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Diffstat (limited to 'thirdparty/meshoptimizer/simplifier.cpp')
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diff --git a/thirdparty/meshoptimizer/simplifier.cpp b/thirdparty/meshoptimizer/simplifier.cpp new file mode 100644 index 0000000000..cf5db4e119 --- /dev/null +++ b/thirdparty/meshoptimizer/simplifier.cpp @@ -0,0 +1,1849 @@ +// This file is part of meshoptimizer library; see meshoptimizer.h for version/license details +#include "meshoptimizer.h" + +#include <assert.h> +#include <float.h> +#include <math.h> +#include <string.h> + +#ifndef TRACE +#define TRACE 0 +#endif + +#if TRACE +#include <stdio.h> +#endif + +#if TRACE +#define TRACESTATS(i) stats[i]++; +#else +#define TRACESTATS(i) (void)0 +#endif + +#define ATTRIBUTES 3 + +// This work is based on: +// Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. 1997 +// Michael Garland. Quadric-based polygonal surface simplification. 1999 +// Peter Lindstrom. Out-of-Core Simplification of Large Polygonal Models. 2000 +// Matthias Teschner, Bruno Heidelberger, Matthias Mueller, Danat Pomeranets, Markus Gross. Optimized Spatial Hashing for Collision Detection of Deformable Objects. 2003 +// Peter Van Sandt, Yannis Chronis, Jignesh M. Patel. Efficiently Searching In-Memory Sorted Arrays: Revenge of the Interpolation Search? 2019 +namespace meshopt +{ + +struct EdgeAdjacency +{ + struct Edge + { + unsigned int next; + unsigned int prev; + }; + + unsigned int* counts; + unsigned int* offsets; + Edge* data; +}; + +static void prepareEdgeAdjacency(EdgeAdjacency& adjacency, size_t index_count, size_t vertex_count, meshopt_Allocator& allocator) +{ + adjacency.counts = allocator.allocate<unsigned int>(vertex_count); + adjacency.offsets = allocator.allocate<unsigned int>(vertex_count); + adjacency.data = allocator.allocate<EdgeAdjacency::Edge>(index_count); +} + +static void updateEdgeAdjacency(EdgeAdjacency& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count, const unsigned int* remap) +{ + size_t face_count = index_count / 3; + + // fill edge counts + memset(adjacency.counts, 0, vertex_count * sizeof(unsigned int)); + + for (size_t i = 0; i < index_count; ++i) + { + unsigned int v = remap ? remap[indices[i]] : indices[i]; + assert(v < vertex_count); + + adjacency.counts[v]++; + } + + // fill offset table + unsigned int offset = 0; + + for (size_t i = 0; i < vertex_count; ++i) + { + adjacency.offsets[i] = offset; + offset += adjacency.counts[i]; + } + + assert(offset == index_count); + + // fill edge data + for (size_t i = 0; i < face_count; ++i) + { + unsigned int a = indices[i * 3 + 0], b = indices[i * 3 + 1], c = indices[i * 3 + 2]; + + if (remap) + { + a = remap[a]; + b = remap[b]; + c = remap[c]; + } + + adjacency.data[adjacency.offsets[a]].next = b; + adjacency.data[adjacency.offsets[a]].prev = c; + adjacency.offsets[a]++; + + adjacency.data[adjacency.offsets[b]].next = c; + adjacency.data[adjacency.offsets[b]].prev = a; + adjacency.offsets[b]++; + + adjacency.data[adjacency.offsets[c]].next = a; + adjacency.data[adjacency.offsets[c]].prev = b; + adjacency.offsets[c]++; + } + + // fix offsets that have been disturbed by the previous pass + for (size_t i = 0; i < vertex_count; ++i) + { + assert(adjacency.offsets[i] >= adjacency.counts[i]); + + adjacency.offsets[i] -= adjacency.counts[i]; + } +} + +struct PositionHasher +{ + const float* vertex_positions; + size_t vertex_stride_float; + + size_t hash(unsigned int index) const + { + const unsigned int* key = reinterpret_cast<const unsigned int*>(vertex_positions + index * vertex_stride_float); + + // scramble bits to make sure that integer coordinates have entropy in lower bits + unsigned int x = key[0] ^ (key[0] >> 17); + unsigned int y = key[1] ^ (key[1] >> 17); + unsigned int z = key[2] ^ (key[2] >> 17); + + // Optimized Spatial Hashing for Collision Detection of Deformable Objects + return (x * 73856093) ^ (y * 19349663) ^ (z * 83492791); + } + + bool equal(unsigned int lhs, unsigned int rhs) const + { + return memcmp(vertex_positions + lhs * vertex_stride_float, vertex_positions + rhs * vertex_stride_float, sizeof(float) * 3) == 0; + } +}; + +static size_t hashBuckets2(size_t count) +{ + size_t buckets = 1; + while (buckets < count + count / 4) + buckets *= 2; + + return buckets; +} + +template <typename T, typename Hash> +static T* hashLookup2(T* table, size_t buckets, const Hash& hash, const T& key, const T& empty) +{ + assert(buckets > 0); + assert((buckets & (buckets - 1)) == 0); + + size_t hashmod = buckets - 1; + size_t bucket = hash.hash(key) & hashmod; + + for (size_t probe = 0; probe <= hashmod; ++probe) + { + T& item = table[bucket]; + + if (item == empty) + return &item; + + if (hash.equal(item, key)) + return &item; + + // hash collision, quadratic probing + bucket = (bucket + probe + 1) & hashmod; + } + + assert(false && "Hash table is full"); // unreachable + return 0; +} + +static void buildPositionRemap(unsigned int* remap, unsigned int* wedge, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, meshopt_Allocator& allocator) +{ + PositionHasher hasher = {vertex_positions_data, vertex_positions_stride / sizeof(float)}; + + size_t table_size = hashBuckets2(vertex_count); + unsigned int* table = allocator.allocate<unsigned int>(table_size); + memset(table, -1, table_size * sizeof(unsigned int)); + + // build forward remap: for each vertex, which other (canonical) vertex does it map to? + // we use position equivalence for this, and remap vertices to other existing vertices + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int index = unsigned(i); + unsigned int* entry = hashLookup2(table, table_size, hasher, index, ~0u); + + if (*entry == ~0u) + *entry = index; + + remap[index] = *entry; + } + + // build wedge table: for each vertex, which other vertex is the next wedge that also maps to the same vertex? + // entries in table form a (cyclic) wedge loop per vertex; for manifold vertices, wedge[i] == remap[i] == i + for (size_t i = 0; i < vertex_count; ++i) + wedge[i] = unsigned(i); + + for (size_t i = 0; i < vertex_count; ++i) + if (remap[i] != i) + { + unsigned int r = remap[i]; + + wedge[i] = wedge[r]; + wedge[r] = unsigned(i); + } +} + +enum VertexKind +{ + Kind_Manifold, // not on an attribute seam, not on any boundary + Kind_Border, // not on an attribute seam, has exactly two open edges + Kind_Seam, // on an attribute seam with exactly two attribute seam edges + Kind_Complex, // none of the above; these vertices can move as long as all wedges move to the target vertex + Kind_Locked, // none of the above; these vertices can't move + + Kind_Count +}; + +// manifold vertices can collapse onto anything +// border/seam vertices can only be collapsed onto border/seam respectively +// complex vertices can collapse onto complex/locked +// a rule of thumb