These files are variants of simplifier.cpp from https://github.com/zeux/meshoptimizer, created for the article https://zeuxcg.org/2019/01/17/is-c-fast/
Simplifier variants
| // 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> | |
| #include <stdlib.h> | |
| #include <stdbool.h> | |
| #ifndef TRACE | |
| #define TRACE 0 | |
| #endif | |
| #if TRACE | |
| #include <stdio.h> | |
| #endif | |
| typedef struct meshopt_Allocator | |
| { | |
| size_t count; | |
| void* blocks[16]; | |
| } meshopt_Allocator; | |
| static void* meshopt_allocate(meshopt_Allocator* alloc, size_t size) | |
| { | |
| void* result = malloc(size); | |
| alloc->blocks[alloc->count++] = result; | |
| return result; | |
| } | |
| static void meshopt_deallocate(meshopt_Allocator* alloc) | |
| { | |
| for (size_t i = 0; i < alloc->count; ++i) | |
| free(alloc->blocks[i]); | |
| } | |
| // 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 | |
| typedef struct EdgeAdjacency | |
| { | |
| unsigned int* counts; | |
| unsigned int* offsets; | |
| unsigned int* data; | |
| } EdgeAdjacency; | |
| static void buildEdgeAdjacency(EdgeAdjacency* adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count, meshopt_Allocator* allocator) | |
| { | |
| size_t face_count = index_count / 3; | |
| // allocate arrays | |
| adjacency->counts = (unsigned int*)meshopt_allocate(allocator, vertex_count * sizeof(unsigned int)); | |
| adjacency->offsets = (unsigned int*)meshopt_allocate(allocator, vertex_count * sizeof(unsigned int)); | |
| adjacency->data = (unsigned int*)meshopt_allocate(allocator, index_count * sizeof(unsigned int)); | |
| // fill edge counts | |
| memset(adjacency->counts, 0, vertex_count * sizeof(unsigned int)); | |
| for (size_t i = 0; i < index_count; ++i) | |
| { | |
| assert(indices[i] < vertex_count); | |
| adjacency->counts[indices[i]]++; | |
| } | |
| // 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]; | |
| adjacency->data[adjacency->offsets[a]++] = b; | |
| adjacency->data[adjacency->offsets[b]++] = c; | |
| adjacency->data[adjacency->offsets[c]++] = a; | |
| } | |
| // 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]; | |
| } | |
| } | |
| typedef struct PositionHasher | |
| { | |
| const float* vertex_positions; | |
| size_t vertex_stride_float; | |
| } PositionHasher; | |
| static size_t hasherHash(const PositionHasher* hasher, unsigned int index) | |
| { | |
| // MurmurHash2 | |
| const unsigned int m = 0x5bd1e995; | |
| const int r = 24; | |
| unsigned int h = 0; | |
| const unsigned int* key = (const unsigned int*)(hasher->vertex_positions + index * hasher->vertex_stride_float); | |
| for (size_t i = 0; i < 3; ++i) | |
| { | |
| unsigned int k = key[i]; | |
| k *= m; | |
| k ^= k >> r; | |
| k *= m; | |
| h *= m; | |
| h ^= k; | |
| } | |
| return h; | |
| } | |
| static bool hasherEqual(const PositionHasher* hasher, unsigned int lhs, unsigned int rhs) | |
| { | |
| return memcmp(hasher->vertex_positions + lhs * hasher->vertex_stride_float, hasher->vertex_positions + rhs * hasher->vertex_stride_float, sizeof(float) * 3) == 0; | |
| } | |
| static size_t hashBuckets2(size_t count) | |
| { | |
| size_t buckets = 1; | |
| while (buckets < count) | |
| buckets *= 2; | |
| return buckets; | |
| } | |
| static unsigned int* hashLookup2(unsigned int* table, size_t buckets, const PositionHasher* hasher, unsigned int key, unsigned int empty) | |
| { | |
| assert(buckets > 0); | |
| assert((buckets & (buckets - 1)) == 0); | |
| size_t hashmod = buckets - 1; | |
| size_t bucket = hasherHash(hasher, key) & hashmod; | |
| for (size_t probe = 0; probe <= hashmod; ++probe) | |
| { | |
| unsigned int* item = &table[bucket]; | |
| if (*item == empty) | |
| return item; | |
| if (hasherEqual(hasher, *item, key)) | |
| return item; | |
| // hash collision, quadratic probing | |
| bucket = (bucket + probe + 1) & hashmod; | |
| } | |
| assert(false && "Hash table is full"); | |
| 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 = (unsigned int*)meshopt_allocate(allocator, table_size * sizeof(unsigned int)); | |
| 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_Locked, // none of the above; these vertices can't move | |
| Kind_Count | |
| }; | |
| // manifold vertices can collapse on anything except locked | |
| // border/seam vertices can only be collapsed onto border/seam respectively | |
| const unsigned char kCanCollapse[Kind_Count][Kind_Count] = { | |
| {1, 1, 1, 1}, | |
| {0, 1, 0, 0}, | |
| {0, 0, 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, 1}, | |
| {1, 0, 1, 0}, | |
| {1, 1, 1, 1}, | |
| {1, 0, 1, 0}, | |
| }; | |
| static bool hasEdge(const EdgeAdjacency* adjacency, unsigned int a, unsigned int b) | |
| { | |
| unsigned int count = adjacency->counts[a]; | |
