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-rw-r--r--thirdparty/README.md11
-rw-r--r--thirdparty/meshoptimizer/indexcodec.cpp2
-rw-r--r--thirdparty/meshoptimizer/meshoptimizer.h20
-rw-r--r--thirdparty/meshoptimizer/simplifier.cpp38
-rw-r--r--thirdparty/misc/patches/polypartition-godot-types.patch819
-rw-r--r--thirdparty/misc/polypartition.cpp1849
-rw-r--r--thirdparty/misc/polypartition.h378
-rw-r--r--thirdparty/misc/triangulator.cpp1550
-rw-r--r--thirdparty/misc/triangulator.h306
9 files changed, 3090 insertions, 1883 deletions
diff --git a/thirdparty/README.md b/thirdparty/README.md
index 5d03458b69..3803e87fea 100644
--- a/thirdparty/README.md
+++ b/thirdparty/README.md
@@ -344,7 +344,7 @@ File extracted from upstream release tarball:
## meshoptimizer
- Upstream: https://github.com/zeux/meshoptimizer
-- Version: git (e4e43fe36e7a8705e602e7ca2f9fb795ded1d0b9, 2020)
+- Version: git (e3f53f66e7a35b9b8764bee478589d79e34fa698, 2021)
- License: MIT
Files extracted from upstream repository:
@@ -424,6 +424,11 @@ Collection of single-file libraries used in Godot components.
* Upstream: http://www.pcg-random.org
* Version: minimal C implementation, http://www.pcg-random.org/download.html
* License: Apache 2.0
+- `polypartition.{cpp,h}`
+ * Upstream: https://github.com/ivanfratric/polypartition (`src/polypartition.{cpp,h}`)
+ * Version: git (7bdffb428b2b19ad1c43aa44c714dcc104177e84, 2021)
+ * Modifications: Change from STL to Godot types (see provided patch).
+ * License: MIT
- `r128.h`
* Upstream: https://github.com/fahickman/r128
* Version: 1.4.4 (cf2e88fc3e7d7dfe99189686f914874cd0bda15e, 2020)
@@ -441,10 +446,6 @@ Collection of single-file libraries used in Godot components.
* Upstream: https://github.com/nothings/stb
* Version: 1.20 (314d0a6f9af5af27e585336eecea333e95c5a2d8, 2020)
* License: Public Domain or Unlicense or MIT
-- `triangulator.{cpp,h}`
- * Upstream: https://github.com/ivanfratric/polypartition (`src/polypartition.cpp`)
- * Version: TBD, class was renamed
- * License: MIT
- `yuv2rgb.h`
* Upstream: http://wss.co.uk/pinknoise/yuv2rgb/ (to check)
* Version: ?
diff --git a/thirdparty/meshoptimizer/indexcodec.cpp b/thirdparty/meshoptimizer/indexcodec.cpp
index 5c35eb43ae..e4495b8586 100644
--- a/thirdparty/meshoptimizer/indexcodec.cpp
+++ b/thirdparty/meshoptimizer/indexcodec.cpp
@@ -108,7 +108,7 @@ static unsigned int decodeVByte(const unsigned char*& data)
for (int i = 0; i < 4; ++i)
{
unsigned char group = *data++;
- result |= (group & 127) << shift;
+ result |= unsigned(group & 127) << shift;
shift += 7;
if (group < 128)
diff --git a/thirdparty/meshoptimizer/meshoptimizer.h b/thirdparty/meshoptimizer/meshoptimizer.h
index 4071f0a371..1714000384 100644
--- a/thirdparty/meshoptimizer/meshoptimizer.h
+++ b/thirdparty/meshoptimizer/meshoptimizer.h
@@ -262,7 +262,7 @@ MESHOPTIMIZER_EXPERIMENTAL void meshopt_decodeFilterExp(void* buffer, size_t ver
* The resulting index buffer references vertices from the original vertex buffer.
* If the original vertex data isn't required, creating a compact vertex buffer using meshopt_optimizeVertexFetch is recommended.
*
- * destination must contain enough space for the *source* index buffer (since optimization is iterative, this means index_count elements - *not* target_index_count!)
+ * destination must contain enough space for the target index buffer, worst case is index_count elements (*not* target_index_count)!
* vertex_positions should have float3 position in the first 12 bytes of each vertex - similar to glVertexPointer
* target_error represents the error relative to mesh extents that can be tolerated, e.g. 0.01 = 1% deformation
* result_error can be NULL; when it's not NULL, it will contain the resulting (relative) error after simplification
@@ -272,15 +272,17 @@ MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplify(unsigned int* destination, co
/**
* Experimental: Mesh simplifier (sloppy)
* Reduces the number of triangles in the mesh, sacrificing mesh apperance for simplification performance
- * The algorithm doesn't preserve mesh topology but is always able to reach target triangle count.
+ * The algorithm doesn't preserve mesh topology but can stop short of the target goal based on target error.
* Returns the number of indices after simplification, with destination containing new index data
* The resulting index buffer references vertices from the original vertex buffer.
* If the original vertex data isn't required, creating a compact vertex buffer using meshopt_optimizeVertexFetch is recommended.
*
- * destination must contain enough space for the target index buffer
+ * destination must contain enough space for the target index buffer, worst case is index_count elements (*not* target_index_count)!
* vertex_positions should have float3 position in the first 12 bytes of each vertex - similar to glVertexPointer
+ * target_error represents the error relative to mesh extents that can be tolerated, e.g. 0.01 = 1% deformation
+ * result_error can be NULL; when it's not NULL, it will contain the resulting (relative) error after simplification
*/
-MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count);
+MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error);
/**
* Experimental: Point cloud simplifier
@@ -289,7 +291,7 @@ MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifySloppy(unsigned int* destinati
* The resulting index buffer references vertices from the original vertex buffer.
* If the original vertex data isn't required, creating a compact vertex buffer using meshopt_optimizeVertexFetch is recommended.
*
- * destination must contain enough space for the target index buffer
+ * destination must contain enough space for the target index buffer (target_vertex_count elements)
* vertex_positions should have float3 position in the first 12 bytes of each vertex - similar to glVertexPointer
*/
MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifyPoints(unsigned int* destination, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_vertex_count);
@@ -533,7 +535,7 @@ inline int meshopt_decodeIndexSequence(T* destination, size_t index_count, const
template <typename T>
inline size_t meshopt_simplify(T* destination, const T* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error = 0);
template <typename T>
-inline size_t meshopt_simplifySloppy(T* destination, const T* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count);
+inline size_t meshopt_simplifySloppy(T* destination, const T* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error = 0);
template <typename T>
inline size_t meshopt_stripify(T* destination, const T* indices, size_t index_count, size_t vertex_count, T restart_index);
template <typename T>
@@ -855,12 +857,12 @@ inline size_t meshopt_simplify(T* destination, const T* indices, size_t index_co
}
template <typename T>
-inline size_t meshopt_simplifySloppy(T* destination, const T* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count)
+inline size_t meshopt_simplifySloppy(T* destination, const T* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error)
{
meshopt_IndexAdapter<T> in(0, indices, index_count);
- meshopt_IndexAdapter<T> out(destination, 0, target_index_count);
+ meshopt_IndexAdapter<T> out(destination, 0, index_count);
- return meshopt_simplifySloppy(out.data, in.data, index_count, vertex_positions, vertex_count, vertex_positions_stride, target_index_count);
+ return meshopt_simplifySloppy(out.data, in.data, index_count, vertex_positions, vertex_count, vertex_positions_stride, target_index_count, target_error, result_error);
}
template <typename T>
diff --git a/thirdparty/meshoptimizer/simplifier.cpp b/thirdparty/meshoptimizer/simplifier.cpp
index 5205b01172..942db14461 100644
--- a/thirdparty/meshoptimizer/simplifier.cpp
+++ b/thirdparty/meshoptimizer/simplifier.cpp
@@ -1400,7 +1400,7 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
return result_count;
}
-size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count)
+size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* out_result_error)
{
using namespace meshopt;
@@ -1412,9 +1412,6 @@ size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* ind
// we expect to get ~2 triangles/vertex in the output
size_t target_cell_count = target_index_count / 6;
- if (target_cell_count == 0)
- return 0;
-
meshopt_Allocator allocator;
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
@@ -1431,18 +1428,25 @@ size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* ind
const int kInterpolationPasses = 5;
// invariant: # of triangles in min_grid <= target_count
- int min_grid = 0;
+ int min_grid = int(1.f / (target_error < 1e-3f ? 1e-3f : target_error));
int max_grid = 1025;
size_t min_triangles = 0;
size_t max_triangles = index_count / 3;
+ // when we're error-limited, we compute the triangle count for the min. size; this accelerates convergence and provides the correct answer when we can't use a larger grid
+ if (min_grid > 1)
+ {
+ computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid);
+ min_triangles = countTriangles(vertex_ids, indices, index_count);
+ }
+
// instead of starting in the middle, let's guess as to what the answer might be! triangle count usually grows as a square of grid size...
int next_grid_size = int(sqrtf(float(target_cell_count)) + 0.5f);
for (int pass = 0; pass < 10 + kInterpolationPasses; ++pass)
{
- assert(min_triangles < target_index_count / 3);
- assert(max_grid - min_grid > 1);
+ if (min_triangles >= target_index_count / 3 || max_grid - min_grid <= 1)
+ break;
// we clamp the prediction of the grid size to make sure that the search converges
int grid_size = next_grid_size;
@@ -1471,16 +1475,18 @@ size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* ind
max_triangles = triangles;
}
- if (triangles == target_index_count / 3 || max_grid - min_grid <= 1)
- break;
-
// we start by using interpolation search - it usually converges faster
// however, interpolation search has a worst case of O(N) so we switch to binary search after a few iterations which converges in O(logN)
next_grid_size = (pass < kInterpolationPasses) ? int(tip + 0.5f) : (min_grid + max_grid) / 2;
}
if (min_triangles == 0)
+ {
+ if (out_result_error)
+ *out_result_error = 1.f;
+
return 0;
+ }
// build vertex->cell association by mapping all vertices with the same quantized position to the same cell
size_t table_size = hashBuckets2(vertex_count);
@@ -1503,18 +1509,26 @@ size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* ind
fillCellRemap(cell_remap, cell_errors, cell_count, vertex_cells, cell_quadrics, vertex_positions, vertex_count);
+ // compute error
+ float result_error = 0.f;
+
+ for (size_t i = 0; i < cell_count; ++i)
+ result_error = result_error < cell_errors[i] ? cell_errors[i] : result_error;
+
// collapse triangles!
// note that we need to filter out triangles that we've already output because we very frequently generate redundant triangles between cells :(
size_t tritable_size = hashBuckets2(min_triangles);
unsigned int* tritable = allocator.allocate<unsigned int>(tritable_size);
size_t write = filterTriangles(destination, tritable, tritable_size, indices, index_count, vertex_cells, cell_remap);
- assert(write <= target_index_count);
#if TRACE
- printf("result: %d cells, %d triangles (%d unfiltered)\n", int(cell_count), int(write / 3), int(min_triangles));
+ printf("result: %d cells, %d triangles (%d unfiltered), error %e\n", int(cell_count), int(write / 3), int(min_triangles), sqrtf(result_error));
#endif
+ if (out_result_error)
+ *out_result_error = sqrtf(result_error);
+
return write;
}
diff --git a/thirdparty/misc/patches/polypartition-godot-types.patch b/thirdparty/misc/patches/polypartition-godot-types.patch
new file mode 100644
index 0000000000..59fdb2707c
--- /dev/null
+++ b/thirdparty/misc/patches/polypartition-godot-types.patch
@@ -0,0 +1,819 @@
+diff --git a/thirdparty/misc/polypartition.cpp b/thirdparty/misc/polypartition.cpp
+index 3a8a6efa8319..4f1b6dcb21d8 100644
+--- a/thirdparty/misc/polypartition.cpp
++++ b/thirdparty/misc/polypartition.cpp
+@@ -23,10 +23,7 @@
+
+ #include "polypartition.h"
+
+-#include <math.h>
+-#include <string.h>
+ #include <algorithm>
+-#include <vector>
+
+ TPPLPoly::TPPLPoly() {
+ hole = false;
+@@ -186,7 +183,7 @@ int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TP
+ // Removes holes from inpolys by merging them with non-holes.
+ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ TPPLPolyList polys;
+- TPPLPolyList::iterator holeiter, polyiter, iter, iter2;
++ TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2;
+ long i, i2, holepointindex, polypointindex;
+ TPPLPoint holepoint, polypoint, bestpolypoint;
+ TPPLPoint linep1, linep2;
+@@ -198,15 +195,15 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+
+ // Check for the trivial case of no holes.
+ hasholes = false;
+- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) {
+- if (iter->IsHole()) {
++ for (iter = inpolys->front(); iter; iter = iter->next()) {
++ if (iter->get().IsHole()) {
+ hasholes = true;
+ break;
+ }
+ }
+ if (!hasholes) {
+- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) {
+- outpolys->push_back(*iter);
++ for (iter = inpolys->front(); iter; iter = iter->next()) {
++ outpolys->push_back(iter->get());
+ }
+ return 1;
+ }
+@@ -216,8 +213,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ while (1) {
+ // Find the hole point with the largest x.
+ hasholes = false;
+- for (iter = polys.begin(); iter != polys.end(); iter++) {
+- if (!iter->IsHole()) {
++ for (iter = polys.front(); iter; iter = iter->next()) {
++ if (!iter->get().IsHole()) {
+ continue;
+ }
+
+@@ -227,8 +224,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ holepointindex = 0;
+ }
+
+- for (i = 0; i < iter->GetNumPoints(); i++) {
+- if (iter->GetPoint(i).x > holeiter->GetPoint(holepointindex).x) {
++ for (i = 0; i < iter->get().GetNumPoints(); i++) {
++ if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
+ holeiter = iter;
+ holepointindex = i;
+ }
+@@ -237,24 +234,24 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ if (!hasholes) {
+ break;
+ }
+- holepoint = holeiter->GetPoint(holepointindex);
++ holepoint = holeiter->get().GetPoint(holepointindex);
+
+ pointfound = false;
+- for (iter = polys.begin(); iter != polys.end(); iter++) {
+- if (iter->IsHole()) {
++ for (iter = polys.front(); iter; iter = iter->next()) {
++ if (iter->get().IsHole()) {
+ continue;
+ }
+- for (i = 0; i < iter->GetNumPoints(); i++) {
+- if (iter->GetPoint(i).x <= holepoint.x) {
++ for (i = 0; i < iter->get().GetNumPoints(); i++) {
++ if (iter->get().GetPoint(i).x <= holepoint.x) {
+ continue;
+ }
+- if (!InCone(iter->GetPoint((i + iter->GetNumPoints() - 1) % (iter->GetNumPoints())),
+- iter->GetPoint(i),
+- iter->GetPoint((i + 1) % (iter->GetNumPoints())),
++ if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())),
++ iter->get().GetPoint(i),
++ iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())),
+ holepoint)) {
+ continue;
+ }
+- polypoint = iter->GetPoint(i);
++ polypoint = iter->get().GetPoint(i);
+ if (pointfound) {
+ v1 = Normalize(polypoint - holepoint);
+ v2 = Normalize(bestpolypoint - holepoint);
+@@ -263,13 +260,13 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ }
+ }
+ pointvisible = true;
+- for (iter2 = polys.begin(); iter2 != polys.end(); iter2++) {
+- if (iter2->IsHole()) {
++ for (iter2 = polys.front(); iter2; iter2->next()) {
++ if (iter2->get().IsHole()) {
+ continue;
+ }
+- for (i2 = 0; i2 < iter2->GetNumPoints(); i2++) {
+- linep1 = iter2->GetPoint(i2);
+- linep2 = iter2->GetPoint((i2 + 1) % (iter2->GetNumPoints()));
++ for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) {
++ linep1 = iter2->get().GetPoint(i2);
++ linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints()));
+ if (Intersects(holepoint, polypoint, linep1, linep2)) {
+ pointvisible = false;
+ break;
+@@ -292,18 +289,18 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ return 0;
+ }
+
+- newpoly.Init(holeiter->GetNumPoints() + polyiter->GetNumPoints() + 2);
++ newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
+ i2 = 0;
+ for (i = 0; i <= polypointindex; i++) {
+- newpoly[i2] = polyiter->GetPoint(i);
++ newpoly[i2] = polyiter->get().GetPoint(i);
+ i2++;
+ }
+- for (i = 0; i <= holeiter->GetNumPoints(); i++) {
+- newpoly[i2] = holeiter->GetPoint((i + holepointindex) % holeiter->GetNumPoints());
++ for (i = 0; i <= holeiter->get().GetNumPoints(); i++) {
++ newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints());
+ i2++;
+ }
+- for (i = polypointindex; i < polyiter->GetNumPoints(); i++) {
+- newpoly[i2] = polyiter->GetPoint(i);
++ for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) {
++ newpoly[i2] = polyiter->get().GetPoint(i);
+ i2++;
+ }
+
+@@ -312,8 +309,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ polys.push_back(newpoly);
+ }
+
+- for (iter = polys.begin(); iter != polys.end(); iter++) {
+- outpolys->push_back(*iter);
++ for (iter = polys.front(); iter; iter = iter->next()) {
++ outpolys->push_back(iter->get());
+ }
+
+ return 1;
+@@ -524,13 +521,13 @@ int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) {
+
+ int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
+ TPPLPolyList outpolys;
+- TPPLPolyList::iterator iter;
++ TPPLPolyList::Element *iter;
+
+ if (!RemoveHoles(inpolys, &outpolys)) {
+ return 0;
+ }
+- for (iter = outpolys.begin(); iter != outpolys.end(); iter++) {
+- if (!Triangulate_EC(&(*iter), triangles)) {
++ for (iter = outpolys.front(); iter; iter = iter->next()) {
++ if (!Triangulate_EC(&(iter->get()), triangles)) {
+ return 0;
+ }
+ }
+@@ -543,7 +540,7 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
+ }
+
+ TPPLPolyList triangles;
+- TPPLPolyList::iterator iter1, iter2;
++ TPPLPolyList::Element *iter1, *iter2;
+ TPPLPoly *poly1 = NULL, *poly2 = NULL;
+ TPPLPoly newpoly;
+ TPPLPoint d1, d2, p1, p2, p3;
+@@ -578,19 +575,19 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
+ return 0;
+ }
+
+- for (iter1 = triangles.begin(); iter1 != triangles.end(); iter1++) {
+- poly1 = &(*iter1);
++ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
++ poly1 = &(iter1->get());
+ for (i11 = 0; i11 < poly1->GetNumPoints(); i11++) {
+ d1 = poly1->GetPoint(i11);
+ i12 = (i11 + 1) % (poly1->GetNumPoints());
+ d2 = poly1->GetPoint(i12);
+
+ isdiagonal = false;
+- for (iter2 = iter1; iter2 != triangles.end(); iter2++) {
++ for (iter2 = iter1; iter2; iter2 = iter2->next()) {
+ if (iter1 == iter2) {
+ continue;
+ }
+- poly2 = &(*iter2);
++ poly2 = &(iter2->get());
+
+ for (i21 = 0; i21 < poly2->GetNumPoints(); i21++) {
+ if ((d2.x != poly2->GetPoint(i21).x) || (d2.y != poly2->GetPoint(i21).y)) {
+@@ -660,16 +657,16 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
+ }
+
+ triangles.erase(iter2);
+- *iter1 = newpoly;
+- poly1 = &(*iter1);