is that collapsing kind A into kind B preserves the kind B in the target vertex +// for example, while we could collapse Complex into Manifold, this would mean the target vertex isn't Manifold anymore +const unsigned char kCanCollapse[Kind_Count][Kind_Count] = { + {1, 1, 1, 1, 1}, + {0, 1, 0, 0, 0}, + {0, 0, 1, 0, 0}, + {0, 0, 0, 1, 1}, + {0, 0, 0, 0, 0}, +}; + +// if a vertex is manifold or seam, adjoining edges are guaranteed to have an opposite edge +// note that for seam edges, the opposite edge isn't present in the attribute-based topology +// but is present if you consider a position-only mesh variant +const unsigned char kHasOpposite[Kind_Count][Kind_Count] = { + {1, 1, 1, 0, 1}, + {1, 0, 1, 0, 0}, + {1, 1, 1, 0, 1}, + {0, 0, 0, 0, 0}, + {1, 0, 1, 0, 0}, +}; + +static bool hasEdge(const EdgeAdjacency& adjacency, unsigned int a, unsigned int b) +{ + unsigned int count = adjacency.counts[a]; + const EdgeAdjacency::Edge* edges = adjacency.data + adjacency.offsets[a]; + + for (size_t i = 0; i < count; ++i) + if (edges[i].next == b) + return true; + + return false; +} + +static void classifyVertices(unsigned char* result, unsigned int* loop, unsigned int* loopback, size_t vertex_count, const EdgeAdjacency& adjacency, const unsigned int* remap, const unsigned int* wedge) +{ + memset(loop, -1, vertex_count * sizeof(unsigned int)); + memset(loopback, -1, vertex_count * sizeof(unsigned int)); + + // incoming & outgoing open edges: ~0u if no open edges, i if there are more than 1 + // note that this is the same data as required in loop[] arrays; loop[] data is only valid for border/seam + // but here it's okay to fill the data out for other types of vertices as well + unsigned int* openinc = loopback; + unsigned int* openout = loop; + + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int vertex = unsigned(i); + + unsigned int count = adjacency.counts[vertex]; + const EdgeAdjacency::Edge* edges = adjacency.data + adjacency.offsets[vertex]; + + for (size_t j = 0; j < count; ++j) + { + unsigned int target = edges[j].next; + + if (!hasEdge(adjacency, target, vertex)) + { + openinc[target] = (openinc[target] == ~0u) ? vertex : target; + openout[vertex] = (openout[vertex] == ~0u) ? target : vertex; + } + } + } + +#if TRACE + size_t stats[4] = {}; +#endif + + for (size_t i = 0; i < vertex_count; ++i) + { + if (remap[i] == i) + { + if (wedge[i] == i) + { + // no attribute seam, need to check if it's manifold + unsigned int openi = openinc[i], openo = openout[i]; + + // note: we classify any vertices with no open edges as manifold + // this is technically incorrect - if 4 triangles share an edge, we'll classify vertices as manifold + // it's unclear if this is a problem in practice + if (openi == ~0u && openo == ~0u) + { + result[i] = Kind_Manifold; + } + else if (openi != i && openo != i) + { + result[i] = Kind_Border; + } + else + { + result[i] = Kind_Locked; + TRACESTATS(0); + } + } + else if (wedge[wedge[i]] == i) + { + // attribute seam; need to distinguish between Seam and Locked + unsigned int w = wedge[i]; + unsigned int openiv = openinc[i], openov = openout[i]; + unsigned int openiw = openinc[w], openow = openout[w]; + + // seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap + if (openiv != ~0u && openiv != i && openov != ~0u && openov != i && + openiw != ~0u && openiw != w && openow != ~0u && openow != w) + { + if (remap[openiv] == remap[openow] && remap[openov] == remap[openiw]) + { + result[i] = Kind_Seam; + } + else + { + result[i] = Kind_Locked; + TRACESTATS(1); + } + } + else + { + result[i] = Kind_Locked; + TRACESTATS(2); + } + } + else + { + // more than one vertex maps to this one; we don't have classification available + result[i] = Kind_Locked; + TRACESTATS(3); + } + } + else + { + assert(remap[i] < i); + + result[i] = result[remap[i]]; + } + } + +#if TRACE + printf("locked: many open edges %d, disconnected seam %d, many seam edges %d, many wedges %d\n", + int(stats[0]), int(stats[1]), int(stats[2]), int(stats[3])); +#endif +} + +struct Vector3 +{ + float x, y, z; + +#if ATTRIBUTES + float a[ATTRIBUTES]; +#endif +}; + +static float rescalePositions(Vector3* result, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride) +{ + size_t vertex_stride_float = vertex_positions_stride / sizeof(float); + + float minv[3] = {FLT_MAX, FLT_MAX, FLT_MAX}; + float maxv[3] = {-FLT_MAX, -FLT_MAX, -FLT_MAX}; + + for (size_t i = 0; i < vertex_count; ++i) + { + const float* v = vertex_positions_data + i * vertex_stride_float; + + if (result) + { + result[i].x = v[0]; + result[i].y = v[1]; + result[i].z = v[2]; + } + + for (int j = 0; j < 3; ++j) + { + float vj = v[j]; + + minv[j] = minv[j] > vj ? vj : minv[j]; + maxv[j] = maxv[j] < vj ? vj : maxv[j]; + } + } + + float extent = 0.f; + + extent = (maxv[0] - minv[0]) < extent ? extent : (maxv[0] - minv[0]); + extent = (maxv[1] - minv[1]) < extent ? extent : (maxv[1] - minv[1]); + extent = (maxv[2] - minv[2]) < extent ? extent : (maxv[2] - minv[2]); + + if (result) + { + float scale = extent == 0 ? 0.f : 1.f / extent; + + for (size_t i = 0; i < vertex_count; ++i) + { + result[i].x = (result[i].x - minv[0]) * scale; + result[i].y = (result[i].y - minv[1]) * scale; + result[i].z = (result[i].z - minv[2]) * scale; + } + } + + return extent; +} + +struct Quadric +{ + float a00, a11, a22; + float a10, a20, a21; + float b0, b1, b2, c; + float w; + +#if ATTRIBUTES + float gx[ATTRIBUTES]; + float gy[ATTRIBUTES]; + float gz[ATTRIBUTES]; + float gw[ATTRIBUTES]; +#endif +}; + +struct Collapse +{ + unsigned int v0; + unsigned int v1; + + union + { + unsigned int bidi; + float error; + unsigned int errorui; + }; + float distance_error; +}; + +static float normalize(Vector3& v) +{ + float length = sqrtf(v.x * v.x + v.y * v.y + v.z * v.z); + + if (length > 0) + { + v.x /= length; + v.y /= length; + v.z /= length; + } + + return length; +} + +static void quadricAdd(Quadric& Q, const Quadric& R) +{ + Q.a00 += R.a00; + Q.a11 += R.a11; + Q.a22 += R.a22; + Q.a10 += R.a10; + Q.a20 += R.a20; + Q.a21 += R.a21; + Q.b0 += R.b0; + Q.b1 += R.b1; + Q.b2 += R.b2; + Q.c += R.c; + Q.w += R.w; + +#if ATTRIBUTES + for (int k = 0; k < ATTRIBUTES; ++k) + { + Q.gx[k] += R.gx[k]; + Q.gy[k] += R.gy[k]; + Q.gz[k] += R.gz[k]; + Q.gw[k] += R.gw[k]; + } +#endif +} + +static float quadricError(const Quadric& Q, const Vector3& v) +{ + float rx = Q.b0; + float ry = Q.b1; + float rz = Q.b2; + + rx += Q.a10 * v.y; + ry += Q.a21 * v.z; + rz += Q.a20 * v.x; + + rx *= 2; + ry *= 2; + rz *= 2; + + rx += Q.a00 * v.x; + ry += Q.a11 * v.y; + rz += Q.a22 * v.z; + + float r = Q.c; + r += rx * v.x; + r += ry * v.y; + r += rz * v.z; + +#if ATTRIBUTES + // see quadricUpdateAttributes for general derivation; here we need to add the parts of (eval(pos) - attr)^2 that depend on attr + for (int k = 0; k < ATTRIBUTES; ++k) + { + float a = v.a[k]; + + r += a * a * Q.w; + r -= 2 * a * (v.x * Q.gx[k] + v.y * Q.gy[k] + v.z * Q.gz[k] + Q.gw[k]); + } +#endif + + float s = Q.w == 0.f ? 