| const unsigned int* data = adjacency->data + adjacency->offsets[a]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (data[i] == b) | |
| return true; | |
| return false; | |
| } | |
| static unsigned int findWedgeEdge(const EdgeAdjacency* adjacency, const unsigned int* wedge, unsigned int a, unsigned int b) | |
| { | |
| unsigned int v = a; | |
| do | |
| { | |
| if (hasEdge(adjacency, v, b)) | |
| return v; | |
| v = wedge[v]; | |
| } while (v != a); | |
| return ~0u; | |
| } | |
| static size_t countOpenEdges(const EdgeAdjacency* adjacency, unsigned int vertex, unsigned int* last) | |
| { | |
| size_t result = 0; | |
| unsigned int count = adjacency->counts[vertex]; | |
| const unsigned int* data = adjacency->data + adjacency->offsets[vertex]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (!hasEdge(adjacency, data[i], vertex)) | |
| { | |
| result++; | |
| if (last) | |
| *last = data[i]; | |
| } | |
| return result; | |
| } | |
| static void classifyVertices(unsigned char* result, unsigned int* loop, size_t vertex_count, const EdgeAdjacency* adjacency, const unsigned int* remap, const unsigned int* wedge) | |
| { | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| loop[i] = ~0u; | |
| 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 v = 0; | |
| size_t edges = countOpenEdges(adjacency, (unsigned)(i), &v); | |
| // 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 | |
| // also note that we classify vertices as border if they have *one* open edge, not two | |
| // this is because we only have half-edges - so a border vertex would have one incoming and one outgoing edge | |
| if (edges == 0) | |
| { | |
| result[i] = Kind_Manifold; | |
| } | |
| else if (edges == 1) | |
| { | |
| result[i] = Kind_Border; | |
| loop[i] = v; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else if (wedge[wedge[i]] == i) | |
| { | |
| // attribute seam; need to distinguish between Seam and Locked | |
| unsigned int a = 0; | |
| size_t a_count = countOpenEdges(adjacency, (unsigned)(i), &a); | |
| unsigned int b = 0; | |
| size_t b_count = countOpenEdges(adjacency, wedge[i], &b); | |
| // seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap | |
| if (a_count == 1 && b_count == 1) | |
| { | |
| unsigned int ao = findWedgeEdge(adjacency, wedge, a, wedge[i]); | |
| unsigned int bo = findWedgeEdge(adjacency, wedge, b, (unsigned)(i)); | |
| if (ao != ~0u && bo != ~0u) | |
| { | |
| result[i] = Kind_Seam; | |
| loop[i] = a; | |
| loop[wedge[i]] = b; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| // more than one vertex maps to this one; we don't have classification available | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| assert(remap[i] < i); | |
| result[i] = result[remap[i]]; | |
| } | |
| } | |
| } | |
| typedef struct Vector3 | |
| { | |
| float x, y, z; | |
| } Vector3; | |
| static void 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; | |
| 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]); | |
| 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; | |
| } | |
| } | |
| typedef struct Quadric | |
| { | |
| float a00; | |
| float a10, a11; | |
| float a20, a21, a22; | |
| float b0, b1, b2, c; | |
| } Quadric; | |
| typedef struct Collapse | |
| { | |
| unsigned int v0; | |
| unsigned int v1; | |
| union { | |
| unsigned int bidi; | |
| float error; | |
| unsigned int errorui; | |
| }; | |
| } Collapse; | |
| 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->a10 += R->a10; | |
| Q->a11 += R->a11; | |
| Q->a20 += R->a20; | |
| Q->a21 += R->a21; | |
| Q->a22 += R->a22; | |
| Q->b0 += R->b0; | |
| Q->b1 += R->b1; | |
| Q->b2 += R->b2; | |
| Q->c += R->c; | |
| } | |
| static void quadricMul(Quadric* Q, float s) | |
| { | |
| Q->a00 *= s; | |
| Q->a10 *= s; | |
| Q->a11 *= s; | |
| Q->a20 *= s; | |
| Q->a21 *= s; | |
| Q->a22 *= s; | |
| Q->b0 *= s; | |
| Q->b1 *= s; | |
| Q->b2 *= s; | |
| Q->c *= s; | |
| } | |
| 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; | |
| return fabsf(r); | |
| } | |
| static void quadricFromPlane(Quadric* Q, float a, float b, float c, float d) | |
| { | |
| Q->a00 = a * a; | |
| Q->a10 = b * a; | |
| Q->a11 = b * b; | |
| Q->a20 = c * a; | |
| Q->a21 = c * b; | |
| Q->a22 = c * c; | |
| Q->b0 = d * a; | |
| Q->b1 = d * b; | |
| Q->b2 = d * c; | |
| Q->c = d * d; | |
| } | |
| static void quadricFromTriangle(Quadric* Q, const Vector3* p0, const Vector3* p1, const Vector3* p2) | |
| { | |
| 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}; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, area); | |
| } | |
| 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); | |
| 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; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, length * length * weight); | |
| } | |
