
+
+ static float vec_angle(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3)
+ {
+ float dot = vec_angle_cos(v1, v2, v3);
+ return acosf(dot);
+ }
+
+ static void triangle_angles(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3, float *a1, float *a2, float *a3)
+ {
+ *a1 = vec_angle(v3, v1, v2);
+ *a2 = vec_angle(v1, v2, v3);
+ *a3 = PI - *a2 - *a1;
+ }
+
+ static void triangle_cosines(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3, float *a1, float *a2, float *a3)
+ {
+ *a1 = vec_angle_cos(v3, v1, v2);
+ *a2 = vec_angle_cos(v1, v2, v3);
+ *a3 = vec_angle_cos(v2, v3, v1);
+ }
+
+ static void setup_abf_relations(SparseMatrix & A, int row, const HalfEdge::Vertex * v0, const HalfEdge::Vertex * v1, const HalfEdge::Vertex * v2)
+ {
+ int id0 = v0->id;
+ int id1 = v1->id;
+ int id2 = v2->id;
+
+ Vector3 p0 = v0->pos;
+ Vector3 p1 = v1->pos;
+ Vector3 p2 = v2->pos;
+
+#if 1
+ // @@ IC: Wouldn't it be more accurate to return cos and compute 1-cos^2?
+ // It does indeed seem to be a little bit more robust.
+ // @@ Need to revisit this more carefully!
+
+ float a0, a1, a2;
+ triangle_angles(p0, p1, p2, &a0, &a1, &a2);
+
+ float s0 = sinf(a0);
+ float s1 = sinf(a1);
+ float s2 = sinf(a2);
+
+ /*// Hack for degenerate triangles.
+ if (equal(s0, 0) && equal(s1, 0) && equal(s2, 0)) {
+ if (equal(a0, 0)) a0 += 0.001f;
+ if (equal(a1, 0)) a1 += 0.001f;
+ if (equal(a2, 0)) a2 += 0.001f;
+
+ if (equal(a0, PI)) a0 = PI - a1 - a2;
+ if (equal(a1, PI)) a1 = PI - a0 - a2;
+ if (equal(a2, PI)) a2 = PI - a0 - a1;
+
+ s0 = sinf(a0);
+ s1 = sinf(a1);
+ s2 = sinf(a2);
+ }*/
+
+ if (s1 > s0 && s1 > s2)
+ {
+ swap(s1, s2);
+ swap(s0, s1);
+
+ swap(a1, a2);
+ swap(a0, a1);
+
+ swap(id1, id2);
+ swap(id0, id1);
+ }
+ else if (s0 > s1 && s0 > s2)
+ {
+ swap(s0, s2);
+ swap(s0, s1);
+
+ swap(a0, a2);
+ swap(a0, a1);
+
+ swap(id0, id2);
+ swap(id0, id1);
+ }
+
+ float c0 = cosf(a0);
+#else
+ float c0, c1, c2;
+ triangle_cosines(p0, p1, p2, &c0, &c1, &c2);
+
+ float s0 = 1 - c0*c0;
+ float s1 = 1 - c1*c1;
+ float s2 = 1 - c2*c2;
+
+ nvDebugCheck(s0 != 0 || s1 != 0 || s2 != 0);
+
+ if (s1 > s0 && s1 > s2)
+ {
+ swap(s1, s2);
+ swap(s0, s1);
+
+ swap(c1, c2);
+ swap(c0, c1);
+
+ swap(id1, id2);
+ swap(id0, id1);
+ }
+ else if (s0 > s1 && s0 > s2)
+ {
+ swap(s0, s2);
+ swap(s0, s1);
+
+ swap(c0, c2);
+ swap(c0, c1);
+
+ swap(id0, id2);
+ swap(id0, id1);
+ }
+#endif
+
+ float ratio = (s2 == 0.0f) ? 1.0f: s1/s2;
+ float cosine = c0 * ratio;
+ float sine = s0 * ratio;
+
+ // Note : 2*id + 0 --> u
+ // 2*id + 1 --> v
+ int u0_id = 2 * id0 + 0;
+ int v0_id = 2 * id0 + 1;
+ int u1_id = 2 * id1 + 0;
+ int v1_id = 2 * id1 + 1;
+ int u2_id = 2 * id2 + 0;
+ int v2_id = 2 * id2 + 1;
+
+ // Real part
+ A.setCoefficient(u0_id, 2 * row + 0, cosine - 1.0f);
+ A.setCoefficient(v0_id, 2 * row + 0, -sine);
+ A.setCoefficient(u1_id, 2 * row + 0, -cosine);
+ A.setCoefficient(v1_id, 2 * row + 0, sine);
+ A.setCoefficient(u2_id, 2 * row + 0, 1);
+
+ // Imaginary part
+ A.setCoefficient(u0_id, 2 * row + 1, sine);
+ A.setCoefficient(v0_id, 2 * row + 1, cosine - 1.0f);
+ A.setCoefficient(u1_id, 2 * row + 1, -sine);
+ A.setCoefficient(v1_id, 2 * row + 1, -cosine);
+ A.setCoefficient(v2_id, 2 * row + 1, 1);
+ }
+
+} // namespace
+
+
+bool nv::computeLeastSquaresConformalMap(HalfEdge::Mesh * mesh)
+{
+ nvDebugCheck(mesh != NULL);
+
+ // For this to work properly, mesh should not have colocals that have the same
+ // attributes, unless you want the vertices to actually have different texcoords.