0.f : 1.f / Q.w; + + return fabsf(r) * s; +} + +static float quadricErrorNoAttributes(const Quadric& Q, const Vector3& v) +{ + float rx = Q.b0; + float ry = Q.b1; + float rz = Q.b2; + + rx += Q.a10 * v.y; + ry += Q.a21 * v.z; + rz += Q.a20 * v.x; + + rx *= 2; + ry *= 2; + rz *= 2; + + rx += Q.a00 * v.x; + ry += Q.a11 * v.y; + rz += Q.a22 * v.z; + + float r = Q.c; + r += rx * v.x; + r += ry * v.y; + r += rz * v.z; + + float s = Q.w == 0.f ? 0.f : 1.f / Q.w; + + return fabsf(r) * s; +} + +static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d, float w) +{ + float aw = a * w; + float bw = b * w; + float cw = c * w; + float dw = d * w; + + Q.a00 = a * aw; + Q.a11 = b * bw; + Q.a22 = c * cw; + Q.a10 = a * bw; + Q.a20 = a * cw; + Q.a21 = b * cw; + Q.b0 = a * dw; + Q.b1 = b * dw; + Q.b2 = c * dw; + Q.c = d * dw; + Q.w = w; + +#if ATTRIBUTES + memset(Q.gx, 0, sizeof(Q.gx)); + memset(Q.gy, 0, sizeof(Q.gy)); + memset(Q.gz, 0, sizeof(Q.gz)); + memset(Q.gw, 0, sizeof(Q.gw)); +#endif +} + +static void quadricFromPoint(Quadric& Q, float x, float y, float z, float w) +{ + // we need to encode (x - X) ^ 2 + (y - Y)^2 + (z - Z)^2 into the quadric + Q.a00 = w; + Q.a11 = w; + Q.a22 = w; + Q.a10 = 0.f; + Q.a20 = 0.f; + Q.a21 = 0.f; + Q.b0 = -2.f * x * w; + Q.b1 = -2.f * y * w; + Q.b2 = -2.f * z * w; + Q.c = (x * x + y * y + z * z) * w; + Q.w = w; +} + +static void quadricFromTriangle(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float weight) +{ + Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z}; + Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z}; + + // normal = cross(p1 - p0, p2 - p0) + Vector3 normal = {p10.y * p20.z - p10.z * p20.y, p10.z * p20.x - p10.x * p20.z, p10.x * p20.y - p10.y * p20.x}; + float area = normalize(normal); + + float distance = normal.x * p0.x + normal.y * p0.y + normal.z * p0.z; + + // we use sqrtf(area) so that the error is scaled linearly; this tends to improve silhouettes + quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance, sqrtf(area) * weight); +} + +static void quadricFromTriangleEdge(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float weight) +{ + Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z}; + float length = normalize(p10); + + // p20p = length of projection of p2-p0 onto normalize(p1 - p0) + Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z}; + float p20p = p20.x * p10.x + p20.y * p10.y + p20.z * p10.z; + + // normal = altitude of triangle from point p2 onto edge p1-p0 + Vector3 normal = {p20.x - p10.x * p20p, p20.y - p10.y * p20p, p20.z - p10.z * p20p}; + normalize(normal); + + float distance = normal.x * p0.x + normal.y * p0.y + normal.z * p0.z; + + // note: the weight is scaled linearly with edge length; this has to match the triangle weight + quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance, length * weight); +} + +#if ATTRIBUTES +static void quadricUpdateAttributes(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float w) +{ + // for each attribute we want to encode the following function into the quadric: + // (eval(pos) - attr)^2 + // where eval(pos) interpolates attribute across the triangle like so: + // eval(pos) = pos.x * gx + pos.y * gy + pos.z * gz + gw + // where gx/gy/gz/gw are gradients + Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z}; + Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z}; + + // we compute gradients using barycentric coordinates; barycentric coordinates can be computed as follows: + // v = (d11 * d20 - d01 * d21) / denom + // w = (d00 * d21 - d01 * d20) / denom + // u = 1 - v - w + // here v0, v1 are triangle edge vectors, v2 is a vector from point to triangle corner, and dij = dot(vi, vj) + const Vector3& v0 = p10; + const Vector3& v1 = p20; + float d00 = v0.x * v0.x + v0.y * v0.y + v0.z * v0.z; + float d01 = v0.x * v1.x + v0.y * v1.y + v0.z * v1.z; + float d11 = v1.x * v1.x + v1.y * v1.y + v1.z * v1.z; + float denom = d00 * d11 - d01 * d01; + float denomr = denom == 0 ? 0.f : 1.f / denom; + + // precompute gradient factors + // these are derived by directly computing derivative of eval(pos) = a0 * u + a1 * v + a2 * w and factoring out common factors that are shared between attributes + float gx1 = (d11 * v0.x - d01 * v1.x) * denomr; + float gx2 = (d00 * v1.x - d01 * v0.x) * denomr; + float gy1 = (d11 * v0.y - d01 * v1.y) * denomr; + float gy2 = (d00 * v1.y - d01 * v0.y) * denomr; + float gz1 = (d11 * v0.z - d01 * v1.z) * denomr; + float gz2 = (d00 * v1.z - d01 * v0.z) * denomr; + + for (int k = 0; k < ATTRIBUTES; ++k) + { + float a0 = p0.a[k], a1 = p1.a[k], a2 = p2.a[k]; + + // compute gradient of eval(pos) for x/y/z/w + // the formulas below are obtained by directly computing derivative of eval(pos) = a0 * u + a1 * v + a2 * w + float gx = gx1 * (a1 - a0) + gx2 * (a2 - a0); + float gy = gy1 * (a1 - a0) + gy2 * (a2 - a0); + float gz = gz1 * (a1 - a0) + gz2 * (a2 - a0); + float gw = a0 - p0.x * gx - p0.y * gy - p0.z * gz; + + // quadric encodes (eval(pos)-attr)^2; this means that the resulting expansion needs to compute, for example, pos.x * pos.y * K + // since quadrics already encode factors for pos.x * pos.y, we can accumulate almost everything in basic quadric fields + Q.a00 += w * (gx * gx); + Q.a11 += w * (gy * gy); + Q.a22 += w * (gz * gz); + + Q.a10 += w * (gy * gx); + Q.a20 += w * (gz * gx); + Q.a21 += w * (gz * gy); + + Q.b0 += w * (gx * gw); + Q.b1 += w * (gy * gw); + Q.b2 += w * (gz * gw); + + Q.c += w * (gw * gw); + + // the only remaining sum components are ones that depend on attr; these will be addded during error evaluation, see quadricError + Q.gx[k] = w * gx; + Q.gy[k] = w * gy; + Q.gz[k] = w * gz; + Q.gw[k] = w * gw; + +#if TRACE > 2 + printf("attr%d: %e %e %e\n", + k, + (gx * p0.x + gy * p0.y + gz * p0.z + gw - a0), + (gx * p1.x + gy * p1.y + gz * p1.z + gw - a1), + (gx * p2.x + gy * p2.y + gz * p2.z + gw - a2) + ); +#endif + } +} +#endif + +static void fillFaceQuadrics(Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* remap) +{ + for (size_t i = 0; i < index_count; i += 3) + { + unsigned int i0 = indices[i + 0]; + unsigned int i1 = indices[i + 1]; + unsigned int i2 = indices[i + 2]; + + Quadric Q; + quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], 1.f); + quadricAdd(vertex_no_attrib_quadrics[remap[i0]], Q); + quadricAdd(vertex_no_attrib_quadrics[remap[i1]], Q); + quadricAdd(vertex_no_attrib_quadrics[remap[i2]], Q); + +#if ATTRIBUTES + quadricUpdateAttributes(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], Q.w); +#endif + quadricAdd(vertex_quadrics[remap[i0]], Q); + quadricAdd(vertex_quadrics[remap[i1]], Q); + quadricAdd(vertex_quadrics[remap[i2]], Q); + } +} + +static void fillEdgeQuadrics(Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* remap, const