| static void fillFaceQuadrics(Quadric* vertex_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]); | |
| quadricAdd(&vertex_quadrics[remap[i0]], &Q); | |
| quadricAdd(&vertex_quadrics[remap[i1]], &Q); | |
| quadricAdd(&vertex_quadrics[remap[i2]], &Q); | |
| } | |
| } | |
| static void fillEdgeQuadrics(Quadric* vertex_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) | |
| { | |
| 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 i0 and i1 are border/seam and are on the same edge loop | |
| // 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; | |
| 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_Seam) ? kEdgeWeightSeam : kEdgeWeightBorder; | |
| 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); | |
| } | |
| } | |
| } | |
| 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 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; | |
| float ei = quadricError(&vertex_quadrics[remap[i0]], &vertex_positions[i1]); | |
| float ej = quadricError(&vertex_quadrics[remap[j0]], &vertex_positions[j1]); | |
| // pick edge direction with minimal error | |
| c->v0 = ei <= ej ? i0 : j0; | |
| c->v1 = ei <= ej ? i1 : j1; | |
| c->error = ei <= ej ? ei : ej; | |
| } | |
| } | |
| #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]), cerrors[k0][k1]); | |
| } | |
| 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 < (size_t)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, 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, size_t triangle_collapse_goal, float error_limit) | |
| { | |
| size_t edge_collapses = 0; | |
| size_t triangle_collapses = 0; | |
| for (size_t i = 0; i < collapse_count; ++i) | |
| { | |
| const Collapse* c = &collapses[collapse_order[i]]; | |
| if (c->error > error_limit) | |
| break; | |
| if (triangle_collapses >= triangle_collapse_goal) | |
| break; | |
| unsigned int r0 = remap[c->v0]; | |
| unsigned int r1 = remap[c->v1]; | |
| // 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]) | |
| continue; | |
| assert(collapse_remap[r0] == r0); | |
| assert(collapse_remap[r1] == r1); | |
| quadricAdd(&vertex_quadrics[r1], &vertex_quadrics[r0]); | |
| if (vertex_kind[c->v0] == Kind_Seam) | |
| { | |
| // remap v0 to v1 and seam pair of v0 to seam pair of v1 | |
| unsigned int s0 = wedge[c->v0]; | |
| unsigned int s1 = wedge[c->v1]; | |
| assert(s0 != c->v0 && s1 != c->v1); | |
| assert(wedge[s0] == c->v0 && wedge[s1] == c->v1); | |
| collapse_remap[c->v0] = c->v1; | |
| collapse_remap[s0] = s1; | |
| } | |
| else | |
| { | |
| assert(wedge[c->v0] == c->v0); | |
| collapse_remap[c->v0] = c->v1; | |
| } | |
| collapse_locked[r0] = 1; | |
| collapse_locked[r1] = 1; | |
| // border edges collapse 1 triangle, other edges collapse 2 or more | |
| triangle_collapses += (vertex_kind[c->v0] == Kind_Border) ? 1 : 2; | |
| edge_collapses++; | |
| } | |
| 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; | |
| } | |
| } | |
| } | |
| #if TRACE | |
| unsigned char* meshopt_simplifyDebugKind = 0; | |
| unsigned int* meshopt_simplifyDebugLoop = 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) | |
| { | |
| 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); | |
| meshopt_Allocator allocator = {0}; | |
| unsigned int* result = destination; | |
| // build adjacency information | |
| EdgeAdjacency adjacency = {0}; | |
| buildEdgeAdjacency(&adjacency, indices, index_count, vertex_count, &allocator); | |
| // build position remap that maps each vertex to the one with identical position | |
| unsigned int* remap = (unsigned int*)meshopt_allocate(&allocator, vertex_count * sizeof(unsigned int)); | |
| unsigned int* wedge = (unsigned int*)meshopt_allocate(&allocator, vertex_count * sizeof(unsigned int)); | |
| buildPositionRemap(remap, wedge, vertex_positions_data, vertex_count, vertex_positions_stride, &allocator); | |
| // classify vertices; vertex kind determines collapse rules, see kCanCollapse | |
| unsigned char* vertex_kind = (unsigned char*)meshopt_allocate(&allocator, vertex_count); | |
| unsigned int* loop = (unsigned int*)meshopt_allocate(&allocator, vertex_count * sizeof(unsigned int)); | |
| classifyVertices(vertex_kind, loop, 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, locked %d\n", | |
| int(kinds[Kind_Manifold]), int(kinds[Kind_Border]), int(kinds[Kind_Seam]), int(kinds[Kind_Locked])); | |
| #endif | |
| Vector3* vertex_positions = (Vector3*)meshopt_allocate(&allocator, vertex_count * sizeof(Vector3)); | |
| rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride); | |
| Quadric* vertex_quadrics = (Quadric*)meshopt_allocate(&allocator, vertex_count * sizeof(Quadric)); | |
| memset(vertex_quadrics, 0, vertex_count * sizeof(Quadric)); | |
| fillFaceQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap); | |
| fillEdgeQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap, vertex_kind, loop); | |