+
+ const uint vertexCount = mesh->vertexCount();
+ const uint D = 2 * vertexCount;
+ const uint N = 2 * countMeshTriangles(mesh);
+
+ // N is the number of equations (one per triangle)
+ // D is the number of variables (one per vertex; there are 2 pinned vertices).
+ if (N < D - 4) {
+ return false;
+ }
+
+ SparseMatrix A(D, N);
+ FullVector b(N);
+ FullVector x(D);
+
+ // Fill b:
+ b.fill(0.0f);
+
+ // Fill x:
+ HalfEdge::Vertex * v0;
+ HalfEdge::Vertex * v1;
+ if (!findApproximateDiameterVertices(mesh, &v0, &v1))
+ {
+ // Mesh has no boundaries.
+ return false;
+ }
+ if (v0->tex == v1->tex)
+ {
+ // LSCM expects an existing parameterization.
+ return false;
+ }
+
+ for (uint v = 0; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+ nvDebugCheck(vertex != NULL);
+
+ // Initial solution.
+ x[2 * v + 0] = vertex->tex.x;
+ x[2 * v + 1] = vertex->tex.y;
+ }
+
+ // Fill A:
+ const uint faceCount = mesh->faceCount();
+ for (uint f = 0, t = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ nvDebugCheck(face != NULL);
+ nvDebugCheck(face->edgeCount() == 3);
+
+ const HalfEdge::Vertex * vertex0 = NULL;
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+ nvCheck(edge != NULL);
+
+ if (vertex0 == NULL)
+ {
+ vertex0 = edge->vertex;
+ }
+ else if (edge->next->vertex != vertex0)
+ {
+ const HalfEdge::Vertex * vertex1 = edge->from();
+ const HalfEdge::Vertex * vertex2 = edge->to();
+
+ setup_abf_relations(A, t, vertex0, vertex1, vertex2);
+ //setup_conformal_map_relations(A, t, vertex0, vertex1, vertex2);
+
+ t++;
+ }
+ }
+ }
+
+ const uint lockedParameters[] =
+ {
+ 2 * v0->id + 0,
+ 2 * v0->id + 1,
+ 2 * v1->id + 0,
+ 2 * v1->id + 1
+ };
+
+ // Solve
+ LeastSquaresSolver(A, b, x, lockedParameters, 4, 0.000001f);
+
+ // Map x back to texcoords:
+ for (uint v = 0; v < vertexCount; v++)
+ {
+ HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+ nvDebugCheck(vertex != NULL);
+
+ vertex->tex = Vector2(x[2 * v + 0], x[2 * v + 1]);
+ }
+
+ return true;
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.h b/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.h
new file mode 100644
index 0000000000..51fbf193c8
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/LeastSquaresConformalMap.h
@@ -0,0 +1,15 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#pragma once
+#ifndef NV_MESH_LEASTSQUARESCONFORMALMAP_H
+#define NV_MESH_LEASTSQUARESCONFORMALMAP_H
+
+namespace nv
+{
+ namespace HalfEdge { class Mesh; }
+
+ bool computeLeastSquaresConformalMap(HalfEdge::Mesh * mesh);
+
+} // nv namespace
+
+#endif // NV_MESH_LEASTSQUARESCONFORMALMAP_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.cpp b/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.cpp
new file mode 100644
index 0000000000..d6e5e30561
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.cpp
@@ -0,0 +1,99 @@
+// This code is in the public domain -- castano@gmail.com
+
+#include "nvmesh.h" // pch
+
+#include "OrthogonalProjectionMap.h"
+
+#include "nvcore/Array.inl"
+
+#include "nvmath/Fitting.h"
+#include "nvmath/Vector.inl"
+#include "nvmath/Box.inl"
+#include "nvmath/Plane.inl"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Vertex.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/geometry/Bounds.h"
+
+
+using namespace nv;
+
+bool nv::computeOrthogonalProjectionMap(HalfEdge::Mesh * mesh)
+{
+ Vector3 axis[2];
+
+#if 1
+
+ uint vertexCount = mesh->vertexCount();
+ Array<Vector3> points(vertexCount);
+ points.resize(vertexCount);
+
+ for (uint i = 0; i < vertexCount; i++)
+ {
+ points[i] = mesh->vertexAt(i)->pos;
+ }
+
+#if 0
+ axis[0] = Fit::computePrincipalComponent_EigenSolver(vertexCount, points.buffer());
+ axis[0] = normalize(axis[0]);
+
+ Plane plane = Fit::bestPlane(vertexCount, points.buffer());
+
+ Vector3 n = plane.vector();
+
+ axis[1] = cross(axis[0], n);
+ axis[1] = normalize(axis[1]);
+#else
+ // Avoid redundant computations.