++ iter1->get() = newpoly;
++ poly1 = &(iter1->get());
+ i11 = -1;
+
+ continue;
+ }
+ }
+
+- for (iter1 = triangles.begin(); iter1 != triangles.end(); iter1++) {
+- parts->push_back(*iter1);
++ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
++ parts->push_back(iter1->get());
+ }
+
+ return 1;
+@@ -677,13 +674,13 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
+
+ int TPPLPartition::ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts) {
+ TPPLPolyList outpolys;
+- TPPLPolyList::iterator iter;
++ TPPLPolyList::Element *iter;
+
+ if (!RemoveHoles(inpolys, &outpolys)) {
+ return 0;
+ }
+- for (iter = outpolys.begin(); iter != outpolys.end(); iter++) {
+- if (!ConvexPartition_HM(&(*iter), parts)) {
++ for (iter = outpolys.front(); iter; iter = iter->next()) {
++ if (!ConvexPartition_HM(&(iter->get()), parts)) {
+ return 0;
+ }
+ }
+@@ -824,8 +821,8 @@ int TPPLPartition::Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles) {
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_back(newdiagonal);
+- while (!diagonals.empty()) {
+- diagonal = *(diagonals.begin());
++ while (!diagonals.is_empty()) {
++ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex;
+ if (bestvertex == -1) {
+@@ -873,10 +870,10 @@ void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2
+ pairs->push_front(newdiagonal);
+ dpstates[a][b].weight = w;
+ } else {
+- if ((!pairs->empty()) && (i <= pairs->begin()->index1)) {
++ if ((!pairs->is_empty()) && (i <= pairs->front()->get().index1)) {
+ return;
+ }
+- while ((!pairs->empty()) && (pairs->begin()->index2 >= j)) {
++ while ((!pairs->is_empty()) && (pairs->front()->get().index2 >= j)) {
+ pairs->pop_front();
+ }
+ pairs->push_front(newdiagonal);
+@@ -885,7 +882,7 @@ void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2
+
+ void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
+ DiagonalList *pairs = NULL;
+- DiagonalList::iterator iter, lastiter;
++ DiagonalList::Element *iter, *lastiter;
+ long top;
+ long w;
+
+@@ -902,23 +899,23 @@ void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPS
+ }
+ if (j - i > 1) {
+ pairs = &(dpstates[i][j].pairs);
+- iter = pairs->end();
+- lastiter = pairs->end();
+- while (iter != pairs->begin()) {
++ iter = pairs->back();
++ lastiter = pairs->back();
++ while (iter != pairs->front()) {
+ iter--;
+- if (!IsReflex(vertices[iter->index2].p, vertices[j].p, vertices[k].p)) {
++ if (!IsReflex(vertices[iter->get().index2].p, vertices[j].p, vertices[k].p)) {
+ lastiter = iter;
+ } else {
+ break;
+ }
+ }
+- if (lastiter == pairs->end()) {
++ if (lastiter == pairs->back()) {
+ w++;
+ } else {
+- if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->index1].p)) {
++ if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->get().index1].p)) {
+ w++;
+ } else {
+- top = lastiter->index1;
++ top = lastiter->get().index1;
+ }
+ }
+ }
+@@ -927,7 +924,7 @@ void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPS
+
+ void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
+ DiagonalList *pairs = NULL;
+- DiagonalList::iterator iter, lastiter;
++ DiagonalList::Element *iter, *lastiter;
+ long top;
+ long w;
+
+@@ -946,21 +943,21 @@ void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPS
+ if (k - j > 1) {
+ pairs = &(dpstates[j][k].pairs);
+
+- iter = pairs->begin();
+- if ((!pairs->empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->index1].p))) {
++ iter = pairs->front();
++ if ((!pairs->is_empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p))) {
+ lastiter = iter;
+- while (iter != pairs->end()) {
+- if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->index1].p)) {
++ while (iter) {
++ if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p)) {
+ lastiter = iter;
+- iter++;
++ iter = iter->next();
+ } else {
+ break;
+ }
+ }
+- if (IsReflex(vertices[lastiter->index2].p, vertices[k].p, vertices[i].p)) {
++ if (IsReflex(vertices[lastiter->get().index2].p, vertices[k].p, vertices[i].p)) {
+ w++;
+ } else {
+- top = lastiter->index2;
++ top = lastiter->get().index2;
+ }
+ } else {
+ w++;
+@@ -981,11 +978,11 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ DiagonalList diagonals, diagonals2;
+ Diagonal diagonal, newdiagonal;
+ DiagonalList *pairs = NULL, *pairs2 = NULL;
+- DiagonalList::iterator iter, iter2;
++ DiagonalList::Element *iter, *iter2;
+ int ret;
+ TPPLPoly newpoly;
+- std::vector<long> indices;
+- std::vector<long>::iterator iiter;
++ List<long> indices;
++ List<long>::Element *iiter;
+ bool ijreal, jkreal;
+
+ n = poly->GetNumPoints();
+@@ -1110,35 +1107,35 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_front(newdiagonal);
+- while (!diagonals.empty()) {
+- diagonal = *(diagonals.begin());
++ while (!diagonals.is_empty()) {
++ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+ }
+ pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
+- if (pairs->empty()) {
++ if (pairs->is_empty()) {
+ ret = 0;
+ break;
+ }
+ if (!vertices[diagonal.index1].isConvex) {
+- iter = pairs->end();
++ iter = pairs->back();
+ iter--;
+- j = iter->index2;
++ j = iter->get().index2;
+ newdiagonal.index1 = j;
+ newdiagonal.index2 = diagonal.index2;
+ diagonals.push_front(newdiagonal);
+ if ((j - diagonal.index1) > 1) {
+- if (iter->index1 != iter->index2) {
++ if (iter->get().index1 != iter->get().index2) {
+ pairs2 = &(dpstates[diagonal.index1][j].pairs);
+ while (1) {
+- if (pairs2->empty()) {
++ if (pairs2->is_empty()) {
+ ret = 0;
+ break;
+ }
+- iter2 = pairs2->end();
++ iter2 = pairs2->back();
+ iter2--;
+- if (iter->index1 != iter2->index1) {
++ if (iter->get().index1 != iter2->get().index1) {
+ pairs2->pop_back();
+ } else {
+ break;
+@@ -1153,21 +1150,21 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ diagonals.push_front(newdiagonal);
+ }
+ } else {
+- iter = pairs->begin();
+- j = iter->index1;
++ iter = pairs->front();
++ j = iter->get().index1;
+ newdiagonal.index1 = diagonal.index1;
+ newdiagonal.index2 = j;
+ diagonals.push_front(newdiagonal);
+ if ((diagonal.index2 - j) > 1) {
+- if (iter->index1 != iter->index2) {
++ if (iter->get().index1 != iter->get().index2) {
+ pairs2 = &(dpstates[j][diagonal.index2].pairs);
+ while (1) {
+- if (pairs2->empty()) {
++ if (pairs2->is_empty()) {
+ ret = 0;
+ break;
+ }
+- iter2 = pairs2->begin();
+- if (iter->index2 != iter2->index2) {
++ iter2 = pairs2->front();
++ if (iter->get().index2 != iter2->get().index2) {
+ pairs2->pop_front();
+ } else {
+ break;
+@@ -1197,8 +1194,8 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_front(newdiagonal);
+- while (!diagonals.empty()) {
+- diagonal = *(diagonals.begin());
++ while (!diagonals.is_empty()) {
++ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+@@ -1210,8 +1207,8 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ indices.push_back(diagonal.index2);
+ diagonals2.push_front(diagonal);
+
+- while (!diagonals2.empty()) {
+- diagonal = *(diagonals2.begin());
++ while (!diagonals2.is_empty()) {
++ diagonal = diagonals2.front()->get();
+ diagonals2.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+@@ -1220,16 +1217,16 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ jkreal = true;
+ pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
+ if (!vertices[diagonal.index1].isConvex) {
+- iter = pairs->end();
++ iter = pairs->back();
+ iter--;
+- j = iter->index2;
+- if (iter->index1 != iter->index2) {
++ j = iter->get().index2;
++ if (iter->get().index1 != iter->get().index2) {
+ ijreal = false;
+ }
+ } else {
+- iter = pairs->begin();
+- j = iter->index1;
+- if (iter->index1 != iter->index2) {
++ iter = pairs->front();
++ j = iter->get().index1;
++ if (iter->get().index1 != iter->get().index2) {
+ jkreal = false;
+ }
+ }
+@@ -1253,11 +1250,12 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ indices.push_back(j);
+ }
+
+- std::sort(indices.begin(), indices.end());
++ //std::sort(indices.begin(), indices.end());
++ indices.sort();
+ newpoly.Init((long)indices.size());
+ k = 0;
+- for (iiter = indices.begin(); iiter != indices.end(); iiter++) {
+- newpoly[k] = vertices[*iiter].p;
++ for (iiter = indices.front(); iiter != indices.back(); iiter = iiter->next()) {
++ newpoly[k] = vertices[iiter->get()].p;
+ k++;
+ }
+ parts->push_back(newpoly);
+@@ -1281,7 +1279,7 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ // "Computational Geometry: Algorithms and Applications"
+ // by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.
+ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys) {
+- TPPLPolyList::iterator iter;
++ TPPLPolyList::Element *iter;
+ MonotoneVertex *vertices = NULL;
+ long i, numvertices, vindex, vindex2, newnumvertices, maxnumvertices;
+ long polystartindex, polyendindex;
+@@ -1291,11 +1289,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ bool error = false;
+
+ numvertices = 0;
+- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) {
+- if (!iter->Valid()) {
+- return 0;
+- }
+- numvertices += iter->GetNumPoints();
++ for (iter = inpolys->front(); iter; iter++) {
++ numvertices += iter->get().GetNumPoints();
+ }
+
+ maxnumvertices = numvertices * 3;
+@@ -1303,8 +1298,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ newnumvertices = numvertices;
+
+ polystartindex = 0;
+- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) {
+- poly = &(*iter);
++ for (iter = inpolys->front(); iter; iter++) {
++ poly = &(iter->get());
+ polyendindex = polystartindex + poly->GetNumPoints() - 1;
+ for (i = 0; i < poly->GetNumPoints(); i++) {
+ vertices[i + polystartindex].p = poly->GetPoint(i);
+@@ -1360,14 +1355,14 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ // Note that while set doesn't actually have to be implemented as
+ // a tree, complexity requirements for operations are the same as
+ // for the balanced binary search tree.
+- std::set<ScanLineEdge> edgeTree;
++ Set<ScanLineEdge> edgeTree;
+ // Store iterators to the edge tree elements.
+ // This makes deleting existing edges much faster.
+- std::set<ScanLineEdge>::iterator *edgeTreeIterators, edgeIter;
+- edgeTreeIterators = new std::set<ScanLineEdge>::iterator[maxnumvertices];
+- std::pair<std::set<ScanLineEdge>::iterator, bool> edgeTreeRet;
++ Set<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter;
++ edgeTreeIterators = new Set<ScanLineEdge>::Element *[maxnumvertices];
++ //Pair<Set<ScanLineEdge>::iterator, bool> edgeTreeRet;
+ for (i = 0; i < numvertices; i++) {
+- edgeTreeIterators[i] = edgeTree.end();
++ edgeTreeIterators[i] = nullptr;
+ }
+
+ // For each vertex.
+@@ -1387,13 +1382,14 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ newedge.p1 = v->p;
+ newedge.p2 = vertices[v->next].p;
+ newedge.index = vindex;
+- edgeTreeRet = edgeTree.insert(newedge);
+- edgeTreeIterators[vindex] = edgeTreeRet.first;
++ //edgeTreeRet = edgeTree.insert(newedge);
++ //edgeTreeIterators[vindex] = edgeTreeRet.first;
++ edgeTreeIterators[vindex] = edgeTree.insert(newedge);
+ helpers[vindex] = vindex;
+ break;
+
+ case TPPL_VERTEXTYPE_END:
+- if (edgeTreeIterators[v->previous] == edgeTree.end()) {
++ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+@@ -1412,29 +1408,30 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+- if (edgeIter == edgeTree.begin()) {
++ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+ edgeIter--;
+ // Insert the diagonal connecting vi to helper(e_j) in D.
+- AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->index],
++ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ vindex2 = newnumvertices - 2;
+ v2 = &(vertices[vindex2]);
+ // helper(e_j) in v_i.
+- helpers[edgeIter->index] = vindex;
++ helpers[edgeIter->get().index] = vindex;
+ // Insert e_i in T and set helper(e_i) to v_i.
+ newedge.p1 = v2->p;
+ newedge.p2 = vertices[v2->next].p;
+ newedge.index = vindex2;
+- edgeTreeRet = edgeTree.insert(newedge);
+- edgeTreeIterators[vindex2] = edgeTreeRet.first;
++ //edgeTreeRet = edgeTree.insert(newedge);
++ //edgeTreeIterators[vindex2] = edgeTreeRet.first;
++ edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
+ helpers[vindex2] = vindex2;
+ break;
+
+ case TPPL_VERTEXTYPE_MERGE:
+- if (edgeTreeIterators[v->previous] == edgeTree.end()) {
++ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+@@ -1452,25 +1449,25 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+- if (edgeIter == edgeTree.begin()) {
++ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+ edgeIter--;
+ // If helper(e_j) is a merge vertex.
+- if (vertextypes[helpers[edgeIter->index]] == TPPL_VERTEXTYPE_MERGE) {
++ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting v_i to helper(e_j) in D.
+- AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->index],
++ AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ }
+ // helper(e_j) <- v_i
+- helpers[edgeIter->index] = vindex2;
++ helpers[edgeIter->get().index] = vindex2;
+ break;
+
+ case TPPL_VERTEXTYPE_REGULAR:
+ // If the interior of P lies to the right of v_i.
+ if (Below(v->p, vertices[v->previous].p)) {
+- if (edgeTreeIterators[v->previous] == edgeTree.end()) {
++ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+@@ -1488,27 +1485,28 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+ newedge.p1 = v2->p;
+ newedge.p2 = vertices[v2->next].p;
+ newedge.index = vindex2;
+- edgeTreeRet = edgeTree.insert(newedge);
+- edgeTreeIterators[vindex2] = edgeTreeRet.first;
++ //edgeTreeRet = edgeTree.insert(newedge);
++ //edgeTreeIterators[vindex2] = edgeTreeRet.first;
++ edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
+ helpers[vindex2] = vindex;
+ } else {
+ // Search in T to find the edge e_j directly left of v_i.
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+- if (edgeIter == edgeTree.begin()) {
++ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+- edgeIter--;
++ edgeIter = edgeIter->prev();
+ // If helper(e_j) is a merge vertex.
+- if (vertextypes[helpers[edgeIter->index]] == TPPL_VERTEXTYPE_MERGE) {
++ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting v_i to helper(e_j) in D.
+- AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->index],
++ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ }
+ // helper(e_j) <- v_i.
+- helpers[edgeIter->index] = vindex;
++ helpers[edgeIter->get().index] = vindex;
+ }
+ break;
+ }
+@@ -1569,8 +1567,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto
+
+ // Adds a diagonal to the doubly-connected list of vertices.
+ void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
+- TPPLVertexType *vertextypes, std::set<ScanLineEdge>::iterator *edgeTreeIterators,
+- std::set<ScanLineEdge> *edgeTree, long *helpers) {
++ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
++ Set<ScanLineEdge> *edgeTree, long *helpers) {
+ long newindex1, newindex2;
+
+ newindex1 = *numvertices;
+@@ -1597,14 +1595,14 @@ void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, lon
+ vertextypes[newindex1] = vertextypes[index1];
+ edgeTreeIterators[newindex1] = edgeTreeIterators[index1];
+ helpers[newindex1] = helpers[index1];
+- if (edgeTreeIterators[newindex1] != edgeTree->end()) {
+- edgeTreeIterators[newindex1]->index = newindex1;
++ if (edgeTreeIterators[newindex1] != edgeTree->back()) {
++ edgeTreeIterators[newindex1]->get().index = newindex1;
+ }
+ vertextypes[newindex2] = vertextypes[index2];
+ edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
+ helpers[newindex2] = helpers[index2];
+- if (edgeTreeIterators[newindex2] != edgeTree->end()) {
+- edgeTreeIterators[newindex2]->index = newindex2;
++ if (edgeTreeIterators[newindex2] != edgeTree->back()) {
++ edgeTreeIterators[newindex2]->get().index = newindex2;
+ }
+ }
+
+@@ -1830,13 +1828,13 @@ int TPPLPartition::TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles
+
+ int TPPLPartition::Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
+ TPPLPolyList monotone;
+- TPPLPolyList::iterator iter;
++ TPPLPolyList::Element *iter;
+
+ if (!MonotonePartition(inpolys, &monotone)) {
+ return 0;
+ }
+- for (iter = monotone.begin(); iter != monotone.end(); iter++) {
+- if (!TriangulateMonotone(&(*iter), triangles)) {
++ for (iter = monotone.front(); iter; iter = iter->next()) {
++ if (!TriangulateMonotone(&(iter->get()), triangles)) {
+ return 0;
+ }
+ }
+diff --git a/thirdparty/misc/polypartition.h b/thirdparty/misc/polypartition.h
+index f163f5d2173f..b2d905a3ef76 100644
+--- a/thirdparty/misc/polypartition.h
++++ b/thirdparty/misc/polypartition.h
+@@ -24,8 +24,9 @@
+ #ifndef POLYPARTITION_H
+ #define POLYPARTITION_H
+
+-#include <list>
+-#include <set>
++#include "core/math/vector2.h"
++#include "core/templates/list.h"
++#include "core/templates/set.h"
+
+ typedef double tppl_float;
+
+@@ -44,49 +45,7 @@ enum TPPLVertexType {
+ };
+
+ // 2D point structure.
+-struct TPPLPoint {
+- tppl_float x;
+- tppl_float y;
+- // User-specified vertex identifier. Note that this isn't used internally
+- // by the library, but will be faithfully copied around.
+- int id;
+-
+- TPPLPoint operator+(const TPPLPoint &p) const {
+- TPPLPoint r;
+- r.x = x + p.x;
+- r.y = y + p.y;
+- return r;
+- }
+-
+- TPPLPoint operator-(const TPPLPoint &p) const {
+- TPPLPoint r;
+- r.x = x - p.x;
+- r.y = y - p.y;
+- return r;
+- }
+-
+- TPPLPoint operator*(const tppl_float f) const {
+- TPPLPoint r;
+- r.x = x * f;
+- r.y = y * f;
+- return r;
+- }
+-
+- TPPLPoint operator/(const tppl_float f) const {
+- TPPLPoint r;
+- r.x = x / f;
+- r.y = y / f;
+- return r;
+- }
+-
+- bool operator==(const TPPLPoint &p) const {
+- return ((x == p.x) && (y == p.y));
+- }
+-
+- bool operator!=(const TPPLPoint &p) const {
+- return !((x == p.x) && (y == p.y));
+- }
+-};
++typedef Vector2 TPPLPoint;
+
+ // Polygon implemented as an array of points with a "hole" flag.
+ class TPPLPoly {
+@@ -168,9 +127,9 @@ class TPPLPoly {
+ };
+
+ #ifdef TPPL_ALLOCATOR
+-typedef std::list<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList;
++typedef List<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList;
+ #else
+-typedef std::list<TPPLPoly> TPPLPolyList;
++typedef List<TPPLPoly> TPPLPolyList;
+ #endif
+
+ class TPPLPartition {
+@@ -209,9 +168,9 @@ public:
+ };
+
+ #ifdef TPPL_ALLOCATOR
+- typedef std::list<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList;
++ typedef List<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList;
+ #else
+- typedef std::list<Diagonal> DiagonalList;
++ typedef List<Diagonal> DiagonalList;
+ #endif
+
+ // Dynamic programming state for minimum-weight triangulation.
+@@ -265,8 +224,8 @@ public:
+ // Helper functions for MonotonePartition.
+ bool Below(TPPLPoint &p1, TPPLPoint &p2);
+ void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
+- TPPLVertexType *vertextypes, std::set<ScanLineEdge>::iterator *edgeTreeIterators,
+- std::set<ScanLineEdge> *edgeTree, long *helpers);
++ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
++ Set<ScanLineEdge> *edgeTree, long *helpers);
+
+ // Triangulates a monotone polygon, used in Triangulate_MONO.