| if (result != indices) | |
| memcpy(result, indices, index_count * sizeof(unsigned int)); | |
| #if TRACE | |
| size_t pass_count = 0; | |
| float worst_error = 0; | |
| #endif | |
| Collapse* edge_collapses = (Collapse*)meshopt_allocate(&allocator, index_count * sizeof(Collapse)); | |
| unsigned int* collapse_order = (unsigned int*)meshopt_allocate(&allocator, index_count * sizeof(unsigned int)); | |
| unsigned int* collapse_remap = (unsigned int*)meshopt_allocate(&allocator, vertex_count * sizeof(unsigned int)); | |
| unsigned char* collapse_locked = (unsigned char*)meshopt_allocate(&allocator, vertex_count); | |
| size_t result_count = index_count; | |
| while (result_count > target_index_count) | |
| { | |
| 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, remap); | |
| #if TRACE > 1 | |
| dumpEdgeCollapses(edge_collapses, edge_collapse_count, vertex_kind); | |
| #endif | |
| sortEdgeCollapses(collapse_order, edge_collapses, edge_collapse_count); | |
| // 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 triangle_collapse_goal = (result_count - target_index_count) / 3; | |
| size_t edge_collapse_goal = triangle_collapse_goal / 2; | |
| // 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 this factor | |
| const float kPassErrorBound = 1.5f; | |
| float error_goal = edge_collapse_goal < edge_collapse_count ? edge_collapses[collapse_order[edge_collapse_goal]].error * kPassErrorBound : FLT_MAX; | |
| float error_limit = error_goal > target_error ? target_error : error_goal; | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| collapse_remap[i] = (unsigned)(i); | |
| memset(collapse_locked, 0, vertex_count); | |
| size_t collapses = performEdgeCollapses(collapse_remap, collapse_locked, vertex_quadrics, edge_collapses, edge_collapse_count, collapse_order, remap, wedge, vertex_kind, triangle_collapse_goal, error_limit); | |
| // 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); | |
| size_t new_count = remapIndexBuffer(result, result_count, collapse_remap); | |
| assert(new_count < result_count); | |
| #if TRACE | |
| float pass_error = 0.f; | |
| for (size_t i = 0; i < edge_collapse_count; ++i) | |
| { | |
| Collapse& c = edge_collapses[collapse_order[i]]; | |
| if (collapse_remap[c.v0] == c.v1) | |
| pass_error = c.error; | |
| } | |
| pass_count++; | |
| worst_error = (worst_error < pass_error) ? pass_error : worst_error; | |
| printf("pass %d: triangles: %d -> %d, collapses: %d/%d (goal: %d), error: %e (limit %e goal %e)\n", int(pass_count), int(result_count / 3), int(new_count / 3), int(collapses), int(edge_collapse_count), int(edge_collapse_goal), pass_error, error_limit, error_goal); | |
| #endif | |
| result_count = new_count; | |
| } | |
| #if TRACE | |
| printf("passes: %d, worst error: %e\n", int(pass_count), worst_error); | |
| #endif | |
| #if TRACE > 1 | |
| dumpLockedCollapses(result, result_count, vertex_kind); | |
| #endif | |
| #if TRACE | |
| if (meshopt_simplifyDebugKind) | |
| memcpy(meshopt_simplifyDebugKind, vertex_kind, vertex_count); | |
| if (meshopt_simplifyDebugLoop) | |
| memcpy(meshopt_simplifyDebugLoop, loop, vertex_count * sizeof(unsigned int)); | |
| #endif | |
| meshopt_deallocate(&allocator); | |
| return result_count; | |
| } |
| // 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 | |
| // 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 | |
| namespace meshopt | |
| { | |
| struct EdgeAdjacency | |
| { | |
| unsigned int* counts; | |
| unsigned int* offsets; | |
| unsigned int* data; | |
| }; | |
| static void buildEdgeAdjacency(EdgeAdjacency& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count, meshopt_Allocator& allocator) | |
| { | |
| size_t face_count = index_count / 3; | |
| // allocate arrays | |
| adjacency.counts = allocator.allocate<unsigned int>(vertex_count); | |
| adjacency.offsets = allocator.allocate<unsigned int>(vertex_count); | |
| adjacency.data = allocator.allocate<unsigned int>(index_count); | |
| // fill edge counts | |
| memset(adjacency.counts, 0, vertex_count * sizeof(unsigned int)); | |
| for (size_t i = 0; i < index_count; ++i) | |
| { | |
| assert(indices[i] < vertex_count); | |
| adjacency.counts[indices[i]]++; | |
| } | |
| // 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]; | |
| adjacency.data[adjacency.offsets[a]++] = b; | |
| adjacency.data[adjacency.offsets[b]++] = c; | |
| adjacency.data[adjacency.offsets[c]++] = a; | |
| } | |
| // 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 | |
| { | |
| // MurmurHash2 | |
| const unsigned int m = 0x5bd1e995; | |
| const int r = 24; | |
| unsigned int h = 0; | |
| const unsigned int* key = reinterpret_cast<const unsigned int*>(vertex_positions + index * vertex_stride_float); | |
| for (size_t i = 0; i < 3; ++i) | |