+ float matrix[6];
+ Fit::computeCovariance(vertexCount, points.buffer(), matrix);
+
+ if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0) {
+ return false;
+ }
+
+ float eigenValues[3];
+ Vector3 eigenVectors[3];
+ if (!nv::Fit::eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
+ return false;
+ }
+
+ axis[0] = normalize(eigenVectors[0]);
+ axis[1] = normalize(eigenVectors[1]);
+#endif
+
+
+#else
+
+ // IC: I thought this was generally more robust, but turns out it's not even guaranteed to return a valid projection. Imagine a narrow quad perpendicular to one plane, but rotated so that the shortest axis of
+ // the bounding box is in the direction of that plane.
+
+ // Use the shortest box axis
+ Box box = MeshBounds::box(mesh);
+ Vector3 dir = box.extents();
+
+ if (fabs(dir.x) <= fabs(dir.y) && fabs(dir.x) <= fabs(dir.z)) {
+ axis[0] = Vector3(0, 1, 0);
+ axis[1] = Vector3(0, 0, 1);
+ }
+ else if (fabs(dir.y) <= fabs(dir.z)) {
+ axis[0] = Vector3(1, 0, 0);
+ axis[1] = Vector3(0, 0, 1);
+ }
+ else {
+ axis[0] = Vector3(1, 0, 0);
+ axis[1] = Vector3(0, 1, 0);
+ }
+#endif
+
+ // Project vertices to plane.
+ for (HalfEdge::Mesh::VertexIterator it(mesh->vertices()); !it.isDone(); it.advance())
+ {
+ HalfEdge::Vertex * vertex = it.current();
+ vertex->tex.x = dot(axis[0], vertex->pos);
+ vertex->tex.y = dot(axis[1], vertex->pos);
+ }
+
+ return true;
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.h b/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.h
new file mode 100644
index 0000000000..54920413d5
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/OrthogonalProjectionMap.h
@@ -0,0 +1,15 @@
+// This code is in the public domain -- castano@gmail.com
+
+#pragma once
+#ifndef NV_MESH_ORTHOGONALPROJECTIONMAP_H
+#define NV_MESH_ORTHOGONALPROJECTIONMAP_H
+
+namespace nv
+{
+ namespace HalfEdge { class Mesh; }
+
+ bool computeOrthogonalProjectionMap(HalfEdge::Mesh * mesh);
+
+} // nv namespace
+
+#endif // NV_MESH_ORTHOGONALPROJECTIONMAP_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.cpp b/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.cpp
new file mode 100644
index 0000000000..683ee603cd
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.cpp
@@ -0,0 +1,323 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#include "nvmesh.h" // pch
+
+#include "ParameterizationQuality.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/halfedge/Vertex.h"
+#include "nvmesh/halfedge/Edge.h"
+
+#include "nvmath/Vector.inl"
+
+#include "nvcore/Debug.h"
+
+#include <float.h>
+
+
+using namespace nv;
+
+#if 0
+/*
+float triangleConformalEnergy(Vector3 q[3], Vector2 p[3])
+{
+const Vector3 v1 = q[0];
+const Vector3 v2 = q[1];
+const Vector3 v3 = q[2];
+
+const Vector2 w1 = p[0];
+const Vector2 w2 = p[1];
+const Vector2 w3 = p[2];
+
+float x1 = v2.x() - v1.x();
+float x2 = v3.x() - v1.x();
+float y1 = v2.y() - v1.y();
+float y2 = v3.y() - v1.y();
+float z1 = v2.z() - v1.z();
+float z2 = v3.z() - v1.z();
+
+float s1 = w2.x() - w1.x();
+float s2 = w3.x() - w1.x();
+float t1 = w2.y() - w1.y();
+float t2 = w3.y() - w1.y();
+
+float r = 1.0f / (s1 * t2 - s2 * t1);
+Vector3 sdir((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
+Vector3 tdir((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);
+
+Vector3 N = cross(v3-v1, v2-v1);
+
+// Rotate 90 around N.