+ int TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles);
diff --git a/thirdparty/misc/polypartition.cpp b/thirdparty/misc/polypartition.cpp
new file mode 100644
index 0000000000..4f1b6dcb21
--- /dev/null
+++ b/thirdparty/misc/polypartition.cpp
@@ -0,0 +1,1849 @@
+/*************************************************************************/
+/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+
+#include "polypartition.h"
+
+#include <algorithm>
+
+TPPLPoly::TPPLPoly() {
+ hole = false;
+ numpoints = 0;
+ points = NULL;
+}
+
+TPPLPoly::~TPPLPoly() {
+ if (points) {
+ delete[] points;
+ }
+}
+
+void TPPLPoly::Clear() {
+ if (points) {
+ delete[] points;
+ }
+ hole = false;
+ numpoints = 0;
+ points = NULL;
+}
+
+void TPPLPoly::Init(long numpoints) {
+ Clear();
+ this->numpoints = numpoints;
+ points = new TPPLPoint[numpoints];
+}
+
+void TPPLPoly::Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
+ Init(3);
+ points[0] = p1;
+ points[1] = p2;
+ points[2] = p3;
+}
+
+TPPLPoly::TPPLPoly(const TPPLPoly &src) :
+ TPPLPoly() {
+ hole = src.hole;
+ numpoints = src.numpoints;
+
+ if (numpoints > 0) {
+ points = new TPPLPoint[numpoints];
+ memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
+ }
+}
+
+TPPLPoly &TPPLPoly::operator=(const TPPLPoly &src) {
+ Clear();
+ hole = src.hole;
+ numpoints = src.numpoints;
+
+ if (numpoints > 0) {
+ points = new TPPLPoint[numpoints];
+ memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
+ }
+
+ return *this;
+}
+
+TPPLOrientation TPPLPoly::GetOrientation() const {
+ long i1, i2;
+ tppl_float area = 0;
+ for (i1 = 0; i1 < numpoints; i1++) {
+ i2 = i1 + 1;
+ if (i2 == numpoints) {
+ i2 = 0;
+ }
+ area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
+ }
+ if (area > 0) {
+ return TPPL_ORIENTATION_CCW;
+ }
+ if (area < 0) {
+ return TPPL_ORIENTATION_CW;
+ }
+ return TPPL_ORIENTATION_NONE;
+}
+
+void TPPLPoly::SetOrientation(TPPLOrientation orientation) {
+ TPPLOrientation polyorientation = GetOrientation();
+ if (polyorientation != TPPL_ORIENTATION_NONE && polyorientation != orientation) {
+ Invert();
+ }
+}
+
+void TPPLPoly::Invert() {
+ std::reverse(points, points + numpoints);
+}
+
+TPPLPartition::PartitionVertex::PartitionVertex() :
+ previous(NULL), next(NULL) {
+}
+
+TPPLPoint TPPLPartition::Normalize(const TPPLPoint &p) {
+ TPPLPoint r;
+ tppl_float n = sqrt(p.x * p.x + p.y * p.y);
+ if (n != 0) {
+ r = p / n;
+ } else {
+ r.x = 0;
+ r.y = 0;
+ }
+ return r;
+}
+
+tppl_float TPPLPartition::Distance(const TPPLPoint &p1, const TPPLPoint &p2) {
+ tppl_float dx, dy;
+ dx = p2.x - p1.x;
+ dy = p2.y - p1.y;
+ return (sqrt(dx * dx + dy * dy));
+}
+
+// Checks if two lines intersect.
+int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22) {
+ if ((p11.x == p21.x) && (p11.y == p21.y)) {
+ return 0;
+ }
+ if ((p11.x == p22.x) && (p11.y == p22.y)) {
+ return 0;
+ }
+ if ((p12.x == p21.x) && (p12.y == p21.y)) {
+ return 0;
+ }
+ if ((p12.x == p22.x) && (p12.y == p22.y)) {
+ return 0;
+ }
+
+ TPPLPoint v1ort, v2ort, v;
+ tppl_float dot11, dot12, dot21, dot22;
+
+ v1ort.x = p12.y - p11.y;
+ v1ort.y = p11.x - p12.x;
+
+ v2ort.x = p22.y - p21.y;
+ v2ort.y = p21.x - p22.x;
+
+ v = p21 - p11;
+ dot21 = v.x * v1ort.x + v.y * v1ort.y;
+ v = p22 - p11;
+ dot22 = v.x * v1ort.x + v.y * v1ort.y;
+
+ v = p11 - p21;
+ dot11 = v.x * v2ort.x + v.y * v2ort.y;
+ v = p12 - p21;
+ dot12 = v.x * v2ort.x + v.y * v2ort.y;
+
+ if (dot11 * dot12 > 0) {
+ return 0;
+ }
+ if (dot21 * dot22 > 0) {
+ return 0;
+ }
+
+ return 1;
+}
+
+// Removes holes from inpolys by merging them with non-holes.
+int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
+ TPPLPolyList polys;
+ TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2;
+ long i, i2, holepointindex, polypointindex;
+ TPPLPoint holepoint, polypoint, bestpolypoint;
+ TPPLPoint linep1, linep2;
+ TPPLPoint v1, v2;
+ TPPLPoly newpoly;
+ bool hasholes;
+ bool pointvisible;
+ bool pointfound;
+
+ // Check for the trivial case of no holes.
+ hasholes = false;
+ for (iter = inpolys->front(); iter; iter = iter->next()) {
+ if (iter->get().IsHole()) {
+ hasholes = true;
+ break;
+ }
+ }
+ if (!hasholes) {
+ for (iter = inpolys->front(); iter; iter = iter->next()) {
+ outpolys->push_back(iter->get());
+ }
+ return 1;
+ }
+
+ polys = *inpolys;
+
+ while (1) {
+ // Find the hole point with the largest x.
+ hasholes = false;
+ for (iter = polys.front(); iter; iter = iter->next()) {
+ if (!iter->get().IsHole()) {
+ continue;
+ }
+
+ if (!hasholes) {
+ hasholes = true;
+ holeiter = iter;
+ holepointindex = 0;
+ }
+
+ for (i = 0; i < iter->get().GetNumPoints(); i++) {
+ if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
+ holeiter = iter;
+ holepointindex = i;
+ }
+ }
+ }
+ if (!hasholes) {
+ break;
+ }
+ holepoint = holeiter->get().GetPoint(holepointindex);
+
+ pointfound = false;
+ for (iter = polys.front(); iter; iter = iter->next()) {
+ if (iter->get().IsHole()) {
+ continue;
+ }
+ for (i = 0; i < iter->get().GetNumPoints(); i++) {
+ if (iter->get().GetPoint(i).x <= holepoint.x) {
+ continue;
+ }
+ if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())),
+ iter->get().GetPoint(i),
+ iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())),
+ holepoint)) {
+ continue;
+ }
+ polypoint = iter->get().GetPoint(i);
+ if (pointfound) {
+ v1 = Normalize(polypoint - holepoint);
+ v2 = Normalize(bestpolypoint - holepoint);
+ if (v2.x > v1.x) {
+ continue;
+ }
+ }
+ pointvisible = true;
+ for (iter2 = polys.front(); iter2; iter2->next()) {
+ if (iter2->get().IsHole()) {
+ continue;
+ }
+ for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) {
+ linep1 = iter2->get().GetPoint(i2);
+ linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints()));
+ if (Intersects(holepoint, polypoint, linep1, linep2)) {
+ pointvisible = false;
+ break;
+ }
+ }
+ if (!pointvisible) {
+ break;
+ }
+ }
+ if (pointvisible) {
+ pointfound = true;
+ bestpolypoint = polypoint;
+ polyiter = iter;
+ polypointindex = i;
+ }
+ }
+ }
+
+ if (!pointfound) {
+ return 0;
+ }
+
+ newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
+ i2 = 0;
+ for (i = 0; i <= polypointindex; i++) {
+ newpoly[i2] = polyiter->get().GetPoint(i);
+ i2++;
+ }
+ for (i = 0; i <= holeiter->get().GetNumPoints(); i++) {
+ newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints());
+ i2++;
+ }
+ for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) {
+ newpoly[i2] = polyiter->get().GetPoint(i);
+ i2++;
+ }
+
+ polys.erase(holeiter);
+ polys.erase(polyiter);
+ polys.push_back(newpoly);
+ }
+
+ for (iter = polys.front(); iter; iter = iter->next()) {
+ outpolys->push_back(iter->get());
+ }
+
+ return 1;
+}
+
+bool TPPLPartition::IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
+ tppl_float tmp;
+ tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
+ if (tmp > 0) {
+ return 1;
+ } else {
+ return 0;
+ }
+}
+
+bool TPPLPartition::IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
+ tppl_float tmp;
+ tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
+ if (tmp < 0) {
+ return 1;
+ } else {
+ return 0;
+ }
+}
+
+bool TPPLPartition::IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
+ if (IsConvex(p1, p, p2)) {
+ return false;
+ }
+ if (IsConvex(p2, p, p3)) {
+ return false;
+ }
+ if (IsConvex(p3, p, p1)) {
+ return false;
+ }
+ return true;
+}
+
+bool TPPLPartition::InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
+ bool convex;
+
+ convex = IsConvex(p1, p2, p3);
+
+ if (convex) {
+ if (!IsConvex(p1, p2, p)) {
+ return false;
+ }
+ if (!IsConvex(p2, p3, p)) {
+ return false;
+ }
+ return true;
+ } else {
+ if (IsConvex(p1, p2, p)) {
+ return true;
+ }
+ if (IsConvex(p2, p3, p)) {
+ return true;
+ }
+ return false;
+ }
+}
+
+bool TPPLPartition::InCone(PartitionVertex *v, TPPLPoint &p) {
+ TPPLPoint p1, p2, p3;
+
+ p1 = v->previous->p;
+ p2 = v->p;
+ p3 = v->next->p;
+
+ return InCone(p1, p2, p3, p);
+}
+
+void TPPLPartition::UpdateVertexReflexity(PartitionVertex *v) {
+ PartitionVertex *v1 = NULL, *v3 = NULL;
+ v1 = v->previous;
+ v3 = v->next;
+ v->isConvex = !IsReflex(v1->p, v->p, v3->p);
+}
+
+void TPPLPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
+ long i;
+ PartitionVertex *v1 = NULL, *v3 = NULL;
+ TPPLPoint vec1, vec3;
+
+ v1 = v->previous;
+ v3 = v->next;
+
+ v->isConvex = IsConvex(v1->p, v->p, v3->p);
+
+ vec1 = Normalize(v1->p - v->p);
+ vec3 = Normalize(v3->p - v->p);
+ v->angle = vec1.x * vec3.x + vec1.y * vec3.y;
+
+ if (v->isConvex) {
+ v->isEar = true;
+ for (i = 0; i < numvertices; i++) {
+ if ((vertices[i].p.x == v->p.x) && (vertices[i].p.y == v->p.y)) {
+ continue;
+ }
+ if ((vertices[i].p.x == v1->p.x) && (vertices[i].p.y == v1->p.y)) {
+ continue;
+ }
+ if ((vertices[i].p.x == v3->p.x) && (vertices[i].p.y == v3->p.y)) {
+ continue;
+ }
+ if (IsInside(v1->p, v->p, v3->p, vertices[i].p)) {
+ v->isEar = false;
+ break;
+ }
+ }
+ } else {
+ v->isEar = false;
+ }
+}
+
+// Triangulation by ear removal.
+int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) {
+ if (!poly->Valid()) {
+ return 0;
+ }
+
+ long numvertices;
+ PartitionVertex *vertices = NULL;
+ PartitionVertex *ear = NULL;
+ TPPLPoly triangle;
+ long i, j;
+ bool earfound;
+
+ if (poly->GetNumPoints() < 3) {
+ return 0;
+ }
+ if (poly->GetNumPoints() == 3) {
+ triangles->push_back(*poly);
+ return 1;
+ }
+
+ numvertices = poly->GetNumPoints();
+
+ vertices = new PartitionVertex[numvertices];
+ for (i = 0; i < numvertices; i++) {
+ vertices[i].isActive = true;
+ vertices[i].p = poly->GetPoint(i);
+ if (i == (numvertices - 1)) {
+ vertices[i].next = &(vertices[0]);
+ } else {
+ vertices[i].next = &(vertices[i + 1]);
+ }
+ if (i == 0) {
+ vertices[i].previous = &(vertices[numvertices - 1]);
+ } else {
+ vertices[i].previous = &(vertices[i - 1]);
+ }
+ }
+ for (i = 0; i < numvertices; i++) {
+ UpdateVertex(&vertices[i], vertices, numvertices);
+ }
+
+ for (i = 0; i < numvertices - 3; i++) {
+ earfound = false;
+ // Find the most extruded ear.
+ for (j = 0; j < numvertices; j++) {
+ if (!vertices[j].isActive) {
+ continue;
+ }
+ if (!vertices[j].isEar) {
+ continue;
+ }
+ if (!earfound) {
+ earfound = true;
+ ear = &(vertices[j]);
+ } else {
+ if (vertices[j].angle > ear->angle) {
+ ear = &(vertices[j]);
+ }
+ }
+ }
+ if (!earfound) {
+ delete[] vertices;
+ return 0;
+ }
+
+ triangle.Triangle(ear->previous->p, ear->p, ear->next->p);
+ triangles->push_back(triangle);
+
+ ear->isActive = false;
+ ear->previous->next = ear->next;
+ ear->next->previous = ear->previous;
+
+ if (i == numvertices - 4) {
+ break;
+ }
+
+ UpdateVertex(ear->previous, vertices, numvertices);
+ UpdateVertex(ear->next, vertices, numvertices);
+ }
+ for (i = 0; i < numvertices; i++) {
+ if (vertices[i].isActive) {
+ triangle.Triangle(vertices[i].previous->p, vertices[i].p, vertices[i].next->p);
+ triangles->push_back(triangle);
+ break;
+ }
+ }
+
+ delete[] vertices;
+
+ return 1;
+}
+
+int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
+ TPPLPolyList outpolys;
+ TPPLPolyList::Element *iter;
+
+ if (!RemoveHoles(inpolys, &outpolys)) {
+ return 0;
+ }
+ for (iter = outpolys.front(); iter; iter = iter->next()) {
+ if (!Triangulate_EC(&(iter->get()), triangles)) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
+ if (!poly->Valid()) {
+ return 0;
+ }
+
+ TPPLPolyList triangles;
+ TPPLPolyList::Element *iter1, *iter2;
+ TPPLPoly *poly1 = NULL, *poly2 = NULL;
+ TPPLPoly newpoly;
+ TPPLPoint d1, d2, p1, p2, p3;
+ long i11, i12, i21, i22, i13, i23, j, k;
+ bool isdiagonal;
+ long numreflex;
+
+ // Check if the poly is already convex.
+ numreflex = 0;
+ for (i11 = 0; i11 < poly->GetNumPoints(); i11++) {
+ if (i11 == 0) {
+ i12 = poly->GetNumPoints() - 1;
+ } else {
+ i12 = i11 - 1;
+ }
+ if (i11 == (poly->GetNumPoints() - 1)) {
+ i13 = 0;
+ } else {
+ i13 = i11 + 1;
+ }
+ if (IsReflex(poly->GetPoint(i12), poly->GetPoint(i11), poly->GetPoint(i13))) {
+ numreflex = 1;
+ break;
+ }
+ }
+ if (numreflex == 0) {
+ parts->push_back(*poly);
+ return 1;
+ }
+
+ if (!Triangulate_EC(poly, &triangles)) {
+ return 0;
+ }
+
+ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
+ poly1 = &(iter1->get());
+ for (i11 = 0; i11 < poly1->GetNumPoints(); i11++) {
+ d1 = poly1->GetPoint(i11);
+ i12 = (i11 + 1) % (poly1->GetNumPoints());
+ d2 = poly1->GetPoint(i12);
+
+ isdiagonal = false;
+ for (iter2 = iter1; iter2; iter2 = iter2->next()) {
+ if (iter1 == iter2) {
+ continue;
+ }
+ poly2 = &(iter2->get());
+
+ for (i21 = 0; i21 < poly2->GetNumPoints(); i21++) {
+ if ((d2.x != poly2->GetPoint(i21).x) || (d2.y != poly2->GetPoint(i21).y)) {
+ continue;
+ }
+ i22 = (i21 + 1) % (poly2->GetNumPoints());
+ if ((d1.x != poly2->GetPoint(i22).x) || (d1.y != poly2->GetPoint(i22).y)) {
+ continue;
+ }
+ isdiagonal = true;
+ break;
+ }
+ if (isdiagonal) {
+ break;
+ }
+ }
+
+ if (!isdiagonal) {
+ continue;
+ }
+
+ p2 = poly1->GetPoint(i11);
+ if (i11 == 0) {
+ i13 = poly1->GetNumPoints() - 1;
+ } else {
+ i13 = i11 - 1;
+ }
+ p1 = poly1->GetPoint(i13);
+ if (i22 == (poly2->GetNumPoints() - 1)) {
+ i23 = 0;
+ } else {
+ i23 = i22 + 1;
+ }
+ p3 = poly2->GetPoint(i23);
+
+ if (!IsConvex(p1, p2, p3)) {
+ continue;
+ }
+
+ p2 = poly1->GetPoint(i12);
+ if (i12 == (poly1->GetNumPoints() - 1)) {
+ i13 = 0;
+ } else {
+ i13 = i12 + 1;
+ }
+ p3 = poly1->GetPoint(i13);
+ if (i21 == 0) {
+ i23 = poly2->GetNumPoints() - 1;
+ } else {
+ i23 = i21 - 1;
+ }
+ p1 = poly2->GetPoint(i23);
+
+ if (!IsConvex(p1, p2, p3)) {
+ continue;
+ }
+
+ newpoly.Init(poly1->GetNumPoints() + poly2->GetNumPoints() - 2);
+ k = 0;
+ for (j = i12; j != i11; j = (j + 1) % (poly1->GetNumPoints())) {
+ newpoly[k] = poly1->GetPoint(j);
+ k++;
+ }
+ for (j = i22; j != i21; j = (j + 1) % (poly2->GetNumPoints())) {
+ newpoly[k] = poly2->GetPoint(j);
+ k++;
+ }
+
+ triangles.erase(iter2);
+ iter1->get() = newpoly;
+ poly1 = &(iter1->get());
+ i11 = -1;
+
+ continue;
+ }
+ }
+
+ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
+ parts->push_back(iter1->get());
+ }
+
+ return 1;
+}
+
+int TPPLPartition::ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts) {
+ TPPLPolyList outpolys;
+ TPPLPolyList::Element *iter;
+
+ if (!RemoveHoles(inpolys, &outpolys)) {
+ return 0;
+ }
+ for (iter = outpolys.front(); iter; iter = iter->next()) {
+ if (!ConvexPartition_HM(&(iter->get()), parts)) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+// Minimum-weight polygon triangulation by dynamic programming.
+// Time complexity: O(n^3)
+// Space complexity: O(n^2)
+int TPPLPartition::Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles) {
+ if (!poly->Valid()) {
+ return 0;
+ }
+
+ long i, j, k, gap, n;
+ DPState **dpstates = NULL;
+ TPPLPoint p1, p2, p3, p4;
+ long bestvertex;
+ tppl_float weight, minweight, d1, d2;
+ Diagonal diagonal, newdiagonal;
+ DiagonalList diagonals;
+ TPPLPoly triangle;
+ int ret = 1;
+
+ n = poly->GetNumPoints();
+ dpstates = new DPState *[n];
+ for (i = 1; i < n; i++) {
+ dpstates[i] = new DPState[i];
+ }
+
+ // Initialize states and visibility.
+ for (i = 0; i < (n - 1); i++) {
+ p1 = poly->GetPoint(i);
+ for (j = i + 1; j < n; j++) {
+ dpstates[j][i].visible = true;
+ dpstates[j][i].weight = 0;
+ dpstates[j][i].bestvertex = -1;
+ if (j != (i + 1)) {
+ p2 = poly->GetPoint(j);
+
+ // Visibility check.