| { | |
| unsigned int k = key[i]; | |
| k *= m; | |
| k ^= k >> r; | |
| k *= m; | |
| h *= m; | |
| h ^= k; | |
| } | |
| return h; | |
| } | |
| 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) | |
| 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"); | |
| 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_Locked, // none of the above; these vertices can't move | |
| Kind_Count | |
| }; | |
| // manifold vertices can collapse on anything except locked | |
| // border/seam vertices can only be collapsed onto border/seam respectively | |
| const unsigned char kCanCollapse[Kind_Count][Kind_Count] = { | |
| {1, 1, 1, 1}, | |
| {0, 1, 0, 0}, | |
| {0, 0, 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, 1}, | |
| {1, 0, 1, 0}, | |
| {1, 1, 1, 1}, | |
| {1, 0, 1, 0}, | |
| }; | |
| static bool hasEdge(const EdgeAdjacency& adjacency, unsigned int a, unsigned int b) | |
| { | |
| unsigned int count = adjacency.counts[a]; | |
| const unsigned int* data = adjacency.data + adjacency.offsets[a]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (data[i] == b) | |
| return true; | |
| return false; | |
| } | |
| static unsigned int findWedgeEdge(const EdgeAdjacency& adjacency, const unsigned int* wedge, unsigned int a, unsigned int b) | |
| { | |
| unsigned int v = a; | |
| do | |
| { | |
| if (hasEdge(adjacency, v, b)) | |
| return v; | |
| v = wedge[v]; | |
| } while (v != a); | |
| return ~0u; | |
| } | |
| static size_t countOpenEdges(const EdgeAdjacency& adjacency, unsigned int vertex, unsigned int* last = 0) | |
| { | |
| size_t result = 0; | |
| unsigned int count = adjacency.counts[vertex]; | |
| const unsigned int* data = adjacency.data + adjacency.offsets[vertex]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (!hasEdge(adjacency, data[i], vertex)) | |
| { | |
| result++; | |
| if (last) | |
| *last = data[i]; | |
| } | |
| return result; | |
| } | |
| static void classifyVertices(unsigned char* result, unsigned int* loop, size_t vertex_count, const EdgeAdjacency& adjacency, const unsigned int* remap, const unsigned int* wedge) | |
| { | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| loop[i] = ~0u; | |
| 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 v = 0; | |
| size_t edges = countOpenEdges(adjacency, unsigned(i), &v); | |
| // 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 | |
| // also note that we classify vertices as border if they have *one* open edge, not two | |
| // this is because we only have half-edges - so a border vertex would have one incoming and one outgoing edge | |
| if (edges == 0) | |
| { | |
| result[i] = Kind_Manifold; | |
| } | |
| else if (edges == 1) | |
| { | |
| result[i] = Kind_Border; | |
| loop[i] = v; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else if (wedge[wedge[i]] == i) | |
| { | |
| // attribute seam; need to distinguish between Seam and Locked | |
| unsigned int a = 0; | |
| size_t a_count = countOpenEdges(adjacency, unsigned(i), &a); | |
| unsigned int b = 0; | |
| size_t b_count = countOpenEdges(adjacency, wedge[i], &b); | |
| // seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap | |
| if (a_count == 1 && b_count == 1) | |
| { | |
| unsigned int ao = findWedgeEdge(adjacency, wedge, a, wedge[i]); | |
| unsigned int bo = findWedgeEdge(adjacency, wedge, b, unsigned(i)); | |
| if (ao != ~0u && bo != ~0u) | |
| { | |
| result[i] = Kind_Seam; | |
| loop[i] = a; | |
| loop[wedge[i]] = b; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| // more than one vertex maps to this one; we don't have classification available | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| assert(remap[i] < i); | |
| result[i] = result[remap[i]]; | |
| } | |
| } | |
| } | |
| struct Vector3 | |
| { | |
| float x, y, z; | |
| }; | |
| static void 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; | |
| 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]); | |
| 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; | |
| } | |
| } | |
| struct Quadric | |
| { | |
| float a00; | |
| float a10, a11; | |
| float a20, a21, a22; | |
| float b0, b1, b2, c; | |
| }; | |
| struct Collapse | |
| { | |
| unsigned int v0; | |
| unsigned int v1; | |
| union { | |
| unsigned int bidi; | |
| float error; | |
| unsigned int errorui; | |
| }; | |
| }; | |
| 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.a10 += R.a10; | |
| Q.a11 += R.a11; | |
| Q.a20 += R.a20; | |
| Q.a21 += R.a21; | |
| Q.a22 += R.a22; | |
| Q.b0 += R.b0; | |
| Q.b1 += R.b1; | |
| Q.b2 += R.b2; | |
| Q.c += R.c; | |
| } | |
| static void quadricMul(Quadric& Q, float s) | |
| { | |
| Q.a00 *= s; | |
| Q.a10 *= s; | |
| Q.a11 *= s; | |
| Q.a20 *= s; | |
| Q.a21 *= s; | |
| Q.a22 *= s; | |
| Q.b0 *= s; | |
| Q.b1 *= s; | |
| Q.b2 *= s; | |