+}
+*/
+
+static float triangleConformalEnergy(Vector3 q[3], Vector2 p[3])
+{
+ // Using Denis formulas:
+ Vector3 c0 = q[1] - q[2];
+ Vector3 c1 = q[2] - q[0];
+ Vector3 c2 = q[0] - q[1];
+
+ Vector3 N = cross(-c0, c1);
+ float T = length(N); // 2T
+ N = normalize(N, 0);
+
+ float cot_alpha0 = dot(-c1, c2) / length(cross(-c1, c2));
+ float cot_alpha1 = dot(-c2, c0) / length(cross(-c2, c0));
+ float cot_alpha2 = dot(-c0, c1) / length(cross(-c0, c1));
+
+ Vector3 t0 = -cot_alpha1 * c1 + cot_alpha2 * c2;
+ Vector3 t1 = -cot_alpha2 * c2 + cot_alpha0 * c0;
+ Vector3 t2 = -cot_alpha0 * c0 + cot_alpha1 * c1;
+
+ nvCheck(equal(length(t0), length(c0)));
+ nvCheck(equal(length(t1), length(c1)));
+ nvCheck(equal(length(t2), length(c2)));
+ nvCheck(equal(dot(t0, c0), 0));
+ nvCheck(equal(dot(t1, c1), 0));
+ nvCheck(equal(dot(t2, c2), 0));
+
+ // Gradients
+ Vector3 grad_u = 1.0f / T * (p[0].x * t0 + p[1].x * t1 + p[2].x * t2);
+ Vector3 grad_v = 1.0f / T * (p[0].y * t0 + p[1].y * t1 + p[2].y * t2);
+
+ // Rotated gradients
+ Vector3 Jgrad_u = 1.0f / T * (p[0].x * c0 + p[1].x * c1 + p[2].x * c2);
+ Vector3 Jgrad_v = 1.0f / T * (p[0].y * c0 + p[1].y * c1 + p[2].y * c2);
+
+ // Using Lengyel's formulas:
+ {
+ const Vector3 v1 = q[0];
+ const Vector3 v2 = q[1];
+ const Vector3 v3 = q[2];
+
+ const Vector2 w1 = p[0];
+ const Vector2 w2 = p[1];
+ const Vector2 w3 = p[2];
+
+ float x1 = v2.x - v1.x;
+ float x2 = v3.x - v1.x;
+ float y1 = v2.y - v1.y;
+ float y2 = v3.y - v1.y;
+ float z1 = v2.z - v1.z;
+ float z2 = v3.z - v1.z;
+
+ float s1 = w2.x - w1.x;
+ float s2 = w3.x - w1.x;
+ float t1 = w2.y - w1.y;
+ float t2 = w3.y - w1.y;
+
+ float r = 1.0f / (s1 * t2 - s2 * t1);
+ Vector3 sdir((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
+ Vector3 tdir((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);
+
+ Vector3 Jsdir = cross(N, sdir);
+ Vector3 Jtdir = cross(N, tdir);
+
+ float x = 3;
+ }
+
+ // check: sdir == grad_u
+ // check: tdir == grad_v
+
+ return length(grad_u - Jgrad_v);
+}
+#endif // 0
+
+
+ParameterizationQuality::ParameterizationQuality()
+{
+ m_totalTriangleCount = 0;
+ m_flippedTriangleCount = 0;
+ m_zeroAreaTriangleCount = 0;
+
+ m_parametricArea = 0.0f;
+ m_geometricArea = 0.0f;
+
+ m_stretchMetric = 0.0f;
+ m_maxStretchMetric = 0.0f;
+
+ m_conformalMetric = 0.0f;
+ m_authalicMetric = 0.0f;
+}
+
+ParameterizationQuality::ParameterizationQuality(const HalfEdge::Mesh * mesh)
+{
+ nvDebugCheck(mesh != NULL);
+
+ m_totalTriangleCount = 0;
+ m_flippedTriangleCount = 0;
+ m_zeroAreaTriangleCount = 0;
+
+ m_parametricArea = 0.0f;
+ m_geometricArea = 0.0f;
+
+ m_stretchMetric = 0.0f;
+ m_maxStretchMetric = 0.0f;
+
+ m_conformalMetric = 0.0f;
+ m_authalicMetric = 0.0f;
+
+ const uint faceCount = mesh->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(f);
+ const HalfEdge::Vertex * vertex0 = NULL;
+
+ Vector3 p[3];
+ Vector2 t[3];
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+
+ if (vertex0 == NULL)
+ {
+ vertex0 = edge->vertex;
+
+ p[0] = vertex0->pos;
+ t[0] = vertex0->tex;
+ }
+ else if (edge->to() != vertex0)
+ {
+ p[1] = edge->from()->pos;
+ p[2] = edge->to()->pos;
+ t[1] = edge->from()->tex;
+ t[2] = edge->to()->tex;
+
+ processTriangle(p, t);
+ }
+ }
+ }
+
+ if (m_flippedTriangleCount + m_zeroAreaTriangleCount == faceCount)
+ {
+ // If all triangles are flipped, then none is.
+ m_flippedTriangleCount = 0;
+ }
+
+ nvDebugCheck(isFinite(m_parametricArea) && m_parametricArea >= 0);
+ nvDebugCheck(isFinite(m_geometricArea) && m_geometricArea >= 0);
+ nvDebugCheck(isFinite(m_stretchMetric));
+ nvDebugCheck(isFinite(m_maxStretchMetric));
+ nvDebugCheck(isFinite(m_conformalMetric));
+ nvDebugCheck(isFinite(m_authalicMetric));
+}
+
+bool ParameterizationQuality::isValid() const
+{
+ return m_flippedTriangleCount == 0; // @@ Does not test for self-overlaps.