+ if (i == 0) {
+ p3 = poly->GetPoint(n - 1);
+ } else {
+ p3 = poly->GetPoint(i - 1);
+ }
+ if (i == (n - 1)) {
+ p4 = poly->GetPoint(0);
+ } else {
+ p4 = poly->GetPoint(i + 1);
+ }
+ if (!InCone(p3, p1, p4, p2)) {
+ dpstates[j][i].visible = false;
+ continue;
+ }
+
+ if (j == 0) {
+ p3 = poly->GetPoint(n - 1);
+ } else {
+ p3 = poly->GetPoint(j - 1);
+ }
+ if (j == (n - 1)) {
+ p4 = poly->GetPoint(0);
+ } else {
+ p4 = poly->GetPoint(j + 1);
+ }
+ if (!InCone(p3, p2, p4, p1)) {
+ dpstates[j][i].visible = false;
+ continue;
+ }
+
+ for (k = 0; k < n; k++) {
+ p3 = poly->GetPoint(k);
+ if (k == (n - 1)) {
+ p4 = poly->GetPoint(0);
+ } else {
+ p4 = poly->GetPoint(k + 1);
+ }
+ if (Intersects(p1, p2, p3, p4)) {
+ dpstates[j][i].visible = false;
+ break;
+ }
+ }
+ }
+ }
+ }
+ dpstates[n - 1][0].visible = true;
+ dpstates[n - 1][0].weight = 0;
+ dpstates[n - 1][0].bestvertex = -1;
+
+ for (gap = 2; gap < n; gap++) {
+ for (i = 0; i < (n - gap); i++) {
+ j = i + gap;
+ if (!dpstates[j][i].visible) {
+ continue;
+ }
+ bestvertex = -1;
+ for (k = (i + 1); k < j; k++) {
+ if (!dpstates[k][i].visible) {
+ continue;
+ }
+ if (!dpstates[j][k].visible) {
+ continue;
+ }
+
+ if (k <= (i + 1)) {
+ d1 = 0;
+ } else {
+ d1 = Distance(poly->GetPoint(i), poly->GetPoint(k));
+ }
+ if (j <= (k + 1)) {
+ d2 = 0;
+ } else {
+ d2 = Distance(poly->GetPoint(k), poly->GetPoint(j));
+ }
+
+ weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2;
+
+ if ((bestvertex == -1) || (weight < minweight)) {
+ bestvertex = k;
+ minweight = weight;
+ }
+ }
+ if (bestvertex == -1) {
+ for (i = 1; i < n; i++) {
+ delete[] dpstates[i];
+ }
+ delete[] dpstates;
+
+ return 0;
+ }
+
+ dpstates[j][i].bestvertex = bestvertex;
+ dpstates[j][i].weight = minweight;
+ }
+ }
+
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_back(newdiagonal);
+ while (!diagonals.is_empty()) {
+ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex;
+ if (bestvertex == -1) {
+ ret = 0;
+ break;
+ }
+ triangle.Triangle(poly->GetPoint(diagonal.index1), poly->GetPoint(bestvertex), poly->GetPoint(diagonal.index2));
+ triangles->push_back(triangle);
+ if (bestvertex > (diagonal.index1 + 1)) {
+ newdiagonal.index1 = diagonal.index1;
+ newdiagonal.index2 = bestvertex;
+ diagonals.push_back(newdiagonal);
+ }
+ if (diagonal.index2 > (bestvertex + 1)) {
+ newdiagonal.index1 = bestvertex;
+ newdiagonal.index2 = diagonal.index2;
+ diagonals.push_back(newdiagonal);
+ }
+ }
+
+ for (i = 1; i < n; i++) {
+ delete[] dpstates[i];
+ }
+ delete[] dpstates;
+
+ return ret;
+}
+
+void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) {
+ Diagonal newdiagonal;
+ DiagonalList *pairs = NULL;
+ long w2;
+
+ w2 = dpstates[a][b].weight;
+ if (w > w2) {
+ return;
+ }
+
+ pairs = &(dpstates[a][b].pairs);
+ newdiagonal.index1 = i;
+ newdiagonal.index2 = j;
+
+ if (w < w2) {
+ pairs->clear();
+ pairs->push_front(newdiagonal);
+ dpstates[a][b].weight = w;
+ } else {
+ if ((!pairs->is_empty()) && (i <= pairs->front()->get().index1)) {
+ return;
+ }
+ while ((!pairs->is_empty()) && (pairs->front()->get().index2 >= j)) {
+ pairs->pop_front();
+ }
+ pairs->push_front(newdiagonal);
+ }
+}
+
+void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
+ DiagonalList *pairs = NULL;
+ DiagonalList::Element *iter, *lastiter;
+ long top;
+ long w;
+
+ if (!dpstates[i][j].visible) {
+ return;
+ }
+ top = j;
+ w = dpstates[i][j].weight;
+ if (k - j > 1) {
+ if (!dpstates[j][k].visible) {
+ return;
+ }
+ w += dpstates[j][k].weight + 1;
+ }
+ if (j - i > 1) {
+ pairs = &(dpstates[i][j].pairs);
+ iter = pairs->back();
+ lastiter = pairs->back();
+ while (iter != pairs->front()) {
+ iter--;
+ if (!IsReflex(vertices[iter->get().index2].p, vertices[j].p, vertices[k].p)) {
+ lastiter = iter;
+ } else {
+ break;
+ }
+ }
+ if (lastiter == pairs->back()) {
+ w++;
+ } else {
+ if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->get().index1].p)) {
+ w++;
+ } else {
+ top = lastiter->get().index1;
+ }
+ }
+ }
+ UpdateState(i, k, w, top, j, dpstates);
+}
+
+void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
+ DiagonalList *pairs = NULL;
+ DiagonalList::Element *iter, *lastiter;
+ long top;
+ long w;
+
+ if (!dpstates[j][k].visible) {
+ return;
+ }
+ top = j;
+ w = dpstates[j][k].weight;
+
+ if (j - i > 1) {
+ if (!dpstates[i][j].visible) {
+ return;
+ }
+ w += dpstates[i][j].weight + 1;
+ }
+ if (k - j > 1) {
+ pairs = &(dpstates[j][k].pairs);
+
+ iter = pairs->front();
+ if ((!pairs->is_empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p))) {
+ lastiter = iter;
+ while (iter) {
+ if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p)) {
+ lastiter = iter;
+ iter = iter->next();
+ } else {
+ break;
+ }
+ }
+ if (IsReflex(vertices[lastiter->get().index2].p, vertices[k].p, vertices[i].p)) {
+ w++;
+ } else {
+ top = lastiter->get().index2;
+ }
+ } else {
+ w++;
+ }
+ }
+ UpdateState(i, k, w, j, top, dpstates);
+}
+
+int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
+ if (!poly->Valid()) {
+ return 0;
+ }
+
+ TPPLPoint p1, p2, p3, p4;
+ PartitionVertex *vertices = NULL;
+ DPState2 **dpstates = NULL;
+ long i, j, k, n, gap;
+ DiagonalList diagonals, diagonals2;
+ Diagonal diagonal, newdiagonal;
+ DiagonalList *pairs = NULL, *pairs2 = NULL;
+ DiagonalList::Element *iter, *iter2;
+ int ret;
+ TPPLPoly newpoly;
+ List<long> indices;
+ List<long>::Element *iiter;
+ bool ijreal, jkreal;
+
+ n = poly->GetNumPoints();
+ vertices = new PartitionVertex[n];
+
+ dpstates = new DPState2 *[n];
+ for (i = 0; i < n; i++) {
+ dpstates[i] = new DPState2[n];
+ }
+
+ // Initialize vertex information.
+ for (i = 0; i < n; i++) {
+ vertices[i].p = poly->GetPoint(i);
+ vertices[i].isActive = true;
+ if (i == 0) {
+ vertices[i].previous = &(vertices[n - 1]);
+ } else {
+ vertices[i].previous = &(vertices[i - 1]);
+ }
+ if (i == (poly->GetNumPoints() - 1)) {
+ vertices[i].next = &(vertices[0]);
+ } else {
+ vertices[i].next = &(vertices[i + 1]);
+ }
+ }
+ for (i = 1; i < n; i++) {
+ UpdateVertexReflexity(&(vertices[i]));
+ }
+
+ // Initialize states and visibility.
+ for (i = 0; i < (n - 1); i++) {
+ p1 = poly->GetPoint(i);
+ for (j = i + 1; j < n; j++) {
+ dpstates[i][j].visible = true;
+ if (j == i + 1) {
+ dpstates[i][j].weight = 0;
+ } else {
+ dpstates[i][j].weight = 2147483647;
+ }
+ if (j != (i + 1)) {
+ p2 = poly->GetPoint(j);
+
+ // Visibility check.
+ if (!InCone(&vertices[i], p2)) {
+ dpstates[i][j].visible = false;
+ continue;
+ }
+ if (!InCone(&vertices[j], p1)) {
+ dpstates[i][j].visible = false;
+ continue;
+ }
+
+ for (k = 0; k < n; k++) {
+ p3 = poly->GetPoint(k);
+ if (k == (n - 1)) {
+ p4 = poly->GetPoint(0);
+ } else {
+ p4 = poly->GetPoint(k + 1);
+ }
+ if (Intersects(p1, p2, p3, p4)) {
+ dpstates[i][j].visible = false;
+ break;
+ }
+ }
+ }
+ }
+ }
+ for (i = 0; i < (n - 2); i++) {
+ j = i + 2;
+ if (dpstates[i][j].visible) {
+ dpstates[i][j].weight = 0;
+ newdiagonal.index1 = i + 1;
+ newdiagonal.index2 = i + 1;
+ dpstates[i][j].pairs.push_back(newdiagonal);
+ }
+ }
+
+ dpstates[0][n - 1].visible = true;
+ vertices[0].isConvex = false; // By convention.
+
+ for (gap = 3; gap < n; gap++) {
+ for (i = 0; i < n - gap; i++) {
+ if (vertices[i].isConvex) {
+ continue;
+ }
+ k = i + gap;
+ if (dpstates[i][k].visible) {
+ if (!vertices[k].isConvex) {
+ for (j = i + 1; j < k; j++) {
+ TypeA(i, j, k, vertices, dpstates);
+ }
+ } else {
+ for (j = i + 1; j < (k - 1); j++) {
+ if (vertices[j].isConvex) {
+ continue;
+ }
+ TypeA(i, j, k, vertices, dpstates);
+ }
+ TypeA(i, k - 1, k, vertices, dpstates);
+ }
+ }
+ }
+ for (k = gap; k < n; k++) {
+ if (vertices[k].isConvex) {
+ continue;
+ }
+ i = k - gap;
+ if ((vertices[i].isConvex) && (dpstates[i][k].visible)) {
+ TypeB(i, i + 1, k, vertices, dpstates);
+ for (j = i + 2; j < k; j++) {
+ if (vertices[j].isConvex) {
+ continue;
+ }
+ TypeB(i, j, k, vertices, dpstates);
+ }
+ }
+ }
+ }
+
+ // Recover solution.
+ ret = 1;
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_front(newdiagonal);
+ while (!diagonals.is_empty()) {
+ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+ }
+ pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
+ if (pairs->is_empty()) {
+ ret = 0;
+ break;
+ }
+ if (!vertices[diagonal.index1].isConvex) {
+ iter = pairs->back();
+ iter--;
+ j = iter->get().index2;
+ newdiagonal.index1 = j;
+ newdiagonal.index2 = diagonal.index2;
+ diagonals.push_front(newdiagonal);
+ if ((j - diagonal.index1) > 1) {
+ if (iter->get().index1 != iter->get().index2) {
+ pairs2 = &(dpstates[diagonal.index1][j].pairs);
+ while (1) {
+ if (pairs2->is_empty()) {
+ ret = 0;
+ break;
+ }
+ iter2 = pairs2->back();
+ iter2--;
+ if (iter->get().index1 != iter2->get().index1) {
+ pairs2->pop_back();
+ } else {
+ break;
+ }
+ }
+ if (ret == 0) {
+ break;
+ }
+ }
+ newdiagonal.index1 = diagonal.index1;
+ newdiagonal.index2 = j;
+ diagonals.push_front(newdiagonal);
+ }
+ } else {
+ iter = pairs->front();
+ j = iter->get().index1;
+ newdiagonal.index1 = diagonal.index1;
+ newdiagonal.index2 = j;
+ diagonals.push_front(newdiagonal);
+ if ((diagonal.index2 - j) > 1) {
+ if (iter->get().index1 != iter->get().index2) {
+ pairs2 = &(dpstates[j][diagonal.index2].pairs);
+ while (1) {
+ if (pairs2->is_empty()) {
+ ret = 0;
+ break;
+ }
+ iter2 = pairs2->front();
+ if (iter->get().index2 != iter2->get().index2) {
+ pairs2->pop_front();
+ } else {
+ break;
+ }
+ }
+ if (ret == 0) {
+ break;
+ }
+ }
+ newdiagonal.index1 = j;
+ newdiagonal.index2 = diagonal.index2;
+ diagonals.push_front(newdiagonal);
+ }
+ }
+ }
+
+ if (ret == 0) {
+ for (i = 0; i < n; i++) {
+ delete[] dpstates[i];
+ }
+ delete[] dpstates;
+ delete[] vertices;
+
+ return ret;
+ }
+
+ newdiagonal.index1 = 0;
+ newdiagonal.index2 = n - 1;
+ diagonals.push_front(newdiagonal);
+ while (!diagonals.is_empty()) {
+ diagonal = diagonals.front()->get();
+ diagonals.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+ }
+
+ indices.clear();
+ diagonals2.clear();
+ indices.push_back(diagonal.index1);
+ indices.push_back(diagonal.index2);
+ diagonals2.push_front(diagonal);
+
+ while (!diagonals2.is_empty()) {
+ diagonal = diagonals2.front()->get();
+ diagonals2.pop_front();
+ if ((diagonal.index2 - diagonal.index1) <= 1) {
+ continue;
+ }
+ ijreal = true;
+ jkreal = true;
+ pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
+ if (!vertices[diagonal.index1].isConvex) {
+ iter = pairs->back();
+ iter--;
+ j = iter->get().index2;
+ if (iter->get().index1 != iter->get().index2) {
+ ijreal = false;
+ }
+ } else {
+ iter = pairs->front();
+ j = iter->get().index1;
+ if (iter->get().index1 != iter->get().index2) {
+ jkreal = false;
+ }
+ }
+
+ newdiagonal.index1 = diagonal.index1;
+ newdiagonal.index2 = j;
+ if (ijreal) {
+ diagonals.push_back(newdiagonal);
+ } else {
+ diagonals2.push_back(newdiagonal);
+ }
+
+ newdiagonal.index1 = j;
+ newdiagonal.index2 = diagonal.index2;
+ if (jkreal) {
+ diagonals.push_back(newdiagonal);
+ } else {
+ diagonals2.push_back(newdiagonal);
+ }
+
+ indices.push_back(j);
+ }
+
+ //std::sort(indices.begin(), indices.end());
+ indices.sort();
+ newpoly.Init((long)indices.size());
+ k = 0;
+ for (iiter = indices.front(); iiter != indices.back(); iiter = iiter->next()) {
+ newpoly[k] = vertices[iiter->get()].p;
+ k++;
+ }
+ parts->push_back(newpoly);
+ }
+
+ for (i = 0; i < n; i++) {
+ delete[] dpstates[i];
+ }
+ delete[] dpstates;
+ delete[] vertices;
+
+ return ret;
+}
+
+// Creates a monotone partition of a list of polygons that
+// can contain holes. Triangulates a set of polygons by
+// first partitioning them into monotone polygons.
+// Time complexity: O(n*log(n)), n is the number of vertices.
+// Space complexity: O(n)
+// The algorithm used here is outlined in the book
+// "Computational Geometry: Algorithms and Applications"
+// by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.
+int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys) {
+ TPPLPolyList::Element *iter;
+ MonotoneVertex *vertices = NULL;
+ long i, numvertices, vindex, vindex2, newnumvertices, maxnumvertices;
+ long polystartindex, polyendindex;
+ TPPLPoly *poly = NULL;
+ MonotoneVertex *v = NULL, *v2 = NULL, *vprev = NULL, *vnext = NULL;
+ ScanLineEdge newedge;
+ bool error = false;
+
+ numvertices = 0;
+ for (iter = inpolys->front(); iter; iter++) {
+ numvertices += iter->get().GetNumPoints();
+ }
+
+ maxnumvertices = numvertices * 3;
+ vertices = new MonotoneVertex[maxnumvertices];
+ newnumvertices = numvertices;
+
+ polystartindex = 0;
+ for (iter = inpolys->front(); iter; iter++) {
+ poly = &(iter->get());
+ polyendindex = polystartindex + poly->GetNumPoints() - 1;
+ for (i = 0; i < poly->GetNumPoints(); i++) {
+ vertices[i + polystartindex].p = poly->GetPoint(i);
+ if (i == 0) {
+ vertices[i + polystartindex].previous = polyendindex;
+ } else {
+ vertices[i + polystartindex].previous = i + polystartindex - 1;
+ }
+ if (i == (poly->GetNumPoints() - 1)) {
+ vertices[i + polystartindex].next = polystartindex;
+ } else {
+ vertices[i + polystartindex].next = i + polystartindex + 1;
+ }
+ }
+ polystartindex = polyendindex + 1;
+ }
+
+ // Construct the priority queue.
+ long *priority = new long[numvertices];
+ for (i = 0; i < numvertices; i++) {
+ priority[i] = i;
+ }
+ std::sort(priority, &(priority[numvertices]), VertexSorter(vertices));
+
+ // Determine vertex types.
+ TPPLVertexType *vertextypes = new TPPLVertexType[maxnumvertices];
+ for (i = 0; i < numvertices; i++) {
+ v = &(vertices[i]);
+ vprev = &(vertices[v->previous]);
+ vnext = &(vertices[v->next]);
+
+ if (Below(vprev->p, v->p) && Below(vnext->p, v->p)) {
+ if (IsConvex(vnext->p, vprev->p, v->p)) {
+ vertextypes[i] = TPPL_VERTEXTYPE_START;
+ } else {
+ vertextypes[i] = TPPL_VERTEXTYPE_SPLIT;
+ }
+ } else if (Below(v->p, vprev->p) && Below(v->p, vnext->p)) {
+ if (IsConvex(vnext->p, vprev->p, v->p)) {
+ vertextypes[i] = TPPL_VERTEXTYPE_END;
+ } else {
+ vertextypes[i] = TPPL_VERTEXTYPE_MERGE;
+ }
+ } else {
+ vertextypes[i] = TPPL_VERTEXTYPE_REGULAR;
+ }
+ }
+
+ // Helpers.
+ long *helpers = new long[maxnumvertices];
+
+ // Binary search tree that holds edges intersecting the scanline.
+ // Note that while set doesn't actually have to be implemented as
+ // a tree, complexity requirements for operations are the same as
+ // for the balanced binary search tree.
+ Set<ScanLineEdge> edgeTree;
+ // Store iterators to the edge tree elements.
+ // This makes deleting existing edges much faster.
+ Set<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter;
+ edgeTreeIterators = new Set<ScanLineEdge>::Element *[maxnumvertices];
+ //Pair<Set<ScanLineEdge>::iterator, bool> edgeTreeRet;
+ for (i = 0; i < numvertices; i++) {
+ edgeTreeIterators[i] = nullptr;
+ }
+
+ // For each vertex.
+ for (i = 0; i < numvertices; i++) {
+ vindex = priority[i];
+ v = &(vertices[vindex]);
+ vindex2 = vindex;
+ v2 = v;
+
+ // Depending on the vertex type, do the appropriate action.
+ // Comments in the following sections are copied from
+ // "Computational Geometry: Algorithms and Applications".
+ // Notation: e_i = e subscript i, v_i = v subscript i, etc.
+ switch (vertextypes[vindex]) {
+ case TPPL_VERTEXTYPE_START:
+ // Insert e_i in T and set helper(e_i) to v_i.
+ newedge.p1 = v->p;
+ newedge.p2 = vertices[v->next].p;
+ newedge.index = vindex;
+ //edgeTreeRet = edgeTree.insert(newedge);
+ //edgeTreeIterators[vindex] = edgeTreeRet.first;
+ edgeTreeIterators[vindex] = edgeTree.insert(newedge);
+ helpers[vindex] = vindex;
+ break;
+
+ case TPPL_VERTEXTYPE_END:
+ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+ // If helper(e_i - 1) is a merge vertex
+ if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting vi to helper(e_i - 1) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ }
+ // Delete e_i - 1 from T
+ edgeTree.erase(edgeTreeIterators[v->previous]);
+ break;
+
+ case TPPL_VERTEXTYPE_SPLIT:
+ // Search in T to find the edge e_j directly left of v_i.
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+ edgeIter--;
+ // Insert the diagonal connecting vi to helper(e_j) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ vindex2 = newnumvertices - 2;
+ v2 = &(vertices[vindex2]);
+ // helper(e_j) in v_i.
+ helpers[edgeIter->get().index] = vindex;
+ // Insert e_i in T and set helper(e_i) to v_i.
+ newedge.p1 = v2->p;
+ newedge.p2 = vertices[v2->next].p;
+ newedge.index = vindex2;
+ //edgeTreeRet = edgeTree.insert(newedge);
+ //edgeTreeIterators[vindex2] = edgeTreeRet.first;
+ edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
+ helpers[vindex2] = vindex2;
+ break;
+
+ case TPPL_VERTEXTYPE_MERGE:
+ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+ // if helper(e_i - 1) is a merge vertex
+ if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting vi to helper(e_i - 1) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ vindex2 = newnumvertices - 2;
+ v2 = &(vertices[vindex2]);
+ }
+ // Delete e_i - 1 from T.
+ edgeTree.erase(edgeTreeIterators[v->previous]);
+ // Search in T to find the edge e_j directly left of v_i.
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+ edgeIter--;
+ // If helper(e_j) is a merge vertex.
+ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting v_i to helper(e_j) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ }
+ // helper(e_j) <- v_i
+ helpers[edgeIter->get().index] = vindex2;
+ break;
+
+ case TPPL_VERTEXTYPE_REGULAR:
+ // If the interior of P lies to the right of v_i.
+ if (Below(v->p, vertices[v->previous].p)) {
+ if (edgeTreeIterators[v->previous] == edgeTree.back()) {
+ error = true;
+ break;
+ }
+ // If helper(e_i - 1) is a merge vertex.
+ if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting v_i to helper(e_i - 1) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ vindex2 = newnumvertices - 2;
+ v2 = &(vertices[vindex2]);
+ }
+ // Delete e_i - 1 from T.
+ edgeTree.erase(edgeTreeIterators[v->previous]);
+ // Insert e_i in T and set helper(e_i) to v_i.
+ newedge.p1 = v2->p;
+ newedge.p2 = vertices[v2->next].p;
+ newedge.index = vindex2;
+ //edgeTreeRet = edgeTree.insert(newedge);
+ //edgeTreeIterators[vindex2] = edgeTreeRet.first;
+ edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
+ helpers[vindex2] = vindex;
+ } else {
+ // Search in T to find the edge e_j directly left of v_i.
+ newedge.p1 = v->p;
+ newedge.p2 = v->p;
+ edgeIter = edgeTree.lower_bound(newedge);
+ if (edgeIter == edgeTree.front()) {
+ error = true;
+ break;
+ }
+ edgeIter = edgeIter->prev();
+ // If helper(e_j) is a merge vertex.
+ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
+ // Insert the diagonal connecting v_i to helper(e_j) in D.
+ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
+ vertextypes, edgeTreeIterators, &edgeTree, helpers);
+ }
+ // helper(e_j) <- v_i.
+ helpers[edgeIter->get().index] = vindex;
+ }
+ break;
+ }
+
+ if (error)
+ break;
+ }
+
+ char *used = new char[newnumvertices];
+ memset(used, 0, newnumvertices * sizeof(char));
+
+ if (!error) {
+ // Return result.
+ long size;
+ TPPLPoly mpoly;
+ for (i = 0; i < newnumvertices; i++) {
+ if (used[i]) {
+ continue;
+ }
+ v = &(vertices[i]);
+ vnext = &(vertices[v->next]);
+ size = 1;
+ while (vnext != v) {
+ vnext = &(vertices[vnext->next]);
+ size++;
+ }
+ mpoly.Init(size);
+ v = &(vertices[i]);
+ mpoly[0] = v->p;
+ vnext = &(vertices[v->next]);
+ size = 1;
+ used[i] = 1;
+ used[v->next] = 1;
+ while (vnext != v) {
+ mpoly[size] = vnext->p;
+ used[vnext->next] = 1;
+ vnext = &(vertices[vnext->next]);
+ size++;
+ }
+ monotonePolys->push_back(mpoly);
+ }
+ }
+
+ // Cleanup.
+ delete[] vertices;
+ delete[] priority;
+ delete[] vertextypes;
+ delete[] edgeTreeIterators;
+ delete[] helpers;
+ delete[] used;
+
+ if (error) {
+ return 0;
+ } else {
+ return 1;
+ }
+}
+
+// Adds a diagonal to the doubly-connected list of vertices.
+void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
+ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
+ Set<ScanLineEdge> *edgeTree, long *helpers) {
+ long newindex1, newindex2;
+
+ newindex1 = *numvertices;
+ (*numvertices)++;
+ newindex2 = *numvertices;
+ (*numvertices)++;
+
+ vertices[newindex1].p = vertices[index1].p;
+ vertices[newindex2].p = vertices[index2].p;
+
+ vertices[newindex2].next = vertices[index2].next;
+ vertices[newindex1].next = vertices[index1].next;
+
+ vertices[vertices[index2].next].previous = newindex2;
+ vertices[vertices[index1].next].previous = newindex1;
+
+ vertices[index1].next = newindex2;
+ vertices[newindex2].previous = index1;
+
+ vertices[index2].next = newindex1;
+ vertices[newindex1].previous = index2;
+
+ // Update all relevant structures.
+ vertextypes[newindex1] = vertextypes[index1];
+ edgeTreeIterators[newindex1] = edgeTreeIterators[index1];
+ helpers[newindex1] = helpers[index1];
+ if (edgeTreeIterators[newindex1] != edgeTree->back()) {
+ edgeTreeIterators[newindex1]->get().index = newindex1;
+ }
+ vertextypes[newindex2] = vertextypes[index2];
+ edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
+ helpers[newindex2] = helpers[index2];
+ if (edgeTreeIterators[newindex2] != edgeTree->back()) {
+ edgeTreeIterators[newindex2]->get().index = newindex2;
+ }
+}
+
+bool TPPLPartition::Below(TPPLPoint &p1, TPPLPoint &p2) {
+ if (p1.y < p2.y) {
+ return true;
+ } else if (p1.y == p2.y) {
+ if (p1.x < p2.x) {
+ return true;
+ }
+ }
+ return false;
+}
+
+// Sorts in the falling order of y values, if y is equal, x is used instead.
+bool TPPLPartition::VertexSorter::operator()(long index1, long index2) {
+ if (vertices[index1].p.y > vertices[index2].p.y) {
+ return true;
+ } else if (vertices[index1].p.y == vertices[index2].p.y) {
+ if (vertices[index1].p.x > vertices[index2].p.x) {
+ return true;
+ }
+ }
+ return false;
+}
+
+bool TPPLPartition::ScanLineEdge::IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const {
+ tppl_float tmp;
+ tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
+ if (tmp > 0) {
+ return 1;
+ }
+
+ return 0;
+}
+
+bool TPPLPartition::ScanLineEdge::operator<(const ScanLineEdge &other) const {
+ if (other.p1.y == other.p2.y) {
+ if (p1.y == p2.y) {
+ return (p1.y < other.p1.y);
+ }
+ return IsConvex(p1, p2, other.p1);
+ } else if (p1.y == p2.y) {
+ return !IsConvex(other.p1, other.p2, p1);
+ } else if (p1.y < other.p1.y) {
+ return !IsConvex(other.p1, other.p2, p1);
+ } else {
+ return IsConvex(p1, p2, other.p1);
+ }
+}
+
+// Triangulates monotone polygon.
+// Time complexity: O(n)
+// Space complexity: O(n)
+int TPPLPartition::TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles) {
+ if (!inPoly->Valid()) {
+ return 0;
+ }
+
+ long i, i2, j, topindex, bottomindex, leftindex, rightindex, vindex;
+ TPPLPoint *points = NULL;
+ long numpoints;
+ TPPLPoly triangle;
+
+ numpoints = inPoly->GetNumPoints();
+ points = inPoly->GetPoints();
+
+ // Trivial case.
+ if (numpoints == 3) {
+ triangles->push_back(*inPoly);
+ return 1;
+ }
+
+ topindex = 0;
+ bottomindex = 0;
+ for (i = 1; i < numpoints; i++) {
+ if (Below(points[i], points[bottomindex])) {
+ bottomindex = i;
+ }
+ if (Below(points[topindex], points[i])) {
+ topindex = i;
+ }
+ }
+
+ // Check if the poly is really monotone.
+ i = topindex;
+ while (i != bottomindex) {
+ i2 = i + 1;
+ if (i2 >= numpoints) {
+ i2 = 0;
+ }
+ if (!Below(points[i2], points[i])) {
+ return 0;
+ }
+ i = i2;
+ }
+ i = bottomindex;
+ while (i != topindex) {
+ i2 = i + 1;
+ if (i2 >= numpoints) {
+ i2 = 0;
+ }
+ if (!Below(points[i], points[i2])) {
+ return 0;
+ }
+ i = i2;
+ }
+
+ char *vertextypes = new char[numpoints];
+ long *priority = new long[numpoints];
+
+ // Merge left and right vertex chains.
+ priority[0] = topindex;
+ vertextypes[topindex] = 0;
+ leftindex = topindex + 1;
+ if (leftindex >= numpoints) {
+ leftindex = 0;
+ }
+ rightindex = topindex - 1;
+ if (rightindex < 0) {
+ rightindex = numpoints - 1;
+ }
+ for (i = 1; i < (numpoints - 1); i++) {
+ if (leftindex == bottomindex) {
+ priority[i] = rightindex;
+ rightindex--;
+ if (rightindex < 0) {
+ rightindex = numpoints - 1;
+ }
+ vertextypes[priority[i]] = -1;
+ } else if (rightindex == bottomindex) {
+ priority[i] = leftindex;
+ leftindex++;
+ if (leftindex >= numpoints) {
+ leftindex = 0;
+ }
+ vertextypes[priority[i]] = 1;
+ } else {
+ if (Below(points[leftindex], points[rightindex])) {
+ priority[i] = rightindex;
+ rightindex--;
+ if (rightindex < 0) {
+ rightindex = numpoints - 1;
+ }
+ vertextypes[priority[i]] = -1;
+ } else {
+ priority[i] = leftindex;
+ leftindex++;
+ if (leftindex >= numpoints) {
+ leftindex = 0;
+ }
+ vertextypes[priority[i]] = 1;
+ }
+ }
+ }
+ priority[i] = bottomindex;
+ vertextypes[bottomindex] = 0;
+
+ long *stack = new long[numpoints];
+ long stackptr = 0;
+
+ stack[0] = priority[0];
+ stack[1] = priority[1];
+ stackptr = 2;
+
+ // For each vertex from top to bottom trim as many triangles as possible.
+ for (i = 2; i < (numpoints - 1); i++) {
+ vindex = priority[i];
+ if (vertextypes[vindex] != vertextypes[stack[stackptr - 1]]) {
+ for (j = 0; j < (stackptr - 1); j++) {
+ if (vertextypes[vindex] == 1) {
+ triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]);
+ } else {
+ triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]);
+ }
+ triangles->push_back(triangle);
+ }
+ stack[0] = priority[i - 1];
+ stack[1] = priority[i];
+ stackptr = 2;
+ } else {
+ stackptr--;
+ while (stackptr > 0) {
+ if (vertextypes[vindex] == 1) {
+ if (IsConvex(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]])) {
+ triangle.Triangle(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]]);
+ triangles->push_back(triangle);
+ stackptr--;
+ } else {
+ break;
+ }
+ } else {
+ if (IsConvex(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]])) {
+ triangle.Triangle(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]]);
+ triangles->push_back(triangle);
+ stackptr--;
+ } else {
+ break;
+ }
+ }
+ }
+ stackptr++;
+ stack[stackptr] = vindex;
+ stackptr++;
+ }
+ }
+ vindex = priority[i];
+ for (j = 0; j < (stackptr - 1); j++) {
+ if (vertextypes[stack[j + 1]] == 1) {
+ triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]);
+ } else {
+ triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]);
+ }
+ triangles->push_back(triangle);
+ }
+
+ delete[] priority;
+ delete[] vertextypes;
+ delete[] stack;
+
+ return 1;
+}
+
+int TPPLPartition::Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
+ TPPLPolyList monotone;
+ TPPLPolyList::Element *iter;
+
+ if (!MonotonePartition(inpolys, &monotone)) {
+ return 0;
+ }
+ for (iter = monotone.front(); iter; iter = iter->next()) {
+ if (!TriangulateMonotone(&(iter->get()), triangles)) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+int TPPLPartition::Triangulate_MONO(TPPLPoly *poly, TPPLPolyList *triangles) {
+ TPPLPolyList polys;
+ polys.push_back(*poly);
+
+ return Triangulate_MONO(&polys, triangles);
+}
diff --git a/thirdparty/misc/polypartition.h b/thirdparty/misc/polypartition.h
new file mode 100644
index 0000000000..b2d905a3ef
--- /dev/null
+++ b/thirdparty/misc/polypartition.h
@@ -0,0 +1,378 @@
+/*************************************************************************/
+/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+
+#ifndef POLYPARTITION_H
+#define POLYPARTITION_H
+
+#include "core/math/vector2.h"
+#include "core/templates/list.h"
+#include "core/templates/set.h"
+
+typedef double tppl_float;
+
+enum TPPLOrientation {
+ TPPL_ORIENTATION_CW = -1,
+ TPPL_ORIENTATION_NONE = 0,
+ TPPL_ORIENTATION_CCW = 1,
+};
+
+enum TPPLVertexType {
+ TPPL_VERTEXTYPE_REGULAR = 0,
+ TPPL_VERTEXTYPE_START = 1,
+ TPPL_VERTEXTYPE_END = 2,
+ TPPL_VERTEXTYPE_SPLIT = 3,
+ TPPL_VERTEXTYPE_MERGE = 4,
+};
+
+// 2D point structure.
+typedef Vector2 TPPLPoint;
+
+// Polygon implemented as an array of points with a "hole" flag.
+class TPPLPoly {
+ protected:
+ TPPLPoint *points;
+ long numpoints;
+ bool hole;
+
+ public:
+ // Constructors and destructors.
+ TPPLPoly();
+ ~TPPLPoly();
+
+ TPPLPoly(const TPPLPoly &src);
+ TPPLPoly &operator=(const TPPLPoly &src);
+
+ // Getters and setters.
+ long GetNumPoints() const {
+ return numpoints;
+ }
+
+ bool IsHole() const {
+ return hole;
+ }
+
+ void SetHole(bool hole) {
+ this->hole = hole;
+ }
+
+ TPPLPoint &GetPoint(long i) {
+ return points[i];
+ }
+
+ const TPPLPoint &GetPoint(long i) const {
+ return points[i];
+ }
+
+ TPPLPoint *GetPoints() {
+ return points;
+ }
+
+ TPPLPoint &operator[](int i) {
+ return points[i];
+ }
+
+ const TPPLPoint &operator[](int i) const {
+ return points[i];
+ }
+
+ // Clears the polygon points.
+ void Clear();
+
+ // Inits the polygon with numpoints vertices.
+ void Init(long numpoints);
+
+ // Creates a triangle with points p1, p2, and p3.
+ void Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
+
+ // Inverts the orfer of vertices.
+ void Invert();
+
+ // Returns the orientation of the polygon.
+ // Possible values:
+ // TPPL_ORIENTATION_CCW: Polygon vertices are in counter-clockwise order.
+ // TPPL_ORIENTATION_CW: Polygon vertices are in clockwise order.
+ // TPPL_ORIENTATION_NONE: The polygon has no (measurable) area.
+ TPPLOrientation GetOrientation() const;
+
+ // Sets the polygon orientation.
+ // Possible values:
+ // TPPL_ORIENTATION_CCW: Sets vertices in counter-clockwise order.
+ // TPPL_ORIENTATION_CW: Sets vertices in clockwise order.
+ // TPPL_ORIENTATION_NONE: Reverses the orientation of the vertices if there
+ // is one, otherwise does nothing (if orientation is already NONE).
+ void SetOrientation(TPPLOrientation orientation);
+
+ // Checks whether a polygon is valid or not.
+ inline bool Valid() const { return this->numpoints >= 3; }
+};
+
+#ifdef TPPL_ALLOCATOR
+typedef List<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList;
+#else
+typedef List<TPPLPoly> TPPLPolyList;
+#endif
+
+class TPPLPartition {
+ protected:
+ struct PartitionVertex {
+ bool isActive;
+ bool isConvex;
+ bool isEar;
+
+ TPPLPoint p;
+ tppl_float angle;
+ PartitionVertex *previous;
+ PartitionVertex *next;
+
+ PartitionVertex();
+ };
+
+ struct MonotoneVertex {
+ TPPLPoint p;
+ long previous;
+ long next;
+ };
+
+ class VertexSorter {
+ MonotoneVertex *vertices;
+
+public:
+ VertexSorter(MonotoneVertex *v) :
+ vertices(v) {}
+ bool operator()(long index1, long index2);
+ };
+
+ struct Diagonal {
+ long index1;
+ long index2;
+ };
+
+#ifdef TPPL_ALLOCATOR
+ typedef List<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList;
+#else
+ typedef List<Diagonal> DiagonalList;
+#endif
+
+ // Dynamic programming state for minimum-weight triangulation.
+ struct DPState {
+ bool visible;
+ tppl_float weight;
+ long bestvertex;
+ };
+
+ // Dynamic programming state for convex partitioning.
+ struct DPState2 {
+ bool visible;
+ long weight;
+ DiagonalList pairs;
+ };
+
+ // Edge that intersects the scanline.
+ struct ScanLineEdge {
+ mutable long index;
+ TPPLPoint p1;
+ TPPLPoint p2;
+
+ // Determines if the edge is to the left of another edge.
+ bool operator<(const ScanLineEdge &other) const;
+
+ bool IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const;
+ };
+
+ // Standard helper functions.
+ bool IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
+ bool IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
+ bool IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p);
+
+ bool InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p);
+ bool InCone(PartitionVertex *v, TPPLPoint &p);
+
+ int Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22);
+
+ TPPLPoint Normalize(const TPPLPoint &p);
+ tppl_float Distance(const TPPLPoint &p1, const TPPLPoint &p2);
+
+ // Helper functions for Triangulate_EC.
+ void UpdateVertexReflexity(PartitionVertex *v);
+ void UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices);
+
+ // Helper functions for ConvexPartition_OPT.
+ void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates);
+ void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
+ void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
+
+ // Helper functions for MonotonePartition.
+ bool Below(TPPLPoint &p1, TPPLPoint &p2);
+ void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
+ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
+ Set<ScanLineEdge> *edgeTree, long *helpers);
+
+ // Triangulates a monotone polygon, used in Triangulate_MONO.
+ int TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles);
+
+ public:
+ // Simple heuristic procedure for removing holes from a list of polygons.
+ // It works by creating a diagonal from the right-most hole vertex
+ // to some other visible vertex.
+ // Time complexity: O(h*(n^2)), h is the # of holes, n is the # of vertices.
+ // Space complexity: O(n)
+ // params:
+ // inpolys:
+ // A list of polygons that can contain holes.
+ // Vertices of all non-hole polys have to be in counter-clockwise order.
+ // Vertices of all hole polys have to be in clockwise order.
+ // outpolys:
+ // A list of polygons without holes.
+ // Returns 1 on success, 0 on failure.
+ int RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys);
+
+ // Triangulates a polygon by ear clipping.
+ // Time complexity: O(n^2), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // poly:
+ // An input polygon to be triangulated.
+ // Vertices have to be in counter-clockwise order.
+ // triangles:
+ // A list of triangles (result).
+ // Returns 1 on success, 0 on failure.
+ int Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles);
+
+ // Triangulates a list of polygons that may contain holes by ear clipping
+ // algorithm. It first calls RemoveHoles to get rid of the holes, and then
+ // calls Triangulate_EC for each resulting polygon.
+ // Time complexity: O(h*(n^2)), h is the # of holes, n is the # of vertices.
+ // Space complexity: O(n)
+ // params:
+ // inpolys:
+ // A list of polygons to be triangulated (can contain holes).
+ // Vertices of all non-hole polys have to be in counter-clockwise order.
+ // Vertices of all hole polys have to be in clockwise order.
+ // triangles:
+ // A list of triangles (result).
+ // Returns 1 on success, 0 on failure.
+ int Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles);
+
+ // Creates an optimal polygon triangulation in terms of minimal edge length.
+ // Time complexity: O(n^3), n is the number of vertices
+ // Space complexity: O(n^2)
+ // params:
+ // poly:
+ // An input polygon to be triangulated.
+ // Vertices have to be in counter-clockwise order.
+ // triangles:
+ // A list of triangles (result).
+ // Returns 1 on success, 0 on failure.
+ int Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles);
+
+ // Triangulates a polygon by first partitioning it into monotone polygons.
+ // Time complexity: O(n*log(n)), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // poly:
+ // An input polygon to be triangulated.
+ // Vertices have to be in counter-clockwise order.
+ // triangles:
+ // A list of triangles (result).
+ // Returns 1 on success, 0 on failure.
+ int Triangulate_MONO(TPPLPoly *poly, TPPLPolyList *triangles);
+
+ // Triangulates a list of polygons by first
+ // partitioning them into monotone polygons.
+ // Time complexity: O(n*log(n)), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // inpolys:
+ // A list of polygons to be triangulated (can contain holes).
+ // Vertices of all non-hole polys have to be in counter-clockwise order.
+ // Vertices of all hole polys have to be in clockwise order.
+ // triangles:
+ // A list of triangles (result).
+ // Returns 1 on success, 0 on failure.
+ int Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles);
+
+ // Creates a monotone partition of a list of polygons that
+ // can contain holes. Triangulates a set of polygons by
+ // first partitioning them into monotone polygons.