| Q.c *= s; | |
| } | |
| 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; | |
| return fabsf(r); | |
| } | |
| static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d) | |
| { | |
| Q.a00 = a * a; | |
| Q.a10 = b * a; | |
| Q.a11 = b * b; | |
| Q.a20 = c * a; | |
| Q.a21 = c * b; | |
| Q.a22 = c * c; | |
| Q.b0 = d * a; | |
| Q.b1 = d * b; | |
| Q.b2 = d * c; | |
| Q.c = d * d; | |
| } | |
| static void quadricFromTriangle(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2) | |
| { | |
| 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}; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, area); | |
| } | |
| 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); | |
| 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; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, length * length * weight); | |
| } | |
| static void fillFaceQuadrics(Quadric* vertex_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]); | |
| quadricAdd(vertex_quadrics[remap[i0]], Q); | |
| quadricAdd(vertex_quadrics[remap[i1]], Q); | |
| quadricAdd(vertex_quadrics[remap[i2]], Q); | |
| } | |
| } | |
| static void fillEdgeQuadrics(Quadric* vertex_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) | |
| { | |
| 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 i0 and i1 are border/seam and are on the same edge loop | |
| // 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; | |
| 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_Seam) ? kEdgeWeightSeam : kEdgeWeightBorder; | |
| 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); | |
| } | |
| } | |
| } | |
| 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 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; | |
| float ei = quadricError(vertex_quadrics[remap[i0]], vertex_positions[i1]); | |
| float ej = quadricError(vertex_quadrics[remap[j0]], vertex_positions[j1]); | |
| // pick edge direction with minimal error | |
| c.v0 = ei <= ej ? i0 : j0; | |
| c.v1 = ei <= ej ? i1 : j1; | |
| c.error = ei <= ej ? ei : ej; | |
| } | |
| } | |
| #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]), cerrors[k0][k1]); | |
| } | |
| 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, 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, size_t triangle_collapse_goal, float error_limit) | |
| { | |
| size_t edge_collapses = 0; | |
| size_t triangle_collapses = 0; | |
| for (size_t i = 0; i < collapse_count; ++i) | |
| { | |
| const Collapse& c = collapses[collapse_order[i]]; | |
| if (c.error > error_limit) | |
| break; | |
| if (triangle_collapses >= triangle_collapse_goal) | |
| break; | |
| unsigned int r0 = remap[c.v0]; | |
| unsigned int r1 = remap[c.v1]; | |
| // 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]) | |
| continue; | |
| assert(collapse_remap[r0] == r0); | |
| assert(collapse_remap[r1] == r1); | |
| quadricAdd(vertex_quadrics[r1], vertex_quadrics[r0]); | |
| if (vertex_kind[c.v0] == Kind_Seam) | |
| { | |
| // remap v0 to v1 and seam pair of v0 to seam pair of v1 | |
| unsigned int s0 = wedge[c.v0]; | |
| unsigned int s1 = wedge[c.v1]; | |
| assert(s0 != c.v0 && s1 != c.v1); | |
| assert(wedge[s0] == c.v0 && wedge[s1] == c.v1); | |
| collapse_remap[c.v0] = c.v1; | |
| collapse_remap[s0] = s1; | |
| } | |
| else | |
| { | |
| assert(wedge[c.v0] == c.v0); | |
| collapse_remap[c.v0] = c.v1; | |
| } | |
| collapse_locked[r0] = 1; | |
| collapse_locked[r1] = 1; | |
| // border edges collapse 1 triangle, other edges collapse 2 or more | |
| triangle_collapses += (vertex_kind[c.v0] == Kind_Border) ? 1 : 2; | |
| edge_collapses++; | |
| } | |
| 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; | |
| } | |
| } | |
| } | |
| } // namespace meshopt | |
| #if TRACE | |
| unsigned char* meshopt_simplifyDebugKind = 0; | |
| unsigned int* meshopt_simplifyDebugLoop = 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) | |
| { | |
| 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); | |
| meshopt_Allocator allocator; | |
| unsigned int* result = destination; | |
| // build adjacency information | |
| EdgeAdjacency adjacency = {}; | |
| buildEdgeAdjacency(adjacency, indices, index_count, vertex_count, allocator); | |
| // 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_positions_data, vertex_count, vertex_positions_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); | |
| classifyVertices(vertex_kind, loop, 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, locked %d\n", | |
| int(kinds[Kind_Manifold]), int(kinds[Kind_Border]), int(kinds[Kind_Seam]), int(kinds[Kind_Locked])); | |
| #endif | |
| Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count); | |
| rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride); | |
| Quadric* vertex_quadrics = allocator.allocate<Quadric>(vertex_count); | |