+}
+
+float ParameterizationQuality::rmsStretchMetric() const
+{
+ if (m_geometricArea == 0) return 0.0f;
+ float normFactor = sqrtf(m_parametricArea / m_geometricArea);
+ return sqrtf(m_stretchMetric / m_geometricArea) * normFactor;
+}
+
+float ParameterizationQuality::maxStretchMetric() const
+{
+ if (m_geometricArea == 0) return 0.0f;
+ float normFactor = sqrtf(m_parametricArea / m_geometricArea);
+ return m_maxStretchMetric * normFactor;
+}
+
+float ParameterizationQuality::rmsConformalMetric() const
+{
+ if (m_geometricArea == 0) return 0.0f;
+ return sqrtf(m_conformalMetric / m_geometricArea);
+}
+
+float ParameterizationQuality::maxAuthalicMetric() const
+{
+ if (m_geometricArea == 0) return 0.0f;
+ return sqrtf(m_authalicMetric / m_geometricArea);
+}
+
+void ParameterizationQuality::operator += (const ParameterizationQuality & pq)
+{
+ m_totalTriangleCount += pq.m_totalTriangleCount;
+ m_flippedTriangleCount += pq.m_flippedTriangleCount;
+ m_zeroAreaTriangleCount += pq.m_zeroAreaTriangleCount;
+
+ m_parametricArea += pq.m_parametricArea;
+ m_geometricArea += pq.m_geometricArea;
+
+ m_stretchMetric += pq.m_stretchMetric;
+ m_maxStretchMetric = max(m_maxStretchMetric, pq.m_maxStretchMetric);
+
+ m_conformalMetric += pq.m_conformalMetric;
+ m_authalicMetric += pq.m_authalicMetric;
+}
+
+
+void ParameterizationQuality::processTriangle(Vector3 q[3], Vector2 p[3])
+{
+ m_totalTriangleCount++;
+
+ // Evaluate texture stretch metric. See:
+ // - "Texture Mapping Progressive Meshes", Sander, Snyder, Gortler & Hoppe
+ // - "Mesh Parameterization: Theory and Practice", Siggraph'07 Course Notes, Hormann, Levy & Sheffer.
+
+ float t1 = p[0].x;
+ float s1 = p[0].y;
+ float t2 = p[1].x;
+ float s2 = p[1].y;
+ float t3 = p[2].x;
+ float s3 = p[2].y;
+
+ float geometricArea = length(cross(q[1] - q[0], q[2] - q[0])) / 2;
+ float parametricArea = ((s2 - s1)*(t3 - t1) - (s3 - s1)*(t2 - t1)) / 2;
+
+ if (isZero(parametricArea))
+ {
+ m_zeroAreaTriangleCount++;
+ return;
+ }
+
+ Vector3 Ss = (q[0] * (t2- t3) + q[1] * (t3 - t1) + q[2] * (t1 - t2)) / (2 * parametricArea);
+ Vector3 St = (q[0] * (s3- s2) + q[1] * (s1 - s3) + q[2] * (s2 - s1)) / (2 * parametricArea);
+
+ float a = dot(Ss, Ss); // E
+ float b = dot(Ss, St); // F
+ float c = dot(St, St); // G
+
+ // Compute eigen-values of the first fundamental form:
+ float sigma1 = sqrtf(0.5f * max(0.0f, a + c - sqrtf(square(a - c) + 4 * square(b)))); // gamma uppercase, min eigenvalue.
+ float sigma2 = sqrtf(0.5f * max(0.0f, a + c + sqrtf(square(a - c) + 4 * square(b)))); // gamma lowercase, max eigenvalue.
+ nvCheck(sigma2 >= sigma1);
+
+ // isometric: sigma1 = sigma2 = 1
+ // conformal: sigma1 / sigma2 = 1
+ // authalic: sigma1 * sigma2 = 1
+
+ float rmsStretch = sqrtf((a + c) * 0.5f);
+ float rmsStretch2 = sqrtf((square(sigma1) + square(sigma2)) * 0.5f);
+ nvDebugCheck(equal(rmsStretch, rmsStretch2, 0.01f));
+
+ if (parametricArea < 0.0f)
+ {
+ // Count flipped triangles.
+ m_flippedTriangleCount++;
+
+ parametricArea = fabsf(parametricArea);
+ }
+
+ m_stretchMetric += square(rmsStretch) * geometricArea;
+ m_maxStretchMetric = max(m_maxStretchMetric, sigma2);
+
+ if (!isZero(sigma1, 0.000001f)) {
+ // sigma1 is zero when geometricArea is zero.
+ m_conformalMetric += (sigma2 / sigma1) * geometricArea;
+ }
+ m_authalicMetric += (sigma1 * sigma2) * geometricArea;
+
+ // Accumulate total areas.
+ m_geometricArea += geometricArea;
+ m_parametricArea += parametricArea;
+
+
+ //triangleConformalEnergy(q, p);
+}
diff --git a/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.h b/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.h
new file mode 100644
index 0000000000..342e26b889
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.h
@@ -0,0 +1,56 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#pragma once
+#ifndef NV_MESH_PARAMETERIZATIONQUALITY_H
+#define NV_MESH_PARAMETERIZATIONQUALITY_H
+
+#include <nvmesh/nvmesh.h>
+
+namespace nv
+{
+ class Vector2;
+ class Vector3;
+
+ namespace HalfEdge { class Mesh; }
+
+ // Estimate quality of existing parameterization.