unsigned char* vertex_kind, const unsigned int* loop, const unsigned int* loopback) +{ + for (size_t i = 0; i < index_count; i += 3) + { + static const int next[3] = {1, 2, 0}; + + for (int e = 0; e < 3; ++e) + { + unsigned int i0 = indices[i + e]; + unsigned int i1 = indices[i + next[e]]; + + unsigned char k0 = vertex_kind[i0]; + unsigned char k1 = vertex_kind[i1]; + + // check that either i0 or i1 are border/seam and are on the same edge loop + // note that we need to add the error even for edged that connect e.g. border & locked + // if we don't do that, the adjacent border->border edge won't have correct errors for corners + if (k0 != Kind_Border && k0 != Kind_Seam && k1 != Kind_Border && k1 != Kind_Seam) + continue; + + if ((k0 == Kind_Border || k0 == Kind_Seam) && loop[i0] != i1) + continue; + + if ((k1 == Kind_Border || k1 == Kind_Seam) && loopback[i1] != i0) + continue; + + // seam edges should occur twice (i0->i1 and i1->i0) - skip redundant edges + if (kHasOpposite[k0][k1] && remap[i1] > remap[i0]) + continue; + + unsigned int i2 = indices[i + next[next[e]]]; + + // we try hard to maintain border edge geometry; seam edges can move more freely + // due to topological restrictions on collapses, seam quadrics slightly improves collapse structure but aren't critical + const float kEdgeWeightSeam = 1.f; + const float kEdgeWeightBorder = 10.f; + + float edgeWeight = (k0 == Kind_Border || k1 == Kind_Border) ? kEdgeWeightBorder : kEdgeWeightSeam; + + Quadric Q; + quadricFromTriangleEdge(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], edgeWeight); + + quadricAdd(vertex_quadrics[remap[i0]], Q); + quadricAdd(vertex_quadrics[remap[i1]], Q); + + quadricAdd(vertex_no_attrib_quadrics[remap[i0]], Q); + quadricAdd(vertex_no_attrib_quadrics[remap[i1]], Q); + } + } +} + +// does triangle ABC flip when C is replaced with D? +static bool hasTriangleFlip(const Vector3& a, const Vector3& b, const Vector3& c, const Vector3& d) +{ + Vector3 eb = {b.x - a.x, b.y - a.y, b.z - a.z}; + Vector3 ec = {c.x - a.x, c.y - a.y, c.z - a.z}; + Vector3 ed = {d.x - a.x, d.y - a.y, d.z - a.z}; + + Vector3 nbc = {eb.y * ec.z - eb.z * ec.y, eb.z * ec.x - eb.x * ec.z, eb.x * ec.y - eb.y * ec.x}; + Vector3 nbd = {eb.y * ed.z - eb.z * ed.y, eb.z * ed.x - eb.x * ed.z, eb.x * ed.y - eb.y * ed.x}; + + return nbc.x * nbd.x + nbc.y * nbd.y + nbc.z * nbd.z < 0; +} + +static bool hasTriangleFlips(const EdgeAdjacency& adjacency, const Vector3* vertex_positions, const unsigned int* collapse_remap, unsigned int i0, unsigned int i1) +{ + assert(collapse_remap[i0] == i0); + assert(collapse_remap[i1] == i1); + + const Vector3& v0 = vertex_positions[i0]; + const Vector3& v1 = vertex_positions[i1]; + + const EdgeAdjacency::Edge* edges = &adjacency.data[adjacency.offsets[i0]]; + size_t count = adjacency.counts[i0]; + + for (size_t i = 0; i < count; ++i) + { + unsigned int a = collapse_remap[edges[i].next]; + unsigned int b = collapse_remap[edges[i].prev]; + + // skip triangles that get collapsed + // note: this is mathematically redundant as if either of these is true, the dot product in hasTriangleFlip should be 0 + if (a == i1 || b == i1) + continue; + + // early-out when at least one triangle flips due to a collapse + if (hasTriangleFlip(vertex_positions[a], vertex_positions[b], v0, v1)) + return true; + } + + return false; +} + +static size_t pickEdgeCollapses(Collapse* collapses, const unsigned int* indices, size_t index_count, const unsigned int* remap, const unsigned char* vertex_kind, const unsigned int* loop) +{ + size_t collapse_count = 0; + + for (size_t i = 0; i < index_count; i += 3) + { + static const int next[3] = {1, 2, 0}; + + for (int e = 0; e < 3; ++e) + { + unsigned int i0 = indices[i + e]; + unsigned int i1 = indices[i + next[e]]; + + // this can happen either when input has a zero-length edge, or when we perform collapses for complex + // topology w/seams and collapse a manifold vertex that connects to both wedges onto one of them + // we leave edges like this alone since they may be important for preserving mesh integrity + if (remap[i0] == remap[i1]) + continue; + + unsigned char k0 = vertex_kind[i0]; + unsigned char k1 = vertex_kind[i1]; + + // the edge has to be collapsible in at least one direction + if (!(kCanCollapse[k0][k1] | kCanCollapse[k1][k0])) + continue; + + // manifold and seam edges should occur twice (i0->i1 and i1->i0) - skip redundant edges + if (kHasOpposite[k0][k1] && remap[i1] > remap[i0]) + continue; + + // two vertices are on a border or a seam, but there's no direct edge between them + // this indicates that they belong to two different edge loops and we should not collapse this edge + // loop[] tracks half edges so we only need to check i0->i1 + if (k0 == k1 && (k0 == Kind_Border || k0 == Kind_Seam) && loop[i0] != i1) + continue; + + // edge can be collapsed in either direction - we will pick the one with minimum error + // note: we evaluate error later during collapse ranking, here we just tag the edge as bidirectional + if (kCanCollapse[k0][k1] & kCanCollapse[k1][k0]) + { + Collapse c = {i0, i1, {/* bidi= */ 1}}; + collapses[collapse_count++] = c; + } + else + { + // edge can only be collapsed in one direction + unsigned int e0 = kCanCollapse[k0][k1] ? i0 : i1; + unsigned int e1 = kCanCollapse[k0][k1] ? i1 : i0; + + Collapse c = {e0, e1, {/* bidi= */ 0}}; + collapses[collapse_count++] = c; + } + } + } + + return collapse_count; +} + +static void rankEdgeCollapses(Collapse* collapses, size_t collapse_count, const Vector3* vertex_positions, const Quadric* vertex_quadrics, const Quadric* vertex_no_attrib_quadrics, const unsigned int* remap) +{ + for (size_t i = 0; i < collapse_count; ++i) + { + Collapse& c = collapses[i]; + + unsigned int i0 = c.v0; + unsigned int i1 = c.v1; + + // most edges are bidirectional which means we need to evaluate errors for two collapses + // to keep this code branchless we just use the same edge for unidirectional edges + unsigned int j0 = c.bidi ? i1 : i0; + unsigned int j1 = c.bidi ? i0 : i1; + + const Quadric& qi = vertex_quadrics[remap[i0]]; + const Quadric& qj = vertex_quadrics[remap[j0]]; + + float ei = quadricError(qi, vertex_positions[i1]); + float ej = quadricError(qj, vertex_positions[j1]); + + const Quadric& naqi = vertex_no_attrib_quadrics[remap[i0]]; + const Quadric& naqj = vertex_no_attrib_quadrics[remap[j0]]; + + // pick edge direction with minimal error + c.v0 = ei <= ej ? i0 : j0; + c.v1 = ei <= ej ? i1 : j1; + c.error = ei <= ej ? ei : ej; + c.distance_error = ei <= ej ? quadricErrorNoAttributes(naqi, vertex_positions[i1]) : quadricErrorNoAttributes(naqj, vertex_positions[j1]); + } +} + +#if TRACE > 1 +static void dumpEdgeCollapses(const Collapse* collapses, size_t collapse_count, const unsigned char* vertex_kind) +{ + size_t ckinds[Kind_Count][Kind_Count] = {}; + float