| memset(vertex_quadrics, 0, vertex_count * sizeof(Quadric)); | |
| fillFaceQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap); | |
| fillEdgeQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap, vertex_kind, loop); | |
| if (result != indices) | |
| memcpy(result, indices, index_count * sizeof(unsigned int)); | |
| #if TRACE | |
| size_t pass_count = 0; | |
| float worst_error = 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; | |
| while (result_count > target_index_count) | |
| { | |
| 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, remap); | |
| #if TRACE > 1 | |
| dumpEdgeCollapses(edge_collapses, edge_collapse_count, vertex_kind); | |
| #endif | |
| sortEdgeCollapses(collapse_order, edge_collapses, edge_collapse_count); | |
| // 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 triangle_collapse_goal = (result_count - target_index_count) / 3; | |
| size_t edge_collapse_goal = triangle_collapse_goal / 2; | |
| // 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 this factor | |
| const float kPassErrorBound = 1.5f; | |
| float error_goal = edge_collapse_goal < edge_collapse_count ? edge_collapses[collapse_order[edge_collapse_goal]].error * kPassErrorBound : FLT_MAX; | |
| float error_limit = error_goal > target_error ? target_error : error_goal; | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| collapse_remap[i] = unsigned(i); | |
| memset(collapse_locked, 0, vertex_count); | |
| size_t collapses = performEdgeCollapses(collapse_remap, collapse_locked, vertex_quadrics, edge_collapses, edge_collapse_count, collapse_order, remap, wedge, vertex_kind, triangle_collapse_goal, error_limit); | |
| // 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); | |
| size_t new_count = remapIndexBuffer(result, result_count, collapse_remap); | |
| assert(new_count < result_count); | |
| #if TRACE | |
| float pass_error = 0.f; | |
| for (size_t i = 0; i < edge_collapse_count; ++i) | |
| { | |
| Collapse& c = edge_collapses[collapse_order[i]]; | |
| if (collapse_remap[c.v0] == c.v1) | |
| pass_error = c.error; | |
| } | |
| pass_count++; | |
| worst_error = (worst_error < pass_error) ? pass_error : worst_error; | |
| printf("pass %d: triangles: %d -> %d, collapses: %d/%d (goal: %d), error: %e (limit %e goal %e)\n", int(pass_count), int(result_count / 3), int(new_count / 3), int(collapses), int(edge_collapse_count), int(edge_collapse_goal), pass_error, error_limit, error_goal); | |
| #endif | |
| result_count = new_count; | |
| } | |
| #if TRACE | |
| printf("passes: %d, worst error: %e\n", int(pass_count), worst_error); | |
| #endif | |
| #if TRACE > 1 | |
| dumpLockedCollapses(result, result_count, vertex_kind); | |
| #endif | |
| #if TRACE | |
| if (meshopt_simplifyDebugKind) | |
| memcpy(meshopt_simplifyDebugKind, vertex_kind, vertex_count); | |
| if (meshopt_simplifyDebugLoop) | |
| memcpy(meshopt_simplifyDebugLoop, loop, vertex_count * sizeof(unsigned int)); | |
| #endif | |
| return result_count; | |
| } |
| // This file is part of meshoptimizer library; see meshoptimizer.h for version/license details | |
| #include "meshoptimizer.h" | |
| #include <cassert> | |
| #include <cfloat> | |
| #include <cmath> | |
| #include <cstring> | |
| #ifndef TRACE | |
| #define TRACE 0 | |
| #endif | |
| #if TRACE | |
| #include <stdio.h> | |
| #endif | |
| // 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 | |
| namespace meshopt | |
| { | |
| template <typename T> struct meshopt_Buffer | |
| { | |
| T* data; | |
| size_t size; | |
| meshopt_Buffer() | |
| : data(0) | |
| , size(0) | |
| { | |
| } | |
| meshopt_Buffer(size_t size) | |
| : data(new T[size]) | |
| , size(size) | |
| { | |
| } | |
| ~meshopt_Buffer() | |
| { | |
| delete[] data; | |
| } | |
| void resize(size_t new_size) | |
| { | |
| assert(!data); | |
| data = new T[new_size]; | |
| size = new_size; | |
| } | |
| const T& operator[](size_t index) const | |
| { | |
| assert(index < size); | |
| return data[index]; | |
| } | |
| T& operator[](size_t index) | |
| { | |
| assert(index < size); | |
| return data[index]; | |
| } | |
| }; | |
| struct EdgeAdjacency | |
| { | |
| meshopt_Buffer<unsigned int> counts; | |
| meshopt_Buffer<unsigned int> offsets; | |
| meshopt_Buffer<unsigned int> data; | |
| }; | |
| static void buildEdgeAdjacency(EdgeAdjacency& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count) | |
| { | |
| size_t face_count = index_count / 3; | |
| // allocate arrays | |
| adjacency.counts.resize(vertex_count); | |
| adjacency.offsets.resize(vertex_count); | |
| adjacency.data.resize(index_count); | |
| // fill edge counts | |
| memset(&adjacency.counts[0], 0, vertex_count * sizeof(unsigned int)); | |
| for (size_t i = 0; i < index_count; ++i) | |
| { | |
| assert(indices[i] < vertex_count); | |