+ NVMESH_CLASS class ParameterizationQuality
+ {
+ public:
+ ParameterizationQuality();
+ ParameterizationQuality(const HalfEdge::Mesh * mesh);
+
+ bool isValid() const;
+
+ float rmsStretchMetric() const;
+ float maxStretchMetric() const;
+
+ float rmsConformalMetric() const;
+ float maxAuthalicMetric() const;
+
+ void operator += (const ParameterizationQuality & pq);
+
+ private:
+
+ void processTriangle(Vector3 p[3], Vector2 t[3]);
+
+ private:
+
+ uint m_totalTriangleCount;
+ uint m_flippedTriangleCount;
+ uint m_zeroAreaTriangleCount;
+
+ float m_parametricArea;
+ float m_geometricArea;
+
+ float m_stretchMetric;
+ float m_maxStretchMetric;
+
+ float m_conformalMetric;
+ float m_authalicMetric;
+
+ };
+
+} // nv namespace
+
+#endif // NV_MESH_PARAMETERIZATIONQUALITY_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.cpp b/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.cpp
new file mode 100644
index 0000000000..4b205de8bf
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.cpp
@@ -0,0 +1,53 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#include "nvmesh.h" // pch
+
+#include "SingleFaceMap.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Vertex.h"
+#include "nvmesh/halfedge/Face.h"
+
+#include "nvmath/Vector.inl"
+
+using namespace nv;
+
+
+
+void nv::computeSingleFaceMap(HalfEdge::Mesh * mesh)
+{
+ nvDebugCheck(mesh != NULL);
+ nvDebugCheck(mesh->faceCount() == 1);
+
+ HalfEdge::Face * face = mesh->faceAt(0);
+ nvCheck(face != NULL);
+
+ Vector3 p0 = face->edge->from()->pos;
+ Vector3 p1 = face->edge->to()->pos;
+
+ Vector3 X = normalizeSafe(p1 - p0, Vector3(0.0f), 0.0f);
+ Vector3 Z = face->normal();
+ Vector3 Y = normalizeSafe(cross(Z, X), Vector3(0.0f), 0.0f);
+
+ uint i = 0;
+ for (HalfEdge::Face::EdgeIterator it(face->edges()); !it.isDone(); it.advance(), i++)
+ {
+ HalfEdge::Vertex * vertex = it.vertex();
+ nvCheck(vertex != NULL);
+
+ if (i == 0)
+ {
+ vertex->tex = Vector2(0);
+ }
+ else
+ {
+ Vector3 pn = vertex->pos;
+
+ float xn = dot((pn - p0), X);
+ float yn = dot((pn - p0), Y);
+
+ vertex->tex = Vector2(xn, yn);
+ }
+ }
+}
+
diff --git a/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.h b/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.h
new file mode 100644
index 0000000000..b70719f5d8
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/SingleFaceMap.h
@@ -0,0 +1,18 @@
+// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>
+
+#pragma once
+#ifndef NV_MESH_SINGLEFACEMAP_H
+#define NV_MESH_SINGLEFACEMAP_H
+
+namespace nv
+{
+ namespace HalfEdge
+ {
+ class Mesh;
+ }
+
+ void computeSingleFaceMap(HalfEdge::Mesh * mesh);
+
+} // nv namespace
+
+#endif // NV_MESH_SINGLEFACEMAP_H
diff --git a/thirdparty/thekla_atlas/nvmesh/param/Util.cpp b/thirdparty/thekla_atlas/nvmesh/param/Util.cpp
new file mode 100644
index 0000000000..fe7b58edf8
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/Util.cpp
@@ -0,0 +1,326 @@
+// This code is in the public domain -- castano@gmail.com
+
+#include "nvmesh.h" // pch
+
+#include "Util.h"
+
+#include "nvmesh/halfedge/Mesh.h"
+#include "nvmesh/halfedge/Face.h"
+#include "nvmesh/halfedge/Vertex.h"
+
+#include "nvmath/Vector.inl"
+
+#include "nvcore/Array.inl"
+
+
+using namespace nv;
+
+// Determine if the given mesh is a quad mesh.
+bool nv::isQuadMesh(const HalfEdge::Mesh * mesh)
+{
+ nvDebugCheck(mesh != NULL);
+
+ const uint faceCount = mesh->faceCount();
+ for(uint i = 0; i < faceCount; i++) {
+ const HalfEdge::Face * face = mesh->faceAt(i);
+ if (face->edgeCount() != 4) {
+ return false;
+ }
+ }
+
+ return true;
+}
+
+bool nv::isTriangularMesh(const HalfEdge::Mesh * mesh)
+{
+ for (HalfEdge::Mesh::ConstFaceIterator it(mesh->faces()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Face * face = it.current();
+ if (face->edgeCount() != 3) return false;
+ }
+ return true;
+}
+
+
+uint nv::countMeshTriangles(const HalfEdge::Mesh * mesh)
+{
+ const uint faceCount = mesh->faceCount();
+
+ uint triangleCount = 0;
+
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = mesh->faceAt(f);
+
+ uint edgeCount = face->edgeCount();
+ nvDebugCheck(edgeCount > 2);
+
+ triangleCount += edgeCount - 2;
+ }
+
+ return triangleCount;
+}
+
+const HalfEdge::Vertex * nv::findBoundaryVertex(const HalfEdge::Mesh * mesh)
+{
+ const uint vertexCount = mesh->vertexCount();
+
+ for (uint v = 0; v < vertexCount; v++)
+ {
+ const HalfEdge::Vertex * vertex = mesh->vertexAt(v);
+ if (vertex->isBoundary()) return vertex;
+ }
+
+ return NULL;
+}
+
+
+HalfEdge::Mesh * nv::unifyVertices(const HalfEdge::Mesh * inputMesh)
+{
+ HalfEdge::Mesh * mesh = new HalfEdge::Mesh;
+
+ // Only add the first colocal.