+ // Time complexity: O(n*log(n)), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // inpolys:
+ // A list of polygons to be triangulated (can contain holes).
+ // Vertices of all non-hole polys have to be in counter-clockwise order.
+ // Vertices of all hole polys have to be in clockwise order.
+ // monotonePolys:
+ // A list of monotone polygons (result).
+ // Returns 1 on success, 0 on failure.
+ int MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys);
+
+ // Partitions a polygon into convex polygons by using the
+ // Hertel-Mehlhorn algorithm. The algorithm gives at most four times
+ // the number of parts as the optimal algorithm, however, in practice
+ // it works much better than that and often gives optimal partition.
+ // It uses triangulation obtained by ear clipping as intermediate result.
+ // Time complexity O(n^2), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // poly:
+ // An input polygon to be partitioned.
+ // Vertices have to be in counter-clockwise order.
+ // parts:
+ // Resulting list of convex polygons.
+ // Returns 1 on success, 0 on failure.
+ int ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts);
+
+ // Partitions a list of polygons into convex parts by using the
+ // Hertel-Mehlhorn algorithm. The algorithm gives at most four times
+ // the number of parts as the optimal algorithm, however, in practice
+ // it works much better than that and often gives optimal partition.
+ // It uses triangulation obtained by ear clipping as intermediate result.
+ // Time complexity O(n^2), n is the number of vertices.
+ // Space complexity: O(n)
+ // params:
+ // inpolys:
+ // An input list of polygons to be partitioned. Vertices of
+ // all non-hole polys have to be in counter-clockwise order.
+ // Vertices of all hole polys have to be in clockwise order.
+ // parts:
+ // Resulting list of convex polygons.
+ // Returns 1 on success, 0 on failure.
+ int ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts);
+
+ // Optimal convex partitioning (in terms of number of resulting
+ // convex polygons) using the Keil-Snoeyink algorithm.
+ // For reference, see M. Keil, J. Snoeyink, "On the time bound for
+ // convex decomposition of simple polygons", 1998.
+ // Time complexity O(n^3), n is the number of vertices.
+ // Space complexity: O(n^3)
+ // params:
+ // poly:
+ // An input polygon to be partitioned.
+ // Vertices have to be in counter-clockwise order.
+ // parts:
+ // Resulting list of convex polygons.
+ // Returns 1 on success, 0 on failure.
+ int ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts);
+};
+
+#endif
diff --git a/thirdparty/misc/triangulator.cpp b/thirdparty/misc/triangulator.cpp
deleted file mode 100644
index d6b63c6638..0000000000
--- a/thirdparty/misc/triangulator.cpp
+++ /dev/null
@@ -1,1550 +0,0 @@
-//Copyright (C) 2011 by Ivan Fratric
-//
-//Permission is hereby granted, free of charge, to any person obtaining a copy
-//of this software and associated documentation files (the "Software"), to deal
-//in the Software without restriction, including without limitation the rights
-//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-//copies of the Software, and to permit persons to whom the Software is
-//furnished to do so, subject to the following conditions:
-//
-//The above copyright notice and this permission notice shall be included in
-//all copies or substantial portions of the Software.
-//
-//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-//THE SOFTWARE.
-
-
-#include <stdio.h>
-#include <string.h>
-#include <math.h>
-
-#include "triangulator.h"
-
-
-#define TRIANGULATOR_VERTEXTYPE_REGULAR 0
-#define TRIANGULATOR_VERTEXTYPE_START 1
-#define TRIANGULATOR_VERTEXTYPE_END 2
-#define TRIANGULATOR_VERTEXTYPE_SPLIT 3
-#define TRIANGULATOR_VERTEXTYPE_MERGE 4
-
-TriangulatorPoly::TriangulatorPoly() {
- hole = false;
- numpoints = 0;
- points = NULL;
-}
-
-TriangulatorPoly::~TriangulatorPoly() {
- if(points) delete [] points;
-}
-
-void TriangulatorPoly::Clear() {
- if(points) delete [] points;
- hole = false;
- numpoints = 0;
- points = NULL;
-}
-
-void TriangulatorPoly::Init(long numpoints) {
- Clear();
- this->numpoints = numpoints;
- points = new Vector2[numpoints];
-}
-
-void TriangulatorPoly::Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3) {
- Init(3);
- points[0] = p1;
- points[1] = p2;
- points[2] = p3;
-}
-
-TriangulatorPoly::TriangulatorPoly(const TriangulatorPoly &src) {
- hole = src.hole;
- numpoints = src.numpoints;
- points = new Vector2[numpoints];
- memcpy(points, src.points, numpoints*sizeof(Vector2));
-}
-
-TriangulatorPoly& TriangulatorPoly::operator=(const TriangulatorPoly &src) {
- Clear();
- hole = src.hole;
- numpoints = src.numpoints;
- points = new Vector2[numpoints];
- memcpy(points, src.points, numpoints*sizeof(Vector2));
- return *this;
-}
-
-int TriangulatorPoly::GetOrientation() {
- long i1,i2;
- real_t area = 0;
- for(i1=0; i1<numpoints; i1++) {
- i2 = i1+1;
- if(i2 == numpoints) i2 = 0;
- area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
- }
- if(area>0) return TRIANGULATOR_CCW;
- if(area<0) return TRIANGULATOR_CW;
- return 0;
-}
-
-void TriangulatorPoly::SetOrientation(int orientation) {
- int polyorientation = GetOrientation();
- if(polyorientation&&(polyorientation!=orientation)) {
- Invert();
- }
-}
-
-void TriangulatorPoly::Invert() {
- long i;
- Vector2 *invpoints;
-
- invpoints = new Vector2[numpoints];
- for(i=0;i<numpoints;i++) {
- invpoints[i] = points[numpoints-i-1];
- }
-
- delete [] points;
- points = invpoints;
-}
-
-Vector2 TriangulatorPartition::Normalize(const Vector2 &p) {
- Vector2 r;
- real_t n = sqrt(p.x*p.x + p.y*p.y);
- if(n!=0) {
- r = p/n;
- } else {
- r.x = 0;
- r.y = 0;
- }
- return r;
-}
-
-real_t TriangulatorPartition::Distance(const Vector2 &p1, const Vector2 &p2) {
- real_t dx,dy;
- dx = p2.x - p1.x;
- dy = p2.y - p1.y;
- return(sqrt(dx*dx + dy*dy));
-}
-
-//checks if two lines intersect
-int TriangulatorPartition::Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22) {
- if((p11.x == p21.x)&&(p11.y == p21.y)) return 0;
- if((p11.x == p22.x)&&(p11.y == p22.y)) return 0;
- if((p12.x == p21.x)&&(p12.y == p21.y)) return 0;
- if((p12.x == p22.x)&&(p12.y == p22.y)) return 0;
-
- Vector2 v1ort,v2ort,v;
- real_t dot11,dot12,dot21,dot22;
-
- v1ort.x = p12.y-p11.y;
- v1ort.y = p11.x-p12.x;
-
- v2ort.x = p22.y-p21.y;
- v2ort.y = p21.x-p22.x;
-
- v = p21-p11;
- dot21 = v.x*v1ort.x + v.y*v1ort.y;
- v = p22-p11;
- dot22 = v.x*v1ort.x + v.y*v1ort.y;
-
- v = p11-p21;
- dot11 = v.x*v2ort.x + v.y*v2ort.y;
- v = p12-p21;
- dot12 = v.x*v2ort.x + v.y*v2ort.y;
-
- if(dot11*dot12>0) return 0;
- if(dot21*dot22>0) return 0;
-
- return 1;
-}
-
-//removes holes from inpolys by merging them with non-holes
-int TriangulatorPartition::RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys) {
- List<TriangulatorPoly> polys;
- List<TriangulatorPoly>::Element *holeiter,*polyiter,*iter,*iter2;
- long i,i2,holepointindex,polypointindex;
- Vector2 holepoint,polypoint,bestpolypoint;
- Vector2 linep1,linep2;
- Vector2 v1,v2;
- TriangulatorPoly newpoly;
- bool hasholes;
- bool pointvisible;
- bool pointfound;
-
- //check for trivial case (no holes)
- hasholes = false;
- for(iter = inpolys->front(); iter; iter=iter->next()) {
- if(iter->get().IsHole()) {
- hasholes = true;
- break;
- }
- }
- if(!hasholes) {
- for(iter = inpolys->front(); iter; iter=iter->next()) {
- outpolys->push_back(iter->get());
- }
- return 1;
- }
-
- polys = *inpolys;
-
- while(1) {
- //find the hole point with the largest x
- hasholes = false;
- for(iter = polys.front(); iter; iter=iter->next()) {
- if(!iter->get().IsHole()) continue;
-
- if(!hasholes) {
- hasholes = true;
- holeiter = iter;
- holepointindex = 0;
- }
-
- for(i=0; i < iter->get().GetNumPoints(); i++) {
- if(iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
- holeiter = iter;
- holepointindex = i;
- }
- }
- }
- if(!hasholes) break;
- holepoint = holeiter->get().GetPoint(holepointindex);
-
- pointfound = false;
- for(iter = polys.front(); iter; iter=iter->next()) {
- if(iter->get().IsHole()) continue;
- for(i=0; i < iter->get().GetNumPoints(); i++) {
- if(iter->get().GetPoint(i).x <= holepoint.x) continue;
- if(!InCone(iter->get().GetPoint((i+iter->get().GetNumPoints()-1)%(iter->get().GetNumPoints())),
- iter->get().GetPoint(i),
- iter->get().GetPoint((i+1)%(iter->get().GetNumPoints())),
- holepoint))
- continue;
- polypoint = iter->get().GetPoint(i);
- if(pointfound) {
- v1 = Normalize(polypoint-holepoint);
- v2 = Normalize(bestpolypoint-holepoint);
- if(v2.x > v1.x) continue;
- }
- pointvisible = true;
- for(iter2 = polys.front(); iter2; iter2=iter2->next()) {
- if(iter2->get().IsHole()) continue;
- for(i2=0; i2 < iter2->get().GetNumPoints(); i2++) {
- linep1 = iter2->get().GetPoint(i2);
- linep2 = iter2->get().GetPoint((i2+1)%(iter2->get().GetNumPoints()));
- if(Intersects(holepoint,polypoint,linep1,linep2)) {
- pointvisible = false;
- break;
- }
- }
- if(!pointvisible) break;
- }
- if(pointvisible) {
- pointfound = true;
- bestpolypoint = polypoint;
- polyiter = iter;
- polypointindex = i;
- }
- }
- }
-
- if(!pointfound) return 0;
-
- newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
- i2 = 0;
- for(i=0;i<=polypointindex;i++) {
- newpoly[i2] = polyiter->get().GetPoint(i);
- i2++;
- }
- for(i=0;i<=holeiter->get().GetNumPoints();i++) {
- newpoly[i2] = holeiter->get().GetPoint((i+holepointindex)%holeiter->get().GetNumPoints());
- i2++;
- }
- for(i=polypointindex;i<polyiter->get().GetNumPoints();i++) {
- newpoly[i2] = polyiter->get().GetPoint(i);
- i2++;
- }
-
- polys.erase(holeiter);
- polys.erase(polyiter);
- polys.push_back(newpoly);
- }
-
- for(iter = polys.front(); iter; iter=iter->next()) {
- outpolys->push_back(iter->get());
- }
-
- return 1;
-}
-
-bool TriangulatorPartition::IsConvex(Vector2& p1, Vector2& p2, Vector2& p3) {
- real_t tmp;
- tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
- if(tmp>0) return 1;
- else return 0;
-}
-
-bool TriangulatorPartition::IsReflex(Vector2& p1, Vector2& p2, Vector2& p3) {
- real_t tmp;
- tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
- if(tmp<0) return 1;
- else return 0;
-}
-
-bool TriangulatorPartition::IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p) {
- if(IsConvex(p1,p,p2)) return false;
- if(IsConvex(p2,p,p3)) return false;
- if(IsConvex(p3,p,p1)) return false;
- return true;
-}
-
-bool TriangulatorPartition::InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p) {
- bool convex;
-
- convex = IsConvex(p1,p2,p3);
-
- if(convex) {
- if(!IsConvex(p1,p2,p)) return false;
- if(!IsConvex(p2,p3,p)) return false;
- return true;
- } else {
- if(IsConvex(p1,p2,p)) return true;
- if(IsConvex(p2,p3,p)) return true;
- return false;
- }
-}
-
-bool TriangulatorPartition::InCone(PartitionVertex *v, Vector2 &p) {
- Vector2 p1,p2,p3;
-
- p1 = v->previous->p;
- p2 = v->p;
- p3 = v->next->p;
-
- return InCone(p1,p2,p3,p);
-}
-
-void TriangulatorPartition::UpdateVertexReflexity(PartitionVertex *v) {
- PartitionVertex *v1,*v3;
- v1 = v->previous;
- v3 = v->next;
- v->isConvex = !IsReflex(v1->p,v->p,v3->p);
-}
-
-void TriangulatorPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
- long i;
- PartitionVertex *v1,*v3;
- Vector2 vec1,vec3;
-
- v1 = v->previous;
- v3 = v->next;
-
- v->isConvex = IsConvex(v1->p,v->p,v3->p);
-
- vec1 = Normalize(v1->p - v->p);
- vec3 = Normalize(v3->p - v->p);
- v->angle = vec1.x*vec3.x + vec1.y*vec3.y;
-
- if(v->isConvex) {
- v->isEar = true;
- for(i=0;i<numvertices;i++) {
- if((vertices[i].p.x==v->p.x)&&(vertices[i].p.y==v->p.y)) continue;
- if((vertices[i].p.x==v1->p.x)&&(vertices[i].p.y==v1->p.y)) continue;
- if((vertices[i].p.x==v3->p.x)&&(vertices[i].p.y==v3->p.y)) continue;
- if(IsInside(v1->p,v->p,v3->p,vertices[i].p)) {
- v->isEar = false;
- break;
- }
- }
- } else {
- v->isEar = false;
- }
-}
-
-//triangulation by ear removal
-int TriangulatorPartition::Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
- long numvertices;
- PartitionVertex *vertices;
- PartitionVertex *ear;
- TriangulatorPoly triangle;
- long i,j;
- bool earfound;
-
- if(poly->GetNumPoints() < 3) return 0;
- if(poly->GetNumPoints() == 3) {
- triangles->push_back(*poly);
- return 1;
- }
-
- numvertices = poly->GetNumPoints();
-
- vertices = new PartitionVertex[numvertices];
- for(i=0;i<numvertices;i++) {
- vertices[i].isActive = true;
- vertices[i].p = poly->GetPoint(i);
- if(i==(numvertices-1)) vertices[i].next=&(vertices[0]);
- else vertices[i].next=&(vertices[i+1]);
- if(i==0) vertices[i].previous = &(vertices[numvertices-1]);
- else vertices[i].previous = &(vertices[i-1]);
- }
- for(i=0;i<numvertices;i++) {
- UpdateVertex(&vertices[i],vertices,numvertices);
- }
-
- for(i=0;i<numvertices-3;i++) {
- earfound = false;
- //find the most extruded ear
- for(j=0;j<numvertices;j++) {
- if(!vertices[j].isActive) continue;
- if(!vertices[j].isEar) continue;
- if(!earfound) {
- earfound = true;
- ear = &(vertices[j]);
- } else {
- if(vertices[j].angle > ear->angle) {
- ear = &(vertices[j]);
- }
- }
- }
- if(!earfound) {
- delete [] vertices;
- return 0;
- }
-
- triangle.Triangle(ear->previous->p,ear->p,ear->next->p);
- triangles->push_back(triangle);
-
- ear->isActive = false;
- ear->previous->next = ear->next;
- ear->next->previous = ear->previous;
-
- if(i==numvertices-4) break;
-
- UpdateVertex(ear->previous,vertices,numvertices);
- UpdateVertex(ear->next,vertices,numvertices);
- }
- for(i=0;i<numvertices;i++) {
- if(vertices[i].isActive) {
- triangle.Triangle(vertices[i].previous->p,vertices[i].p,vertices[i].next->p);
- triangles->push_back(triangle);
- break;
- }
- }
-
- delete [] vertices;
-
- return 1;
-}
-
-int TriangulatorPartition::Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) {
- List<TriangulatorPoly> outpolys;
- List<TriangulatorPoly>::Element*iter;
-
- if(!RemoveHoles(inpolys,&outpolys)) return 0;
- for(iter=outpolys.front();iter;iter=iter->next()) {
- if(!Triangulate_EC(&(iter->get()),triangles)) return 0;
- }
- return 1;
-}
-
-int TriangulatorPartition::ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) {
- List<TriangulatorPoly> triangles;
- List<TriangulatorPoly>::Element *iter1,*iter2;
- TriangulatorPoly *poly1,*poly2;
- TriangulatorPoly newpoly;
- Vector2 d1,d2,p1,p2,p3;
- long i11,i12,i21,i22,i13,i23,j,k;
- bool isdiagonal;
- long numreflex;
-
- //check if the poly is already convex
- numreflex = 0;
- for(i11=0;i11<poly->GetNumPoints();i11++) {
- if(i11==0) i12 = poly->GetNumPoints()-1;
- else i12=i11-1;
- if(i11==(poly->GetNumPoints()-1)) i13=0;
- else i13=i11+1;
- if(IsReflex(poly->GetPoint(i12),poly->GetPoint(i11),poly->GetPoint(i13))) {
- numreflex = 1;
- break;
- }
- }
- if(numreflex == 0) {
- parts->push_back(*poly);
- return 1;
- }
-
- if(!Triangulate_EC(poly,&triangles)) return 0;
-
- for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) {
- poly1 = &(iter1->get());
- for(i11=0;i11<poly1->GetNumPoints();i11++) {
- d1 = poly1->GetPoint(i11);
- i12 = (i11+1)%(poly1->GetNumPoints());
- d2 = poly1->GetPoint(i12);
-
- isdiagonal = false;
- for(iter2 = iter1; iter2 ; iter2=iter2->next()) {
- if(iter1 == iter2) continue;
- poly2 = &(iter2->get());
-
- for(i21=0;i21<poly2->GetNumPoints();i21++) {
- if((d2.x != poly2->GetPoint(i21).x)||(d2.y != poly2->GetPoint(i21).y)) continue;
- i22 = (i21+1)%(poly2->GetNumPoints());
- if((d1.x != poly2->GetPoint(i22).x)||(d1.y != poly2->GetPoint(i22).y)) continue;
- isdiagonal = true;
- break;
- }
- if(isdiagonal) break;
- }
-
- if(!isdiagonal) continue;
-
- p2 = poly1->GetPoint(i11);
- if(i11 == 0) i13 = poly1->GetNumPoints()-1;
- else i13 = i11-1;
- p1 = poly1->GetPoint(i13);
- if(i22 == (poly2->GetNumPoints()-1)) i23 = 0;
- else i23 = i22+1;
- p3 = poly2->GetPoint(i23);
-
- if(!IsConvex(p1,p2,p3)) continue;
-
- p2 = poly1->GetPoint(i12);
- if(i12 == (poly1->GetNumPoints()-1)) i13 = 0;
- else i13 = i12+1;
- p3 = poly1->GetPoint(i13);
- if(i21 == 0) i23 = poly2->GetNumPoints()-1;
- else i23 = i21-1;
- p1 = poly2->GetPoint(i23);
-
- if(!IsConvex(p1,p2,p3)) continue;
-
- newpoly.Init(poly1->GetNumPoints()+poly2->GetNumPoints()-2);
- k = 0;
- for(j=i12;j!=i11;j=(j+1)%(poly1->GetNumPoints())) {
- newpoly[k] = poly1->GetPoint(j);
- k++;
- }
- for(j=i22;j!=i21;j=(j+1)%(poly2->GetNumPoints())) {
- newpoly[k] = poly2->GetPoint(j);
- k++;
- }
-
- triangles.erase(iter2);
- iter1->get() = newpoly;
- poly1 = &(iter1->get());
- i11 = -1;
-
- continue;
- }
- }
-
- for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) {