cerrors[Kind_Count][Kind_Count] = {}; + + for (int k0 = 0; k0 < Kind_Count; ++k0) + for (int k1 = 0; k1 < Kind_Count; ++k1) + cerrors[k0][k1] = FLT_MAX; + + for (size_t i = 0; i < collapse_count; ++i) + { + unsigned int i0 = collapses[i].v0; + unsigned int i1 = collapses[i].v1; + + unsigned char k0 = vertex_kind[i0]; + unsigned char k1 = vertex_kind[i1]; + + ckinds[k0][k1]++; + cerrors[k0][k1] = (collapses[i].error < cerrors[k0][k1]) ? collapses[i].error : cerrors[k0][k1]; + } + + for (int k0 = 0; k0 < Kind_Count; ++k0) + for (int k1 = 0; k1 < Kind_Count; ++k1) + if (ckinds[k0][k1]) + printf("collapses %d -> %d: %d, min error %e\n", k0, k1, int(ckinds[k0][k1]), ckinds[k0][k1] ? sqrtf(cerrors[k0][k1]) : 0.f); +} + +static void dumpLockedCollapses(const unsigned int* indices, size_t index_count, const unsigned char* vertex_kind) +{ + size_t locked_collapses[Kind_Count][Kind_Count] = {}; + + for (size_t i = 0; i < index_count; i += 3) + { + static const int next[3] = {1, 2, 0}; + + for (int e = 0; e < 3; ++e) + { + unsigned int i0 = indices[i + e]; + unsigned int i1 = indices[i + next[e]]; + + unsigned char k0 = vertex_kind[i0]; + unsigned char k1 = vertex_kind[i1]; + + locked_collapses[k0][k1] += !kCanCollapse[k0][k1] && !kCanCollapse[k1][k0]; + } + } + + for (int k0 = 0; k0 < Kind_Count; ++k0) + for (int k1 = 0; k1 < Kind_Count; ++k1) + if (locked_collapses[k0][k1]) + printf("locked collapses %d -> %d: %d\n", k0, k1, int(locked_collapses[k0][k1])); +} +#endif + +static void sortEdgeCollapses(unsigned int* sort_order, const Collapse* collapses, size_t collapse_count) +{ + const int sort_bits = 11; + + // fill histogram for counting sort + unsigned int histogram[1 << sort_bits]; + memset(histogram, 0, sizeof(histogram)); + + for (size_t i = 0; i < collapse_count; ++i) + { + // skip sign bit since error is non-negative + unsigned int key = (collapses[i].errorui << 1) >> (32 - sort_bits); + + histogram[key]++; + } + + // compute offsets based on histogram data + size_t histogram_sum = 0; + + for (size_t i = 0; i < 1 << sort_bits; ++i) + { + size_t count = histogram[i]; + histogram[i] = unsigned(histogram_sum); + histogram_sum += count; + } + + assert(histogram_sum == collapse_count); + + // compute sort order based on offsets + for (size_t i = 0; i < collapse_count; ++i) + { + // skip sign bit since error is non-negative + unsigned int key = (collapses[i].errorui << 1) >> (32 - sort_bits); + + sort_order[histogram[key]++] = unsigned(i); + } +} + +static size_t performEdgeCollapses(unsigned int* collapse_remap, unsigned char* collapse_locked, Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const Collapse* collapses, size_t collapse_count, const unsigned int* collapse_order, const unsigned int* remap, const unsigned int* wedge, const unsigned char* vertex_kind, const Vector3* vertex_positions, const EdgeAdjacency& adjacency, size_t triangle_collapse_goal, float error_limit, float& result_error) +{ + size_t edge_collapses = 0; + size_t triangle_collapses = 0; + + // most collapses remove 2 triangles; use this to establish a bound on the pass in terms of error limit + // note that edge_collapse_goal is an estimate; triangle_collapse_goal will be used to actually limit collapses + size_t edge_collapse_goal = triangle_collapse_goal / 2; + +#if TRACE + size_t stats[4] = {}; +#endif + + for (size_t i = 0; i < collapse_count; ++i) + { + const Collapse& c = collapses[collapse_order[i]]; + + TRACESTATS(0); + + if (c.error > error_limit) + break; + + if (triangle_collapses >= triangle_collapse_goal) + break; + + // we limit the error in each pass based on the error of optimal last collapse; since many collapses will be locked + // as they will share vertices with other successfull collapses, we need to increase the acceptable error by some factor + float error_goal = edge_collapse_goal < collapse_count ? 1.5f * collapses[collapse_order[edge_collapse_goal]].error : FLT_MAX; + + // on average, each collapse is expected to lock 6 other collapses; to avoid degenerate passes on meshes with odd + // topology, we only abort if we got over 1/6 collapses accordingly. + if (c.error > error_goal && triangle_collapses > triangle_collapse_goal / 6) + break; + + unsigned int i0 = c.v0; + unsigned int i1 = c.v1; + + unsigned int r0 = remap[i0]; + unsigned int r1 = remap[i1]; + + // we don't collapse vertices that had source or target vertex involved in a collapse + // it's important to not move the vertices twice since it complicates the tracking/remapping logic + // it's important to not move other vertices towards a moved vertex to preserve error since we don't re-rank collapses mid-pass + if (collapse_locked[r0] | collapse_locked[r1]) + { + TRACESTATS(1); + continue; + } + + if (hasTriangleFlips(adjacency, vertex_positions, collapse_remap, r0, r1)) + { + // adjust collapse goal since this collapse is invalid and shouldn't factor into error goal + edge_collapse_goal++; + + TRACESTATS(2); + continue; + } + + assert(collapse_remap[r0] == r0); + assert(collapse_remap[r1] == r1); + + quadricAdd(vertex_quadrics[r1], vertex_quadrics[r0]); + quadricAdd(vertex_no_attrib_quadrics[r1], vertex_no_attrib_quadrics[r0]); + + if (vertex_kind[i0] == Kind_Complex) + { + unsigned int v = i0; + + do + { + collapse_remap[v] = r1; + v = wedge[v]; + } while (v != i0); + } + else if (vertex_kind[i0] == Kind_Seam) + { + // remap v0 to v1 and seam pair of v0 to seam pair of v1 + unsigned int s0 = wedge[i0]; + unsigned int s1 = wedge[i1]; + + assert(s0 != i0 && s1 != i1); + assert(wedge[s0] == i0 && wedge[s1] == i1); + + collapse_remap[i0] = i1; + collapse_remap[s0] = s1; + } + else + { + assert(wedge[i0] == i0); + + collapse_remap[i0] = i1; + } + + collapse_locked[r0] = 1; + collapse_locked[r1] = 1; + + // border edges collapse 1 triangle, other edges collapse 2 or more + triangle_collapses += (vertex_kind[i0] == Kind_Border) ? 