+ const uint vertexCount = inputMesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++) {
+ const HalfEdge::Vertex * vertex = inputMesh->vertexAt(v);
+
+ if (vertex->isFirstColocal()) {
+ mesh->addVertex(vertex->pos);
+ }
+ }
+
+ nv::Array<uint> indexArray;
+
+ // Add new faces pointing to first colocals.
+ uint faceCount = inputMesh->faceCount();
+ for (uint f = 0; f < faceCount; f++) {
+ const HalfEdge::Face * face = inputMesh->faceAt(f);
+
+ indexArray.clear();
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
+ const HalfEdge::Edge * edge = it.current();
+ const HalfEdge::Vertex * vertex = edge->vertex->firstColocal();
+
+ indexArray.append(vertex->id);
+ }
+
+ mesh->addFace(indexArray);
+ }
+
+ mesh->linkBoundary();
+
+ return mesh;
+}
+
+#include "nvmath/Basis.h"
+
+static bool pointInTriangle(const Vector2 & p, const Vector2 & a, const Vector2 & b, const Vector2 & c)
+{
+ return triangleArea(a, b, p) >= 0.00001f &&
+ triangleArea(b, c, p) >= 0.00001f &&
+ triangleArea(c, a, p) >= 0.00001f;
+}
+
+
+// This is doing a simple ear-clipping algorithm that skips invalid triangles. Ideally, we should
+// also sort the ears by angle, start with the ones that have the smallest angle and proceed in order.
+HalfEdge::Mesh * nv::triangulate(const HalfEdge::Mesh * inputMesh)
+{
+ HalfEdge::Mesh * mesh = new HalfEdge::Mesh;
+
+ // Add all vertices.
+ const uint vertexCount = inputMesh->vertexCount();
+ for (uint v = 0; v < vertexCount; v++) {
+ const HalfEdge::Vertex * vertex = inputMesh->vertexAt(v);
+ mesh->addVertex(vertex->pos);
+ }
+
+ Array<int> polygonVertices;
+ Array<float> polygonAngles;
+ Array<Vector2> polygonPoints;
+
+ const uint faceCount = inputMesh->faceCount();
+ for (uint f = 0; f < faceCount; f++)
+ {
+ const HalfEdge::Face * face = inputMesh->faceAt(f);
+ nvDebugCheck(face != NULL);
+
+ const uint edgeCount = face->edgeCount();
+ nvDebugCheck(edgeCount >= 3);
+
+ polygonVertices.clear();
+ polygonVertices.reserve(edgeCount);
+
+ if (edgeCount == 3) {
+ // Simple case for triangles.
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+ const HalfEdge::Vertex * vertex = edge->vertex;
+ polygonVertices.append(vertex->id);
+ }
+
+ int v0 = polygonVertices[0];
+ int v1 = polygonVertices[1];
+ int v2 = polygonVertices[2];
+
+ mesh->addFace(v0, v1, v2);
+ }
+ else {
+ // Build 2D polygon projecting vertices onto normal plane.
+ // Faces are not necesarily planar, this is for example the case, when the face comes from filling a hole. In such cases
+ // it's much better to use the best fit plane.
+ const Vector3 fn = face->normal();
+
+ Basis basis;
+ basis.buildFrameForDirection(fn);
+
+ polygonPoints.clear();
+ polygonPoints.reserve(edgeCount);
+ polygonAngles.clear();
+ polygonAngles.reserve(edgeCount);
+
+ for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
+ {
+ const HalfEdge::Edge * edge = it.current();
+ const HalfEdge::Vertex * vertex = edge->vertex;
+ polygonVertices.append(vertex->id);
+
+ Vector2 p;
+ p.x = dot(basis.tangent, vertex->pos);
+ p.y = dot(basis.bitangent, vertex->pos);
+
+ polygonPoints.append(p);
+ }
+ polygonAngles.resize(edgeCount);
+
+ while (polygonVertices.size() > 2) {
+ uint size = polygonVertices.size();
+
+ // Update polygon angles. @@ Update only those that have changed.
+ float minAngle = 2 * PI;
+ uint bestEar = 0; // Use first one if none of them is valid.
+ bool bestIsValid = false;
+ for (uint i = 0; i < size; i++) {
+ uint i0 = i;
+ uint i1 = (i+1) % size; // Use Sean's polygon interation trick.