- parts->push_back(iter1->get());
- }
-
- return 1;
-}
-
-int TriangulatorPartition::ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts) {
- List<TriangulatorPoly> outpolys;
- List<TriangulatorPoly>::Element* iter;
-
- if(!RemoveHoles(inpolys,&outpolys)) return 0;
- for(iter=outpolys.front();iter;iter=iter->next()) {
- if(!ConvexPartition_HM(&(iter->get()),parts)) return 0;
- }
- return 1;
-}
-
-//minimum-weight polygon triangulation by dynamic programming
-//O(n^3) time complexity
-//O(n^2) space complexity
-int TriangulatorPartition::Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
- long i,j,k,gap,n;
- DPState **dpstates;
- Vector2 p1,p2,p3,p4;
- long bestvertex;
- real_t weight,minweight,d1,d2;
- Diagonal diagonal,newdiagonal;
- List<Diagonal> diagonals;
- TriangulatorPoly triangle;
- int ret = 1;
-
- n = poly->GetNumPoints();
- dpstates = new DPState *[n];
- for(i=1;i<n;i++) {
- dpstates[i] = new DPState[i];
- }
-
- //init states and visibility
- for(i=0;i<(n-1);i++) {
- p1 = poly->GetPoint(i);
- for(j=i+1;j<n;j++) {
- dpstates[j][i].visible = true;
- dpstates[j][i].weight = 0;
- dpstates[j][i].bestvertex = -1;
- if(j!=(i+1)) {
- p2 = poly->GetPoint(j);
-
- //visibility check
- if(i==0) p3 = poly->GetPoint(n-1);
- else p3 = poly->GetPoint(i-1);
- if(i==(n-1)) p4 = poly->GetPoint(0);
- else p4 = poly->GetPoint(i+1);
- if(!InCone(p3,p1,p4,p2)) {
- dpstates[j][i].visible = false;
- continue;
- }
-
- if(j==0) p3 = poly->GetPoint(n-1);
- else p3 = poly->GetPoint(j-1);
- if(j==(n-1)) p4 = poly->GetPoint(0);
- else p4 = poly->GetPoint(j+1);
- if(!InCone(p3,p2,p4,p1)) {
- dpstates[j][i].visible = false;
- continue;
- }
-
- for(k=0;k<n;k++) {
- p3 = poly->GetPoint(k);
- if(k==(n-1)) p4 = poly->GetPoint(0);
- else p4 = poly->GetPoint(k+1);
- if(Intersects(p1,p2,p3,p4)) {
- dpstates[j][i].visible = false;
- break;
- }
- }
- }
- }
- }
- dpstates[n-1][0].visible = true;
- dpstates[n-1][0].weight = 0;
- dpstates[n-1][0].bestvertex = -1;
-
- for(gap = 2; gap<n; gap++) {
- for(i=0; i<(n-gap); i++) {
- j = i+gap;
- if(!dpstates[j][i].visible) continue;
- bestvertex = -1;
- for(k=(i+1);k<j;k++) {
- if(!dpstates[k][i].visible) continue;
- if(!dpstates[j][k].visible) continue;
-
- if(k<=(i+1)) d1=0;
- else d1 = Distance(poly->GetPoint(i),poly->GetPoint(k));
- if(j<=(k+1)) d2=0;
- else d2 = Distance(poly->GetPoint(k),poly->GetPoint(j));
-
- weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2;
-
- if((bestvertex == -1)||(weight<minweight)) {
- bestvertex = k;
- minweight = weight;
- }
- }
- if(bestvertex == -1) {
- for(i=1;i<n;i++) {
- delete [] dpstates[i];
- }
- delete [] dpstates;
-
- return 0;
- }
-
- dpstates[j][i].bestvertex = bestvertex;
- dpstates[j][i].weight = minweight;
- }
- }
-
- newdiagonal.index1 = 0;
- newdiagonal.index2 = n-1;
- diagonals.push_back(newdiagonal);
- while(!diagonals.is_empty()) {
- diagonal = (diagonals.front()->get());
- diagonals.pop_front();
- bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex;
- if(bestvertex == -1) {
- ret = 0;
- break;
- }
- triangle.Triangle(poly->GetPoint(diagonal.index1),poly->GetPoint(bestvertex),poly->GetPoint(diagonal.index2));
- triangles->push_back(triangle);
- if(bestvertex > (diagonal.index1+1)) {
- newdiagonal.index1 = diagonal.index1;
- newdiagonal.index2 = bestvertex;
- diagonals.push_back(newdiagonal);
- }
- if(diagonal.index2 > (bestvertex+1)) {
- newdiagonal.index1 = bestvertex;
- newdiagonal.index2 = diagonal.index2;
- diagonals.push_back(newdiagonal);
- }
- }
-
- for(i=1;i<n;i++) {
- delete [] dpstates[i];
- }
- delete [] dpstates;
-
- return ret;
-}
-
-void TriangulatorPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) {
- Diagonal newdiagonal;
- List<Diagonal> *pairs;
- long w2;
-
- w2 = dpstates[a][b].weight;
- if(w>w2) return;
-
- pairs = &(dpstates[a][b].pairs);
- newdiagonal.index1 = i;
- newdiagonal.index2 = j;
-
- if(w<w2) {
- pairs->clear();
- pairs->push_front(newdiagonal);
- dpstates[a][b].weight = w;
- } else {
- if((!pairs->is_empty())&&(i <= pairs->front()->get().index1)) return;
- while((!pairs->is_empty())&&(pairs->front()->get().index2 >= j)) pairs->pop_front();
- pairs->push_front(newdiagonal);
- }
-}
-
-void TriangulatorPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
- List<Diagonal> *pairs;
- List<Diagonal>::Element *iter,*lastiter;
- long top;
- long w;
-
- if(!dpstates[i][j].visible) return;
- top = j;
- w = dpstates[i][j].weight;
- if(k-j > 1) {
- if (!dpstates[j][k].visible) return;
- w += dpstates[j][k].weight + 1;
- }
- if(j-i > 1) {
- pairs = &(dpstates[i][j].pairs);
- iter = NULL;
- lastiter = NULL;
- while(iter!=pairs->front()) {
- if (!iter)
- iter=pairs->back();
- else
- iter=iter->prev();
-
- if(!IsReflex(vertices[iter->get().index2].p,vertices[j].p,vertices[k].p)) lastiter = iter;
- else break;
- }
- if(lastiter == NULL) w++;
- else {
- if(IsReflex(vertices[k].p,vertices[i].p,vertices[lastiter->get().index1].p)) w++;
- else top = lastiter->get().index1;
- }
- }
- UpdateState(i,k,w,top,j,dpstates);
-}
-
-void TriangulatorPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
- List<Diagonal> *pairs;
- List<Diagonal>::Element* iter,*lastiter;
- long top;
- long w;
-
- if(!dpstates[j][k].visible) return;
- top = j;
- w = dpstates[j][k].weight;
-
- if (j-i > 1) {
- if (!dpstates[i][j].visible) return;
- w += dpstates[i][j].weight + 1;
- }
- if (k-j > 1) {
- pairs = &(dpstates[j][k].pairs);
-
- iter = pairs->front();
- if((!pairs->is_empty())&&(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p))) {
- lastiter = iter;
- while(iter!=NULL) {
- if(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p)) {
- lastiter = iter;
- iter=iter->next();
- }
- else break;
- }
- if(IsReflex(vertices[lastiter->get().index2].p,vertices[k].p,vertices[i].p)) w++;
- else top = lastiter->get().index2;
- } else w++;
- }
- UpdateState(i,k,w,j,top,dpstates);
-}
-
-int TriangulatorPartition::ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) {
- Vector2 p1,p2,p3,p4;
- PartitionVertex *vertices;
- DPState2 **dpstates;
- long i,j,k,n,gap;
- List<Diagonal> diagonals,diagonals2;
- Diagonal diagonal,newdiagonal;
- List<Diagonal> *pairs,*pairs2;
- List<Diagonal>::Element* iter,*iter2;
- int ret;
- TriangulatorPoly newpoly;
- List<long> indices;
- List<long>::Element* iiter;
- bool ijreal,jkreal;
-
- n = poly->GetNumPoints();
- vertices = new PartitionVertex[n];
-
- dpstates = new DPState2 *[n];
- for(i=0;i<n;i++) {
- dpstates[i] = new DPState2[n];
- }
-
- //init vertex information
- for(i=0;i<n;i++) {
- vertices[i].p = poly->GetPoint(i);
- vertices[i].isActive = true;
- if(i==0) vertices[i].previous = &(vertices[n-1]);
- else vertices[i].previous = &(vertices[i-1]);
- if(i==(poly->GetNumPoints()-1)) vertices[i].next = &(vertices[0]);
- else vertices[i].next = &(vertices[i+1]);
- }
- for(i=1;i<n;i++) {
- UpdateVertexReflexity(&(vertices[i]));
- }
-
- //init states and visibility
- for(i=0;i<(n-1);i++) {
- p1 = poly->GetPoint(i);
- for(j=i+1;j<n;j++) {
- dpstates[i][j].visible = true;
- if(j==i+1) {
- dpstates[i][j].weight = 0;
- } else {
- dpstates[i][j].weight = 2147483647;
- }
- if(j!=(i+1)) {
- p2 = poly->GetPoint(j);
-
- //visibility check
- if(!InCone(&vertices[i],p2)) {
- dpstates[i][j].visible = false;
- continue;
- }
- if(!InCone(&vertices[j],p1)) {
- dpstates[i][j].visible = false;
- continue;
- }
-
- for(k=0;k<n;k++) {
- p3 = poly->GetPoint(k);
- if(k==(n-1)) p4 = poly->GetPoint(0);
- else p4 = poly->GetPoint(k+1);
- if(Intersects(p1,p2,p3,p4)) {
- dpstates[i][j].visible = false;
- break;
- }
- }
- }
- }
- }
- for(i=0;i<(n-2);i++) {
- j = i+2;
- if(dpstates[i][j].visible) {
- dpstates[i][j].weight = 0;
- newdiagonal.index1 = i+1;
- newdiagonal.index2 = i+1;
- dpstates[i][j].pairs.push_back(newdiagonal);
- }
- }
-
- dpstates[0][n-1].visible = true;
- vertices[0].isConvex = false; //by convention
-
- for(gap=3; gap<n; gap++) {
- for(i=0;i<n-gap;i++) {
- if(vertices[i].isConvex) continue;
- k = i+gap;
- if(dpstates[i][k].visible) {
- if(!vertices[k].isConvex) {
- for(j=i+1;j<k;j++) TypeA(i,j,k,vertices,dpstates);
- } else {
- for(j=i+1;j<(k-1);j++) {
- if(vertices[j].isConvex) continue;
- TypeA(i,j,k,vertices,dpstates);
- }
- TypeA(i,k-1,k,vertices,dpstates);
- }
- }
- }
- for(k=gap;k<n;k++) {
- if(vertices[k].isConvex) continue;
- i = k-gap;
- if((vertices[i].isConvex)&&(dpstates[i][k].visible)) {
- TypeB(i,i+1,k,vertices,dpstates);
- for(j=i+2;j<k;j++) {
- if(vertices[j].isConvex) continue;
- TypeB(i,j,k,vertices,dpstates);
- }
- }
- }
- }
-
-
- //recover solution
- ret = 1;
- newdiagonal.index1 = 0;
- newdiagonal.index2 = n-1;
- diagonals.push_front(newdiagonal);
- while(!diagonals.is_empty()) {
- diagonal = (diagonals.front()->get());
- diagonals.pop_front();
- if((diagonal.index2 - diagonal.index1) <=1) continue;
- pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
- if(pairs->is_empty()) {
- ret = 0;
- break;
- }
- if(!vertices[diagonal.index1].isConvex) {
- iter = pairs->back();
-
- j = iter->get().index2;
- newdiagonal.index1 = j;
- newdiagonal.index2 = diagonal.index2;
- diagonals.push_front(newdiagonal);
- if((j - diagonal.index1)>1) {
- if(iter->get().index1 != iter->get().index2) {
- pairs2 = &(dpstates[diagonal.index1][j].pairs);
- while(1) {
- if(pairs2->is_empty()) {
- ret = 0;
- break;
- }
- iter2 = pairs2->back();
-
- if(iter->get().index1 != iter2->get().index1) pairs2->pop_back();
- else break;
- }
- if(ret == 0) break;
- }
- newdiagonal.index1 = diagonal.index1;
- newdiagonal.index2 = j;
- diagonals.push_front(newdiagonal);
- }
- } else {
- iter = pairs->front();
- j = iter->get().index1;
- newdiagonal.index1 = diagonal.index1;
- newdiagonal.index2 = j;
- diagonals.push_front(newdiagonal);
- if((diagonal.index2 - j) > 1) {
- if(iter->get().index1 != iter->get().index2) {
- pairs2 = &(dpstates[j][diagonal.index2].pairs);
- while(1) {
- if(pairs2->is_empty()) {
- ret = 0;
- break;
- }
- iter2 = pairs2->front();
- if(iter->get().index2 != iter2->get().index2) pairs2->pop_front();
- else break;
- }
- if(ret == 0) break;
- }
- newdiagonal.index1 = j;
- newdiagonal.index2 = diagonal.index2;
- diagonals.push_front(newdiagonal);
- }
- }
- }
-
- if(ret == 0) {
- for(i=0;i<n;i++) {
- delete [] dpstates[i];
- }
- delete [] dpstates;
- delete [] vertices;
-
- return ret;
- }
-
- newdiagonal.index1 = 0;
- newdiagonal.index2 = n-1;
- diagonals.push_front(newdiagonal);
- while(!diagonals.is_empty()) {
- diagonal = (diagonals.front())->get();
- diagonals.pop_front();
- if((diagonal.index2 - diagonal.index1) <= 1) continue;
-
- indices.clear();
- diagonals2.clear();
- indices.push_back(diagonal.index1);
- indices.push_back(diagonal.index2);
- diagonals2.push_front(diagonal);
-
- while(!diagonals2.is_empty()) {
- diagonal = (diagonals2.front()->get());
- diagonals2.pop_front();
- if((diagonal.index2 - diagonal.index1) <= 1) continue;
- ijreal = true;
- jkreal = true;
- pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
- if(!vertices[diagonal.index1].isConvex) {
- iter = pairs->back();
- j = iter->get().index2;
- if(iter->get().index1 != iter->get().index2) ijreal = false;
- } else {
- iter = pairs->front();
- j = iter->get().index1;
- if(iter->get().index1 != iter->get().index2) jkreal = false;
- }
-
- newdiagonal.index1 = diagonal.index1;
- newdiagonal.index2 = j;
- if(ijreal) {
- diagonals.push_back(newdiagonal);
- } else {
- diagonals2.push_back(newdiagonal);
- }
-
- newdiagonal.index1 = j;
- newdiagonal.index2 = diagonal.index2;
- if(jkreal) {
- diagonals.push_back(newdiagonal);
- } else {
- diagonals2.push_back(newdiagonal);
- }
-
- indices.push_back(j);
- }
-
- indices.sort();
- newpoly.Init((long)indices.size());
- k=0;
- for(iiter = indices.front();iiter;iiter=iiter->next()) {
- newpoly[k] = vertices[iiter->get()].p;
- k++;
- }
- parts->push_back(newpoly);
- }
-
- for(i=0;i<n;i++) {
- delete [] dpstates[i];
- }
- delete [] dpstates;
- delete [] vertices;
-
- return ret;
-}
-
-//triangulates a set of polygons by first partitioning them into monotone polygons
-//O(n*log(n)) time complexity, O(n) space complexity
-//the algorithm used here is outlined in the book
-//"Computational Geometry: Algorithms and Applications"
-//by Mark de Berg, Otfried Cheong, Marc van Kreveld and Mark Overmars
-int TriangulatorPartition::MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys) {
- List<TriangulatorPoly>::Element *iter;
- MonotoneVertex *vertices;
- long i,numvertices,vindex,vindex2,newnumvertices,maxnumvertices;
- long polystartindex, polyendindex;
- TriangulatorPoly *poly;
- MonotoneVertex *v,*v2,*vprev,*vnext;
- ScanLineEdge newedge;
- bool error = false;
-
- numvertices = 0;
- for(iter = inpolys->front(); iter ; iter=iter->next()) {
- numvertices += iter->get().GetNumPoints();
- }
-
- maxnumvertices = numvertices*3;
- vertices = new MonotoneVertex[maxnumvertices];
- newnumvertices = numvertices;
-
- polystartindex = 0;
- for(iter = inpolys->front(); iter ; iter=iter->next()) {
- poly = &(iter->get());
- polyendindex = polystartindex + poly->GetNumPoints()-1;
- for(i=0;i<poly->GetNumPoints();i++) {
- vertices[i+polystartindex].p = poly->GetPoint(i);
- if(i==0) vertices[i+polystartindex].previous = polyendindex;
- else vertices[i+polystartindex].previous = i+polystartindex-1;
- if(i==(poly->GetNumPoints()-1)) vertices[i+polystartindex].next = polystartindex;
- else vertices[i+polystartindex].next = i+polystartindex+1;
- }
- polystartindex = polyendindex+1;
- }
-
- //construct the priority queue
- long *priority = new long [numvertices];
- for(i=0;i<numvertices;i++) priority[i] = i;
- SortArray<long,VertexSorter> sorter;
- sorter.compare.vertices=vertices;
- sorter.sort(priority,numvertices);
-
- //determine vertex types
- char *vertextypes = new char[maxnumvertices];
- for(i=0;i<numvertices;i++) {
- v = &(vertices[i]);
- vprev = &(vertices[v->previous]);
- vnext = &(vertices[v->next]);
-
- if(Below(vprev->p,v->p)&&Below(vnext->p,v->p)) {
- if(IsConvex(vnext->p,vprev->p,v->p)) {
- vertextypes[i] = TRIANGULATOR_VERTEXTYPE_START;
- } else {
- vertextypes[i] = TRIANGULATOR_VERTEXTYPE_SPLIT;
- }
- } else if(Below(v->p,vprev->p)&&Below(v->p,vnext->p)) {
- if(IsConvex(vnext->p,vprev->p,v->p))
- {
- vertextypes[i] = TRIANGULATOR_VERTEXTYPE_END;
- } else {
- vertextypes[i] = TRIANGULATOR_VERTEXTYPE_MERGE;
- }
- } else {
- vertextypes[i] = TRIANGULATOR_VERTEXTYPE_REGULAR;
- }
- }
-
- //helpers
- long *helpers = new long[maxnumvertices];
-
- //binary search tree that holds edges intersecting the scanline
- //note that while set doesn't actually have to be implemented as a tree
- //complexity requirements for operations are the same as for the balanced binary search tree
- Set<ScanLineEdge> edgeTree;
- //store iterators to the edge tree elements
- //this makes deleting existing edges much faster
- Set<ScanLineEdge>::Element **edgeTreeIterators,*edgeIter;
- edgeTreeIterators = new Set<ScanLineEdge>::Element*[maxnumvertices];
- //Pair<Set<ScanLineEdge>::Element*,bool> edgeTreeRet;
- for(i = 0; i<numvertices; i++) edgeTreeIterators[i] = NULL;
-
- //for each vertex
- for(i=0;i<numvertices;i++) {
- vindex = priority[i];
- v = &(vertices[vindex]);
- vindex2 = vindex;
- v2 = v;
-
- //depending on the vertex type, do the appropriate action
- //comments in the following sections are copied from "Computational Geometry: Algorithms and Applications"
- switch(vertextypes[vindex]) {
- case TRIANGULATOR_VERTEXTYPE_START:
- //Insert ei in T and set helper(ei) to vi.
- newedge.p1 = v->p;
- newedge.p2 = vertices[v->next].p;
- newedge.index = vindex;
- edgeTreeIterators[vindex] = edgeTree.insert(newedge);
- helpers[vindex] = vindex;
- break;
-
- case TRIANGULATOR_VERTEXTYPE_END:
- //if helper(ei-1) is a merge vertex
- if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
- //Insert the diagonal connecting vi to helper(ei-1) in D.
- AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- }
- //Delete ei-1 from T
- edgeTree.erase(edgeTreeIterators[v->previous]);
- break;
-
- case TRIANGULATOR_VERTEXTYPE_SPLIT:
- //Search in T to find the edge e j directly left of vi.
- newedge.p1 = v->p;
- newedge.p2 = v->p;
- edgeIter = edgeTree.lower_bound(newedge);
- if(edgeIter == edgeTree.front()) {
- error = true;
- break;
- }
- edgeIter=edgeIter->prev();
- //Insert the diagonal connecting vi to helper(ej) in D.
- AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- vindex2 = newnumvertices-2;
- v2 = &(vertices[vindex2]);
- //helper(e j)�vi
- helpers[edgeIter->get().index] = vindex;
- //Insert ei in T and set helper(ei) to vi.