1 : 2; + edge_collapses++; + + result_error = result_error < c.distance_error ? c.distance_error : result_error; + } + +#if TRACE + float error_goal_perfect = edge_collapse_goal < collapse_count ? collapses[collapse_order[edge_collapse_goal]].error : 0.f; + + printf("removed %d triangles, error %e (goal %e); evaluated %d/%d collapses (done %d, skipped %d, invalid %d)\n", + int(triangle_collapses), sqrtf(result_error), sqrtf(error_goal_perfect), + int(stats[0]), int(collapse_count), int(edge_collapses), int(stats[1]), int(stats[2])); +#endif + + return edge_collapses; +} + +static size_t remapIndexBuffer(unsigned int* indices, size_t index_count, const unsigned int* collapse_remap) +{ + size_t write = 0; + + for (size_t i = 0; i < index_count; i += 3) + { + unsigned int v0 = collapse_remap[indices[i + 0]]; + unsigned int v1 = collapse_remap[indices[i + 1]]; + unsigned int v2 = collapse_remap[indices[i + 2]]; + + // we never move the vertex twice during a single pass + assert(collapse_remap[v0] == v0); + assert(collapse_remap[v1] == v1); + assert(collapse_remap[v2] == v2); + + if (v0 != v1 && v0 != v2 && v1 != v2) + { + indices[write + 0] = v0; + indices[write + 1] = v1; + indices[write + 2] = v2; + write += 3; + } + } + + return write; +} + +static void remapEdgeLoops(unsigned int* loop, size_t vertex_count, const unsigned int* collapse_remap) +{ + for (size_t i = 0; i < vertex_count; ++i) + { + if (loop[i] != ~0u) + { + unsigned int l = loop[i]; + unsigned int r = collapse_remap[l]; + + // i == r is a special case when the seam edge is collapsed in a direction opposite to where loop goes + loop[i] = (i == r) ? loop[l] : r; + } + } +} + +struct CellHasher +{ + const unsigned int* vertex_ids; + + size_t hash(unsigned int i) const + { + unsigned int h = vertex_ids[i]; + + // MurmurHash2 finalizer + h ^= h >> 13; + h *= 0x5bd1e995; + h ^= h >> 15; + return h; + } + + bool equal(unsigned int lhs, unsigned int rhs) const + { + return vertex_ids[lhs] == vertex_ids[rhs]; + } +}; + +struct IdHasher +{ + size_t hash(unsigned int id) const + { + unsigned int h = id; + + // MurmurHash2 finalizer + h ^= h >> 13; + h *= 0x5bd1e995; + h ^= h >> 15; + return h; + } + + bool equal(unsigned int lhs, unsigned int rhs) const + { + return lhs == rhs; + } +}; + +struct TriangleHasher +{ + const unsigned int* indices; + + size_t hash(unsigned int i) const + { + const unsigned int* tri = indices + i * 3; + + // Optimized Spatial Hashing for Collision Detection of Deformable Objects + return (tri[0] * 73856093) ^ (tri[1] * 19349663) ^ (tri[2] * 83492791); + } + + bool equal(unsigned int lhs, unsigned int rhs) const + { + const unsigned int* lt = indices + lhs * 3; + const unsigned int* rt = indices + rhs * 3; + + return lt[0] == rt[0] && lt[1] == rt[1] && lt[2] == rt[2]; + } +}; + +static void computeVertexIds(unsigned int* vertex_ids, const Vector3* vertex_positions, size_t vertex_count, int grid_size) +{ + assert(grid_size >= 1 && grid_size <= 1024); + float cell_scale = float(grid_size - 1); + + for (size_t i = 0; i < vertex_count; ++i) + { + const Vector3& v = vertex_positions[i]; + + int xi = int(v.x * cell_scale + 0.5f); + int yi = int(v.y * cell_scale + 0.5f); + int zi = int(v.z * cell_scale + 0.5f); + + vertex_ids[i] = (xi << 20) | (yi << 10) | zi; + } +} + +static size_t countTriangles(const unsigned int* vertex_ids, const unsigned int* indices, size_t index_count) +{ + size_t result = 0; + + for (size_t i = 0; i < index_count; i += 3) + { + unsigned int id0 = vertex_ids[indices[i + 0]]; + unsigned int id1 = vertex_ids[indices[i + 1]]; + unsigned int id2 = vertex_ids[indices[i + 2]]; + + result += (id0 != id1) & (id0 != id2) & (id1 != id2); + } + + return result; +} + +static size_t fillVertexCells(unsigned int* table, size_t table_size, unsigned int* vertex_cells, const unsigned int* vertex_ids, size_t vertex_count) +{ + CellHasher hasher = {vertex_ids}; + + memset(table, -1, table_size * sizeof(unsigned int)); + + size_t result = 0; + + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int* entry = hashLookup2(table, table_size, hasher, unsigned(i), ~0u); + + if (*entry == ~0u) + { + *entry = unsigned(i); + vertex_cells[i] = unsigned(result++); + } + else + { + vertex_cells[i] = vertex_cells[*entry]; + } + } + + return result; +} + +static size_t countVertexCells(unsigned int* table, size_t table_size, const unsigned int* vertex_ids, size_t vertex_count) +{ + IdHasher hasher; + + memset(table, -1, table_size * sizeof(unsigned int)); + + size_t result = 0; + + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int id = vertex_ids[i]; + unsigned int* entry = hashLookup2(table, table_size, hasher, id, ~0u); + + result += (*entry == ~0u); + *entry = id; + } + + return result; +} + +static void fillCellQuadrics(Quadric* cell_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* vertex_cells) +{ + for (size_t i = 0; i < index_count; i += 3) + { + unsigned int i0 = indices[i + 0]; + unsigned int i1 = indices[i + 1]; + unsigned int i2 = indices[i + 2]; + + unsigned int c0 = vertex_cells[i0]; + unsigned int c1 = vertex_cells[i1]; + unsigned int c2 = vertex_cells[i2]; + + bool single_cell = (c0 == c1) & (c0 == c2); + + Quadric Q; + quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], single_cell ? 3.f : 1.f); + + if (single_cell) + { + quadricAdd(cell_quadrics[c0], Q); + } + else + { + quadricAdd(cell_quadrics[c0], Q); + quadricAdd(cell_quadrics[c1], Q); + quadricAdd(cell_quadrics[c2], Q); + } + } +} + +static void fillCellQuadrics(Quadric* cell_quadrics, const Vector3* vertex_positions, size_t vertex_count, const unsigned int* vertex_cells) +{ + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int c = vertex_cells[i]; + const Vector3& v = vertex_positions[i]; + + Quadric Q; + quadricFromPoint(Q, v.x, v.y, v.z, 1.f); + + quadricAdd(cell_quadrics[c], Q); + } +} + +static void fillCellRemap(unsigned int* cell_remap, float* cell_errors, size_t cell_count, const unsigned int* vertex_cells, const Quadric* cell_quadrics, const Vector3* vertex_positions, size_t vertex_count) +{ + memset(cell_remap, -1, cell_count * sizeof(unsigned int)); + + for (size_t i = 0; i < vertex_count; ++i) + { + unsigned int cell = vertex_cells[i]; + float error = quadricError(cell_quadrics[cell], vertex_positions[i]); + + if (cell_remap[cell] == ~0u || cell_errors[cell] > error) + { + cell_remap[cell] = unsigned(i); + cell_errors[cell] = error; + } + } +} + +static size_t filterTriangles(unsigned int* destination, unsigned int* tritable, size_t tritable_size, const unsigned int* indices, size_t index_count, const unsigned int* vertex_cells, const unsigned int* cell_remap) +{ + TriangleHasher hasher = {destination}; + + memset(tritable, -1, tritable_size * sizeof(unsigned int)); + + size_t result = 0; + + for (size_t i = 0; i < index_count; i += 3) + { + unsigned int c0 = vertex_cells[indices[i + 0]]; + unsigned int c1 = vertex_cells[indices[i + 1]]; + unsigned int c2 = vertex_cells[indices[i + 2]]; + + if (c0 != c1 && c0 != c2 && c1 != c2) + { + unsigned int a = cell_remap[c0]; + unsigned int b = cell_remap[c1]; + unsigned int c = cell_remap[c2]; + + if (b < a && b < c) + { + unsigned int t = a; + a = b, b = c, c = t; + } + else if (c < a && c < b) + { + unsigned int t = c; + c = b, b = a, a = t; + } + + destination[result * 3 + 0] = a; + destination[result * 3 + 1] = b; + destination[result * 3 + 2] = c; + + unsigned int* entry = hashLookup2(tritable, tritable_size, hasher, unsigned(result), ~0u); + + if (*entry == ~0u) + *entry = unsigned(result++); + } + } + + return result * 3; +} + +static float interpolate(float y, float x0, float y0, float x1, float y1, float x2, float y2) +{ + // three point interpolation from "revenge of interpolation search" paper + float num = (y1 - y) * (x1 - x2) * (x1 - x0) * (y2 - y0); + float den = (y2 - y) * (x1 - x2) * (y0 - y1) + (y0 - y) * (x1 - x0) * (y1 - y2); + return x1 + num / den; +} + +} // namespace meshopt + +#ifndef NDEBUG +// Note: this is only exposed for debug visualization purposes; do *not* use these in debug builds +MESHOPTIMIZER_API unsigned char* meshopt_simplifyDebugKind = 0; +MESHOPTIMIZER_API unsigned int* meshopt_simplifyDebugLoop = 0; +MESHOPTIMIZER_API unsigned int* meshopt_simplifyDebugLoopBack = 0; +#endif + +size_t meshopt_simplify(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) +{ + return meshopt_simplifyWithAttributes(destination, indices, index_count, vertex_positions_data, vertex_count, vertex_positions_stride, target_index_count, target_error, out_result_error, 0, 0, 0); +} + +size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float* out_result_error, const float* attributes, const float* attribute_weights, size_t attribute_count) +{ + using namespace meshopt; + + assert(index_count % 3 == 0); + assert(vertex_stride > 0 && vertex_stride <= 256); + assert(vertex_stride % sizeof(float) == 0); + assert(target_index_count <= index_count); + assert(attribute_count <= ATTRIBUTES); + + meshopt_Allocator allocator; + + unsigned int* result = destination; + + // build adjacency information + EdgeAdjacency adjacency = {}; + prepareEdgeAdjacency(adjacency, index_count, vertex_count, allocator); + updateEdgeAdjacency(adjacency, indices, index_count, vertex_count, NULL); + + // build position remap that maps each vertex to the one with identical position + unsigned int* remap = allocator.allocate<unsigned int>(vertex_count); + unsigned int* wedge = allocator.allocate<unsigned int>(vertex_count); + buildPositionRemap(remap, wedge, vertex_data, vertex_count, vertex_stride, allocator); + + // classify vertices; vertex kind determines collapse rules, see kCanCollapse + unsigned char* vertex_kind = allocator.allocate<unsigned char>(vertex_count); + unsigned int* loop = allocator.allocate<unsigned int>(vertex_count); + unsigned int* loopback = allocator.allocate<unsigned int>(vertex_count); + classifyVertices(vertex_kind, loop, loopback, vertex_count, adjacency, remap, wedge); + +#if TRACE + size_t unique_positions = 0; + for (size_t i = 0; i < vertex_count; ++i) + unique_positions += remap[i] == i; + + printf("position remap: %d vertices => %d positions\n", int(vertex_count), int(unique_positions)); + + size_t kinds[Kind_Count] = {}; + for (size_t i = 0; i < vertex_count; ++i) + kinds[vertex_kind[i]] += remap[i] == i; + + printf("kinds: manifold %d, border %d, seam %d, complex %d, locked %d\n", + int(kinds[Kind_Manifold]), int(kinds[Kind_Border]), int(kinds[Kind_Seam]), int(kinds[Kind_Complex]), int(kinds[Kind_Locked])); +#endif + + Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count); + rescalePositions(vertex_positions, vertex_data, vertex_count, vertex_stride); + +#if ATTRIBUTES + for (size_t i = 0; i < vertex_count; ++i) + { + memset(vertex_positions[i].a, 0, sizeof(vertex_positions[i].a)); + + for (size_t k = 0; k < attribute_count; ++k) + { + float a = attributes[i * attribute_count + k]; + + vertex_positions[i].a[k] = a * attribute_weights[k]; + } + } +#endif + + Quadric* vertex_quadrics = allocator.allocate<Quadric>(vertex_count); + memset(vertex_quadrics, 0, vertex_count * sizeof(Quadric)); + Quadric* vertex_no_attrib_quadrics = allocator.allocate<Quadric>(vertex_count); + memset(vertex_no_attrib_quadrics, 0, vertex_count * sizeof(Quadric)); + + fillFaceQuadrics(vertex_quadrics, vertex_no_attrib_quadrics, indices, index_count, vertex_positions, remap); + fillEdgeQuadrics(vertex_quadrics, vertex_no_attrib_quadrics, indices, index_count, vertex_positions, remap, vertex_kind, loop, loopback); + + if (result != indices) + memcpy(result, indices, index_count * sizeof(unsigned int)); + +#if TRACE + size_t pass_count = 0; +#endif + + Collapse* edge_collapses = allocator.allocate<Collapse>(index_count); + unsigned int* collapse_order = allocator.allocate<unsigned int>(index_count); + unsigned int* collapse_remap = allocator.allocate<unsigned int>(vertex_count); + unsigned char* collapse_locked = allocator.allocate<unsigned char>(vertex_count); + + size_t result_count = index_count; + float result_error = 0; + + // target_error input is linear; we need to adjust it to match quadricError units + float error_limit = target_error * target_error; + + while (result_count > target_index_count) + { + // note: throughout the simplification process adjacency structure reflects welded topology for result-in-progress + updateEdgeAdjacency(adjacency, result, result_count, vertex_count, remap); + + size_t edge_collapse_count = pickEdgeCollapses(edge_collapses, result, result_count, remap, vertex_kind, loop); + + // no edges can be collapsed any more due to topology restrictions + if (edge_collapse_count == 0) + break; + + rankEdgeCollapses(edge_collapses, edge_collapse_count, vertex_positions, vertex_quadrics, vertex_no_attrib_quadrics, remap); + +#if TRACE > 1 + dumpEdgeCollapses(edge_collapses, edge_collapse_count, vertex_kind); +#endif + + sortEdgeCollapses(collapse_order, edge_collapses, edge_collapse_count); + + size_t triangle_collapse_goal = (result_count - target_index_count) / 3; + + for (size_t i = 0; i < vertex_count; ++i) + collapse_remap[i] = unsigned(i); + + memset(collapse_locked, 0, vertex_count); + +#if TRACE + printf("pass %d: ", int(pass_count++)); +#endif + + size_t collapses = performEdgeCollapses(collapse_remap, collapse_locked, vertex_quadrics, vertex_no_attrib_quadrics, edge_collapses, edge_collapse_count, collapse_order, remap, wedge, vertex_kind, vertex_positions, adjacency, triangle_collapse_goal, error_limit, result_error); + + // no edges can be collapsed any more due to hitting the error limit or triangle collapse limit + if (collapses == 0) + break; + + remapEdgeLoops(loop, vertex_count, collapse_remap); + remapEdgeLoops(loopback, vertex_count, collapse_remap); + + size_t new_count = remapIndexBuffer(result, result_count, collapse_remap); + assert(new_count < result_count); + + result_count = new_count; + } + +#if TRACE + printf("result: %d triangles, error: %e; total %d passes\n", int(result_count), sqrtf(result_error), int(pass_count)); +#endif + +#if TRACE > 1 + dumpLockedCollapses(result, result_count, vertex_kind); +#endif + +#ifndef NDEBUG + if (meshopt_simplifyDebugKind) + memcpy(meshopt_simplifyDebugKind, vertex_kind, vertex_count); + + if (meshopt_simplifyDebugLoop) + memcpy(meshopt_simplifyDebugLoop, loop, vertex_count * sizeof(unsigned int)); + + if (meshopt_simplifyDebugLoopBack) + memcpy(meshopt_simplifyDebugLoopBack, loopback, vertex_count * sizeof(unsigned int)); +#endif + + // result_error is quadratic; we need to remap it back to linear + if (out_result_error) + { + *out_result_error = sqrtf(result_error); + } + + 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, float