+ uint i2 = (i+2) % size;
+
+ Vector2 p0 = polygonPoints[i0];
+ Vector2 p1 = polygonPoints[i1];
+ Vector2 p2 = polygonPoints[i2];
+
+ float d = clamp(dot(p0-p1, p2-p1) / (length(p0-p1) * length(p2-p1)), -1.0f, 1.0f);
+ float angle = acosf(d);
+
+ float area = triangleArea(p0, p1, p2);
+ if (area < 0.0f) angle = 2.0f * PI - angle;
+
+ polygonAngles[i1] = angle;
+
+ if (angle < minAngle || !bestIsValid) {
+
+ // Make sure this is a valid ear, if not, skip this point.
+ bool valid = true;
+ for (uint j = 0; j < size; j++) {
+ if (j == i0 || j == i1 || j == i2) continue;
+ Vector2 p = polygonPoints[j];
+
+ if (pointInTriangle(p, p0, p1, p2)) {
+ valid = false;
+ break;
+ }
+ }
+
+ if (valid || !bestIsValid) {
+ minAngle = angle;
+ bestEar = i1;
+ bestIsValid = valid;
+ }
+ }
+ }
+
+ nvDebugCheck(minAngle <= 2 * PI);
+
+ // Clip best ear:
+
+ uint i0 = (bestEar+size-1) % size;
+ uint i1 = (bestEar+0) % size;
+ uint i2 = (bestEar+1) % size;
+
+ int v0 = polygonVertices[i0];
+ int v1 = polygonVertices[i1];
+ int v2 = polygonVertices[i2];
+
+ mesh->addFace(v0, v1, v2);
+
+ polygonVertices.removeAt(i1);
+ polygonPoints.removeAt(i1);
+ polygonAngles.removeAt(i1);
+ }
+ }
+
+#if 0
+
+ uint i = 0;
+ while (polygonVertices.size() > 2 && i < polygonVertices.size()) {
+ uint size = polygonVertices.size();
+ uint i0 = (i+0) % size;
+ uint i1 = (i+1) % size;
+ uint i2 = (i+2) % size;
+
+ const HalfEdge::Vertex * v0 = polygonVertices[i0];
+ const HalfEdge::Vertex * v1 = polygonVertices[i1];
+ const HalfEdge::Vertex * v2 = polygonVertices[i2];
+
+ const Vector3 p0 = v0->pos;
+ const Vector3 p1 = v1->pos;
+ const Vector3 p2 = v2->pos;
+
+ const Vector3 e0 = p2 - p1;
+ const Vector3 e1 = p0 - p1;
+
+ // If this ear forms a valid triangle, setup relations, remove v1 and repeat.
+ Vector3 n = cross(e0, e1);
+ float len = dot(fn, n); // = sin(angle)
+
+ float angle = asin(len);
+
+
+ if (len > 0.0f) {
+ mesh->addFace(v0->id(), v1->id(), v2->id());
+ polygonVertices.removeAt(i1);
+ polygonAngles.removeAt(i1);
+ if (i2 > i1) i2--;
+ // @@ Update angles at i0 and i2
+ }
+ else {
+ i++;
+ }
+ }
+
+ // @@ Create a few degenerate triangles to avoid introducing holes.
+ i = 0;
+ const uint size = polygonVertices.size();
+ while (i < size - 2) {
+ uint i0 = (i+0) % size;
+ uint i1 = (i+1) % size;
+ uint i2 = (i+2) % size;
+
+ const HalfEdge::Vertex * v0 = polygonVertices[i0];
+ const HalfEdge::Vertex * v1 = polygonVertices[i1];
+ const HalfEdge::Vertex * v2 = polygonVertices[i2];
+
+ mesh->addFace(v0->id(), v1->id(), v2->id());
+ i++;
+ }
+#endif
+ }
+
+ mesh->linkBoundary();
+
+ return mesh;
+}
+
+
diff --git a/thirdparty/thekla_atlas/nvmesh/param/Util.h b/thirdparty/thekla_atlas/nvmesh/param/Util.h
new file mode 100644
index 0000000000..774563ac0b
--- /dev/null
+++ b/thirdparty/thekla_atlas/nvmesh/param/Util.h
@@ -0,0 +1,18 @@
+// This code is in the public domain -- castano@gmail.com
+
+#include "nvmesh/nvmesh.h"
+
+namespace nv {
+
+ namespace HalfEdge { class Mesh; class Vertex; }
+
+ bool isQuadMesh(const HalfEdge::Mesh * mesh);
+ bool isTriangularMesh(const HalfEdge::Mesh * mesh);
+
+ uint countMeshTriangles(const HalfEdge::Mesh * mesh);
+ const HalfEdge::Vertex * findBoundaryVertex(const HalfEdge::Mesh * mesh);
+
+ HalfEdge::Mesh * unifyVertices(const HalfEdge::Mesh * inputMesh);
+ HalfEdge::Mesh * triangulate(const HalfEdge::Mesh * inputMesh);
+
+} // nv namespace