- newedge.p1 = v2->p;
- newedge.p2 = vertices[v2->next].p;
- newedge.index = vindex2;
-
- edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
- helpers[vindex2] = vindex2;
- break;
-
- case TRIANGULATOR_VERTEXTYPE_MERGE:
- //if helper(ei-1) is a merge vertex
- if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
- //Insert the diagonal connecting vi to helper(ei-1) in D.
- AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- vindex2 = newnumvertices-2;
- v2 = &(vertices[vindex2]);
- }
- //Delete ei-1 from T.
- edgeTree.erase(edgeTreeIterators[v->previous]);
- //Search in T to find the edge e j directly left of vi.
- newedge.p1 = v->p;
- newedge.p2 = v->p;
- edgeIter = edgeTree.lower_bound(newedge);
- if(edgeIter == edgeTree.front()) {
- error = true;
- break;
- }
- edgeIter=edgeIter->prev();
- //if helper(ej) is a merge vertex
- if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
- //Insert the diagonal connecting vi to helper(e j) in D.
- AddDiagonal(vertices,&newnumvertices,vindex2,helpers[edgeIter->get().index],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- }
- //helper(e j)�vi
- helpers[edgeIter->get().index] = vindex2;
- break;
-
- case TRIANGULATOR_VERTEXTYPE_REGULAR:
- //if the interior of P lies to the right of vi
- if(Below(v->p,vertices[v->previous].p)) {
- //if helper(ei-1) is a merge vertex
- if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
- //Insert the diagonal connecting vi to helper(ei-1) in D.
- AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- vindex2 = newnumvertices-2;
- v2 = &(vertices[vindex2]);
- }
- //Delete ei-1 from T.
- edgeTree.erase(edgeTreeIterators[v->previous]);
- //Insert ei in T and set helper(ei) to vi.
- newedge.p1 = v2->p;
- newedge.p2 = vertices[v2->next].p;
- newedge.index = vindex2;
- edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
- helpers[vindex2] = vindex;
- } else {
- //Search in T to find the edge ej directly left of vi.
- newedge.p1 = v->p;
- newedge.p2 = v->p;
- edgeIter = edgeTree.lower_bound(newedge);
- if(edgeIter == edgeTree.front()) {
- error = true;
- break;
- }
- edgeIter=edgeIter->prev();
- //if helper(ej) is a merge vertex
- if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
- //Insert the diagonal connecting vi to helper(e j) in D.
- AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index],
- vertextypes, edgeTreeIterators, &edgeTree, helpers);
- }
- //helper(e j)�vi
- helpers[edgeIter->get().index] = vindex;
- }
- break;
- }
-
- if(error) break;
- }
-
- char *used = new char[newnumvertices];
- memset(used,0,newnumvertices*sizeof(char));
-
- if(!error) {
- //return result
- long size;
- TriangulatorPoly mpoly;
- for(i=0;i<newnumvertices;i++) {
- if(used[i]) continue;
- v = &(vertices[i]);
- vnext = &(vertices[v->next]);
- size = 1;
- while(vnext!=v) {
- vnext = &(vertices[vnext->next]);
- size++;
- }
- mpoly.Init(size);
- v = &(vertices[i]);
- mpoly[0] = v->p;
- vnext = &(vertices[v->next]);
- size = 1;
- used[i] = 1;
- used[v->next] = 1;
- while(vnext!=v) {
- mpoly[size] = vnext->p;
- used[vnext->next] = 1;
- vnext = &(vertices[vnext->next]);
- size++;
- }
- monotonePolys->push_back(mpoly);
- }
- }
-
- //cleanup
- delete [] vertices;
- delete [] priority;
- delete [] vertextypes;
- delete [] edgeTreeIterators;
- delete [] helpers;
- delete [] used;
-
- if(error) {
- return 0;
- } else {
- return 1;
- }
-}
-
-//adds a diagonal to the doubly-connected list of vertices
-void TriangulatorPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
- char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
- Set<ScanLineEdge> *edgeTree, long *helpers)
-{
- long newindex1,newindex2;
-
- newindex1 = *numvertices;
- (*numvertices)++;
- newindex2 = *numvertices;
- (*numvertices)++;
-
- vertices[newindex1].p = vertices[index1].p;
- vertices[newindex2].p = vertices[index2].p;
-
- vertices[newindex2].next = vertices[index2].next;
- vertices[newindex1].next = vertices[index1].next;
-
- vertices[vertices[index2].next].previous = newindex2;
- vertices[vertices[index1].next].previous = newindex1;
-
- vertices[index1].next = newindex2;
- vertices[newindex2].previous = index1;
-
- vertices[index2].next = newindex1;
- vertices[newindex1].previous = index2;
-
- //update all relevant structures
- vertextypes[newindex1] = vertextypes[index1];
- edgeTreeIterators[newindex1] = edgeTreeIterators[index1];
- helpers[newindex1] = helpers[index1];
- if(edgeTreeIterators[newindex1] != NULL)
- edgeTreeIterators[newindex1]->get().index = newindex1;
- vertextypes[newindex2] = vertextypes[index2];
- edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
- helpers[newindex2] = helpers[index2];
- if(edgeTreeIterators[newindex2] != NULL)
- edgeTreeIterators[newindex2]->get().index = newindex2;
-}
-
-bool TriangulatorPartition::Below(Vector2 &p1, Vector2 &p2) {
- if(p1.y < p2.y) return true;
- else if(p1.y == p2.y) {
- if(p1.x < p2.x) return true;
- }
- return false;
-}
-
-
-
-
-
-//sorts in the falling order of y values, if y is equal, x is used instead
-bool TriangulatorPartition::VertexSorter::operator() (long index1, long index2) const {
- if(vertices[index1].p.y > vertices[index2].p.y) return true;
- else if(vertices[index1].p.y == vertices[index2].p.y) {
- if(vertices[index1].p.x > vertices[index2].p.x) return true;
- }
- return false;
-}
-
-bool TriangulatorPartition::ScanLineEdge::IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const {
- real_t tmp;
- tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
- if(tmp>0) return 1;
- else return 0;
-}
-
-bool TriangulatorPartition::ScanLineEdge::operator < (const ScanLineEdge & other) const {
- if(other.p1.y == other.p2.y) {
- if(p1.y == p2.y) {
- if(p1.y < other.p1.y) return true;
- else return false;
- }
- if(IsConvex(p1,p2,other.p1)) return true;
- else return false;
- } else if(p1.y == p2.y) {
- if(IsConvex(other.p1,other.p2,p1)) return false;
- else return true;
- } else if(p1.y < other.p1.y) {
- if(IsConvex(other.p1,other.p2,p1)) return false;
- else return true;
- } else {
- if(IsConvex(p1,p2,other.p1)) return true;
- else return false;
- }
-}
-
-//triangulates monotone polygon
-//O(n) time, O(n) space complexity
-int TriangulatorPartition::TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles) {
- long i,i2,j,topindex,bottomindex,leftindex,rightindex,vindex;
- Vector2 *points;
- long numpoints;
- TriangulatorPoly triangle;
-
- numpoints = inPoly->GetNumPoints();
- points = inPoly->GetPoints();
-
- //trivial calses
- if(numpoints < 3) return 0;
- if(numpoints == 3) {
- triangles->push_back(*inPoly);
- }
-
- topindex = 0; bottomindex=0;
- for(i=1;i<numpoints;i++) {
- if(Below(points[i],points[bottomindex])) bottomindex = i;
- if(Below(points[topindex],points[i])) topindex = i;
- }
-
- //check if the poly is really monotone
- i = topindex;
- while(i!=bottomindex) {
- i2 = i+1; if(i2>=numpoints) i2 = 0;
- if(!Below(points[i2],points[i])) return 0;
- i = i2;
- }
- i = bottomindex;
- while(i!=topindex) {
- i2 = i+1; if(i2>=numpoints) i2 = 0;
- if(!Below(points[i],points[i2])) return 0;
- i = i2;
- }
-
- char *vertextypes = new char[numpoints];
- long *priority = new long[numpoints];
-
- //merge left and right vertex chains
- priority[0] = topindex;
- vertextypes[topindex] = 0;
- leftindex = topindex+1; if(leftindex>=numpoints) leftindex = 0;
- rightindex = topindex-1; if(rightindex<0) rightindex = numpoints-1;
- for(i=1;i<(numpoints-1);i++) {
- if(leftindex==bottomindex) {
- priority[i] = rightindex;
- rightindex--; if(rightindex<0) rightindex = numpoints-1;
- vertextypes[priority[i]] = -1;
- } else if(rightindex==bottomindex) {
- priority[i] = leftindex;
- leftindex++; if(leftindex>=numpoints) leftindex = 0;
- vertextypes[priority[i]] = 1;
- } else {
- if(Below(points[leftindex],points[rightindex])) {
- priority[i] = rightindex;
- rightindex--; if(rightindex<0) rightindex = numpoints-1;
- vertextypes[priority[i]] = -1;
- } else {
- priority[i] = leftindex;
- leftindex++; if(leftindex>=numpoints) leftindex = 0;
- vertextypes[priority[i]] = 1;
- }
- }
- }
- priority[i] = bottomindex;
- vertextypes[bottomindex] = 0;
-
- long *stack = new long[numpoints];
- long stackptr = 0;
-
- stack[0] = priority[0];
- stack[1] = priority[1];
- stackptr = 2;
-
- //for each vertex from top to bottom trim as many triangles as possible
- for(i=2;i<(numpoints-1);i++) {
- vindex = priority[i];
- if(vertextypes[vindex]!=vertextypes[stack[stackptr-1]]) {
- for(j=0;j<(stackptr-1);j++) {
- if(vertextypes[vindex]==1) {
- triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]);
- } else {
- triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]);
- }
- triangles->push_back(triangle);
- }
- stack[0] = priority[i-1];
- stack[1] = priority[i];
- stackptr = 2;
- } else {
- stackptr--;
- while(stackptr>0) {
- if(vertextypes[vindex]==1) {
- if(IsConvex(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]])) {
- triangle.Triangle(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]]);
- triangles->push_back(triangle);
- stackptr--;
- } else {
- break;
- }
- } else {
- if(IsConvex(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]])) {
- triangle.Triangle(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]]);
- triangles->push_back(triangle);
- stackptr--;
- } else {
- break;
- }
- }
- }
- stackptr++;
- stack[stackptr] = vindex;
- stackptr++;
- }
- }
- vindex = priority[i];
- for(j=0;j<(stackptr-1);j++) {
- if(vertextypes[stack[j+1]]==1) {
- triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]);
- } else {
- triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]);
- }
- triangles->push_back(triangle);
- }
-
- delete [] priority;
- delete [] vertextypes;
- delete [] stack;
-
- return 1;
-}
-
-int TriangulatorPartition::Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) {
- List<TriangulatorPoly> monotone;
- List<TriangulatorPoly>::Element* iter;
-
- if(!MonotonePartition(inpolys,&monotone)) return 0;
- for(iter = monotone.front(); iter;iter=iter->next()) {
- if(!TriangulateMonotone(&(iter->get()),triangles)) return 0;
- }
- return 1;
-}
-
-int TriangulatorPartition::Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
- List<TriangulatorPoly> polys;
- polys.push_back(*poly);
-
- return Triangulate_MONO(&polys, triangles);
-}
diff --git a/thirdparty/misc/triangulator.h b/thirdparty/misc/triangulator.h
deleted file mode 100644
index 24b79e7d34..0000000000
--- a/thirdparty/misc/triangulator.h
+++ /dev/null
@@ -1,306 +0,0 @@
-//Copyright (C) 2011 by Ivan Fratric
-//
-//Permission is hereby granted, free of charge, to any person obtaining a copy
-//of this software and associated documentation files (the "Software"), to deal
-//in the Software without restriction, including without limitation the rights
-//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-//copies of the Software, and to permit persons to whom the Software is
-//furnished to do so, subject to the following conditions:
-//
-//The above copyright notice and this permission notice shall be included in
-//all copies or substantial portions of the Software.
-//
-//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-//THE SOFTWARE.
-
-#ifndef TRIANGULATOR_H
-#define TRIANGULATOR_H
-
-#include "core/templates/list.h"
-#include "core/math/vector2.h"
-#include "core/templates/set.h"
-
-//2D point structure
-
-#define TRIANGULATOR_CCW 1
-#define TRIANGULATOR_CW -1
-//Polygon implemented as an array of points with a 'hole' flag
-class TriangulatorPoly {
-protected:
-
-
-
- Vector2 *points;
- long numpoints;
- bool hole;
-
-public:
-
- //constructors/destructors
- TriangulatorPoly();
- ~TriangulatorPoly();
-
- TriangulatorPoly(const TriangulatorPoly &src);
- TriangulatorPoly& operator=(const TriangulatorPoly &src);
-
- //getters and setters
- long GetNumPoints() {
- return numpoints;
- }
-
- bool IsHole() {
- return hole;
- }
-
- void SetHole(bool hole) {
- this->hole = hole;
- }
-
- Vector2 &GetPoint(long i) {
- return points[i];
- }
-
- Vector2 *GetPoints() {
- return points;
- }
-
- Vector2& operator[] (int i) {
- return points[i];
- }
-
- //clears the polygon points
- void Clear();
-
- //inits the polygon with numpoints vertices
- void Init(long numpoints);
-
- //creates a triangle with points p1,p2,p3
- void Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3);
-
- //inverts the orfer of vertices
- void Invert();
-
- //returns the orientation of the polygon
- //possible values:
- // Triangulator_CCW : polygon vertices are in counter-clockwise order
- // Triangulator_CW : polygon vertices are in clockwise order
- // 0 : the polygon has no (measurable) area
- int GetOrientation();
-
- //sets the polygon orientation
- //orientation can be
- // Triangulator_CCW : sets vertices in counter-clockwise order
- // Triangulator_CW : sets vertices in clockwise order
- void SetOrientation(int orientation);
-};
-
-class TriangulatorPartition {
-protected:
- struct PartitionVertex {
- bool isActive;
- bool isConvex;
- bool isEar;
-
- Vector2 p;
- real_t angle;
- PartitionVertex *previous;
- PartitionVertex *next;
- };
-
- struct MonotoneVertex {
- Vector2 p;
- long previous;
- long next;
- };
-
- struct VertexSorter{
- mutable MonotoneVertex *vertices;
- bool operator() (long index1, long index2) const;
- };
-
- struct Diagonal {
- long index1;
- long index2;
- };
-
- //dynamic programming state for minimum-weight triangulation
- struct DPState {
- bool visible;
- real_t weight;
- long bestvertex;
- };
-
- //dynamic programming state for convex partitioning
- struct DPState2 {
- bool visible;
- long weight;
- List<Diagonal> pairs;
- };
-
- //edge that intersects the scanline
- struct ScanLineEdge {
- mutable long index;
- Vector2 p1;
- Vector2 p2;
-
- //determines if the edge is to the left of another edge
- bool operator< (const ScanLineEdge & other) const;
-
- bool IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const;
- };
-
- //standard helper functions
- bool IsConvex(Vector2& p1, Vector2& p2, Vector2& p3);
- bool IsReflex(Vector2& p1, Vector2& p2, Vector2& p3);
- bool IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p);
-
- bool InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p);
- bool InCone(PartitionVertex *v, Vector2 &p);
-
- int Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22);
-
- Vector2 Normalize(const Vector2 &p);
- real_t Distance(const Vector2 &p1, const Vector2 &p2);
-
- //helper functions for Triangulate_EC
- void UpdateVertexReflexity(PartitionVertex *v);
- void UpdateVertex(PartitionVertex *v,PartitionVertex *vertices, long numvertices);
-
- //helper functions for ConvexPartition_OPT
- void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates);
- void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
- void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
-
- //helper functions for MonotonePartition
- bool Below(Vector2 &p1, Vector2 &p2);
- void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
- char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
- Set<ScanLineEdge> *edgeTree, long *helpers);
-
- //triangulates a monotone polygon, used in Triangulate_MONO
- int TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles);
-
-public:
-
- //simple heuristic procedure for removing holes from a list of polygons
- //works by creating a diagonal from the rightmost hole vertex to some visible vertex
- //time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
- //space complexity: O(n)
- //params:
- // inpolys : a list of polygons that can contain holes
- // vertices of all non-hole polys have to be in counter-clockwise order
- // vertices of all hole polys have to be in clockwise order
- // outpolys : a list of polygons without holes
- //returns 1 on success, 0 on failure
- int RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys);
-
- //triangulates a polygon by ear clipping
- //time complexity O(n^2), n is the number of vertices
- //space complexity: O(n)
- //params:
- // poly : an input polygon to be triangulated
- // vertices have to be in counter-clockwise order
- // triangles : a list of triangles (result)
- //returns 1 on success, 0 on failure
- int Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
-
- //triangulates a list of polygons that may contain holes by ear clipping algorithm
- //first calls RemoveHoles to get rid of the holes, and then Triangulate_EC for each resulting polygon
- //time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
- //space complexity: O(n)
- //params:
- // inpolys : a list of polygons to be triangulated (can contain holes)
- // vertices of all non-hole polys have to be in counter-clockwise order
- // vertices of all hole polys have to be in clockwise order
- // triangles : a list of triangles (result)
- //returns 1 on success, 0 on failure
- int Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles);
-
- //creates an optimal polygon triangulation in terms of minimal edge length
- //time complexity: O(n^3), n is the number of vertices
- //space complexity: O(n^2)
- //params:
- // poly : an input polygon to be triangulated
- // vertices have to be in counter-clockwise order
- // triangles : a list of triangles (result)
- //returns 1 on success, 0 on failure
- int Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
-
- //triangulates a polygons by firstly partitioning it into monotone polygons
- //time complexity: O(n*log(n)), n is the number of vertices
- //space complexity: O(n)
- //params:
- // poly : an input polygon to be triangulated
- // vertices have to be in counter-clockwise order
- // triangles : a list of triangles (result)
- //returns 1 on success, 0 on failure
- int Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
-
- //triangulates a list of polygons by firstly partitioning them into monotone polygons
- //time complexity: O(n*log(n)), n is the number of vertices
- //space complexity: O(n)
- //params:
- // inpolys : a list of polygons to be triangulated (can contain holes)
- // vertices of all non-hole polys have to be in counter-clockwise order
- // vertices of all hole polys have to be in clockwise order
- // triangles : a list of triangles (result)
- //returns 1 on success, 0 on failure
- int Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles);
-
- //creates a monotone partition of a list of polygons that can contain holes
- //time complexity: O(n*log(n)), n is the number of vertices
- //space complexity: O(n)
- //params:
- // inpolys : a list of polygons to be triangulated (can contain holes)
- // vertices of all non-hole polys have to be in counter-clockwise order
- // vertices of all hole polys have to be in clockwise order
- // monotonePolys : a list of monotone polygons (result)
- //returns 1 on success, 0 on failure
- int MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys);
-
- //partitions a polygon into convex polygons by using Hertel-Mehlhorn algorithm
- //the algorithm gives at most four times the number of parts as the optimal algorithm
- //however, in practice it works much better than that and often gives optimal partition
- //uses triangulation obtained by ear clipping as intermediate result
- //time complexity O(n^2), n is the number of vertices
- //space complexity: O(n)
- //params:
- // poly : an input polygon to be partitioned
- // vertices have to be in counter-clockwise order
- // parts : resulting list of convex polygons
- //returns 1 on success, 0 on failure
- int ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts);
-
- //partitions a list of polygons into convex parts by using Hertel-Mehlhorn algorithm
- //the algorithm gives at most four times the number of parts as the optimal algorithm
- //however, in practice it works much better than that and often gives optimal partition
- //uses triangulation obtained by ear clipping as intermediate result
- //time complexity O(n^2), n is the number of vertices
- //space complexity: O(n)
- //params:
- // inpolys : an input list of polygons to be partitioned
- // vertices of all non-hole polys have to be in counter-clockwise order
- // vertices of all hole polys have to be in clockwise order
- // parts : resulting list of convex polygons
- //returns 1 on success, 0 on failure
- int ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts);
-
- //optimal convex partitioning (in terms of number of resulting convex polygons)
- //using the Keil-Snoeyink algorithm
- //M. Keil, J. Snoeyink, "On the time bound for convex decomposition of simple polygons", 1998
- //time complexity O(n^3), n is the number of vertices
- //space complexity: O(n^3)
- // poly : an input polygon to be partitioned
- // vertices have to be in counter-clockwise order
- // parts : resulting list of convex polygons
- //returns 1 on success, 0 on failure
- int ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts);
-};
-
-
-#endif
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