target_error, float* out_result_error) +{ + using namespace meshopt; + + assert(index_count % 3 == 0); + assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256); + assert(vertex_positions_stride % sizeof(float) == 0); + assert(target_index_count <= index_count); + + // we expect to get ~2 triangles/vertex in the output + size_t target_cell_count = target_index_count / 6; + + meshopt_Allocator allocator; + + Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count); + rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride); + + // find the optimal grid size using guided binary search +#if TRACE + printf("source: %d vertices, %d triangles\n", int(vertex_count), int(index_count / 3)); + printf("target: %d cells, %d triangles\n", int(target_cell_count), int(target_index_count / 3)); +#endif + + unsigned int* vertex_ids = allocator.allocate<unsigned int>(vertex_count); + + const int kInterpolationPasses = 5; + + // invariant: # of triangles in min_grid <= target_count + 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) + { + 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; + grid_size = (grid_size <= min_grid) ? min_grid + 1 : (grid_size >= max_grid) ? max_grid - 1 : grid_size; + + computeVertexIds(vertex_ids, vertex_positions, vertex_count, grid_size); + size_t triangles = countTriangles(vertex_ids, indices, index_count); + +#if TRACE + printf("pass %d (%s): grid size %d, triangles %d, %s\n", + pass, (pass == 0) ? "guess" : (pass <= kInterpolationPasses) ? "lerp" : "binary", + grid_size, int(triangles), + (triangles <= target_index_count / 3) ? "under" : "over"); +#endif + + float tip = interpolate(float(target_index_count / 3), float(min_grid), float(min_triangles), float(grid_size), float(triangles), float(max_grid), float(max_triangles)); + + if (triangles <= target_index_count / 3) + { + min_grid = grid_size; + min_triangles = triangles; + } + else + { + max_grid = grid_size; + max_triangles = triangles; + } + + // 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); + unsigned int* table = allocator.allocate<unsigned int>(table_size); + + unsigned int* vertex_cells = allocator.allocate<unsigned int>(vertex_count); + + computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid); + size_t cell_count = fillVertexCells(table, table_size, vertex_cells, vertex_ids, vertex_count); + + // build a quadric for each target cell + Quadric* cell_quadrics = allocator.allocate<Quadric>(cell_count); + memset(cell_quadrics, 0, cell_count * sizeof(Quadric)); + + fillCellQuadrics(cell_quadrics, indices, index_count, vertex_positions, vertex_cells); + + // for each target cell, find the vertex with the minimal error + unsigned int* cell_remap = allocator.allocate<unsigned int>(cell_count); + float* cell_errors = allocator.allocate<float>(cell_count); + + 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); + +#if TRACE + 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; +} + +size_t meshopt_simplifyPoints(unsigned int* destination, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_vertex_count) +{ + using namespace meshopt; + + assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256); + assert(vertex_positions_stride % sizeof(float) == 0); + assert(target_vertex_count <= vertex_count); + + size_t target_cell_count = target_vertex_count; + + if (target_cell_count == 0) + return 0; + + meshopt_Allocator allocator; + + Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count); + rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride); + + // find the optimal grid size using guided binary search +#if TRACE + printf("source: %d vertices\n", int(vertex_count)); + printf("target: %d cells\n", int(target_cell_count)); +#endif + + unsigned int* vertex_ids = allocator.allocate<unsigned int>(vertex_count); + + size_t table_size = hashBuckets2(vertex_count); + unsigned int* table = allocator.allocate<unsigned int>(table_size); + + const int kInterpolationPasses = 5; + + // invariant: # of vertices in min_grid <= target_count + int min_grid = 0; + int max_grid = 1025; + size_t min_vertices = 0; + size_t max_vertices = vertex_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_vertices < target_vertex_count); + assert(max_grid - min_grid > 1); + + // we clamp the prediction of the grid size to make sure that the search converges + int grid_size = next_grid_size; + grid_size = (grid_size <= min_grid) ? min_grid + 1 : (grid_size >= max_grid) ? max_grid - 1 : grid_size; + + computeVertexIds(vertex_ids, vertex_positions, vertex_count, grid_size); + size_t vertices = countVertexCells(table, table_size, vertex_ids, vertex_count); + +#if TRACE + printf("pass %d (%s): grid size %d, vertices %d, %s\n", + pass, (pass == 0) ? "guess" : (pass <= kInterpolationPasses) ? "lerp" : "binary", + grid_size, int(vertices), + (vertices <= target_vertex_count) ? "under" : "over"); +#endif + + float tip = interpolate(float(target_vertex_count), float(min_grid), float(min_vertices), float(grid_size), float(vertices), float(max_grid), float(max_vertices)); + + if (vertices <= target_vertex_count) + { + min_grid = grid_size; + min_vertices = vertices; + } + else + { + max_grid = grid_size; + max_vertices = vertices; + } + + if (vertices == target_vertex_count || 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_vertices == 0) + return 0; + + // build vertex->cell association by mapping all vertices with the same quantized position to the same cell + unsigned int* vertex_cells = allocator.allocate<unsigned int>(vertex_count); + + computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid); + size_t cell_count = fillVertexCells(table, table_size, vertex_cells, vertex_ids, vertex_count); + + // build a quadric for each target cell + Quadric* cell_quadrics = allocator.allocate<Quadric>(cell_count); + memset(cell_quadrics, 0, cell_count * sizeof(Quadric)); + + fillCellQuadrics(cell_quadrics, vertex_positions, vertex_count, vertex_cells); + + // for each target cell, find the vertex with the minimal error + unsigned int* cell_remap = allocator.allocate<unsigned int>(cell_count); + float* cell_errors = allocator.allocate<float>(cell_count); + + fillCellRemap(cell_remap, cell_errors, cell_count, vertex_cells, cell_quadrics, vertex_positions, vertex_count); + + // copy results to the output + assert(cell_count <= target_vertex_count); + memcpy(destination, cell_remap, sizeof(unsigned int) * cell_count); + +#if TRACE + printf("result: %d cells\n", int(cell_count)); +#endif + + return cell_count; +} + +float meshopt_simplifyScale(const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride) +{ + using namespace meshopt; + + assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256); + assert(vertex_positions_stride % sizeof(float) == 0); + + float extent = rescalePositions(NULL, vertex_positions, vertex_count, vertex_positions_stride); + + return extent; +} |