| adjacency.counts[indices[i]]++; | |
| } | |
| // 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]; | |
| adjacency.data[adjacency.offsets[a]++] = b; | |
| adjacency.data[adjacency.offsets[b]++] = c; | |
| adjacency.data[adjacency.offsets[c]++] = a; | |
| } | |
| // 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 | |
| { | |
| // MurmurHash2 | |
| const unsigned int m = 0x5bd1e995; | |
| const int r = 24; | |
| unsigned int h = 0; | |
| const unsigned int* key = reinterpret_cast<const unsigned int*>(vertex_positions + index * vertex_stride_float); | |
| for (size_t i = 0; i < 3; ++i) | |
| { | |
| unsigned int k = key[i]; | |
| k *= m; | |
| k ^= k >> r; | |
| k *= m; | |
| h *= m; | |
| h ^= k; | |
| } | |
| return h; | |
| } | |
| 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) | |
| buckets *= 2; | |
| return buckets; | |
| } | |
| template <typename T, typename Hash> | |
| static T* hashLookup2(meshopt_Buffer<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"); | |
| return 0; | |
| } | |
| static void buildPositionRemap(meshopt_Buffer<unsigned int>& remap, meshopt_Buffer<unsigned int>& wedge, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride) | |
| { | |
| PositionHasher hasher = {vertex_positions_data, vertex_positions_stride / sizeof(float)}; | |
| size_t table_size = hashBuckets2(vertex_count); | |
| meshopt_Buffer<unsigned int> table(table_size); | |
| memset(&table[0], -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_Locked, // none of the above; these vertices can't move | |
| Kind_Count | |
| }; | |
| // manifold vertices can collapse on anything except locked | |
| // border/seam vertices can only be collapsed onto border/seam respectively | |
| const unsigned char kCanCollapse[Kind_Count][Kind_Count] = { | |
| {1, 1, 1, 1}, | |
| {0, 1, 0, 0}, | |
| {0, 0, 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, 1}, | |
| {1, 0, 1, 0}, | |
| {1, 1, 1, 1}, | |
| {1, 0, 1, 0}, | |
| }; | |
| static bool hasEdge(const EdgeAdjacency& adjacency, unsigned int a, unsigned int b) | |
| { | |
| unsigned int count = adjacency.counts[a]; | |
| const unsigned int* data = &adjacency.data[adjacency.offsets[a]]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (data[i] == b) | |
| return true; | |
| return false; | |
| } | |
| static unsigned int findWedgeEdge(const EdgeAdjacency& adjacency, const meshopt_Buffer<unsigned int>& wedge, unsigned int a, unsigned int b) | |
| { | |
| unsigned int v = a; | |
| do | |
| { | |
| if (hasEdge(adjacency, v, b)) | |
| return v; | |
| v = wedge[v]; | |
| } while (v != a); | |
| return ~0u; | |
| } | |
| static size_t countOpenEdges(const EdgeAdjacency& adjacency, unsigned int vertex, unsigned int* last = 0) | |
| { | |
| size_t result = 0; | |
| unsigned int count = adjacency.counts[vertex]; | |
| const unsigned int* data = &adjacency.data[adjacency.offsets[vertex]]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (!hasEdge(adjacency, data[i], vertex)) | |
| { | |
| result++; | |
| if (last) | |
| *last = data[i]; | |
| } | |
| return result; | |
| } | |
| static void classifyVertices(meshopt_Buffer<unsigned char>& result, meshopt_Buffer<unsigned int>& loop, size_t vertex_count, const EdgeAdjacency& adjacency, const meshopt_Buffer<unsigned int>& remap, const meshopt_Buffer<unsigned int>& wedge) | |
| { | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| loop[i] = ~0u; | |
| 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 v = 0; | |
| size_t edges = countOpenEdges(adjacency, unsigned(i), &v); | |
| // 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 | |
| // also note that we classify vertices as border if they have *one* open edge, not two | |
| // this is because we only have half-edges - so a border vertex would have one incoming and one outgoing edge | |
| if (edges == 0) | |
| { | |
| result[i] = Kind_Manifold; | |
| } | |
| else if (edges == 1) | |
| { | |
| result[i] = Kind_Border; | |
| loop[i] = v; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else if (wedge[wedge[i]] == i) | |
| { | |
| // attribute seam; need to distinguish between Seam and Locked | |
| unsigned int a = 0; | |
| size_t a_count = countOpenEdges(adjacency, unsigned(i), &a); | |
| unsigned int b = 0; | |
| size_t b_count = countOpenEdges(adjacency, wedge[i], &b); | |
| // seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap | |
| if (a_count == 1 && b_count == 1) | |
| { | |
| unsigned int ao = findWedgeEdge(adjacency, wedge, a, wedge[i]); | |
| unsigned int bo = findWedgeEdge(adjacency, wedge, b, unsigned(i)); | |
| if (ao != ~0u && bo != ~0u) | |
| { | |
| result[i] = Kind_Seam; | |
| loop[i] = a; | |
| loop[wedge[i]] = b; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| // more than one vertex maps to this one; we don't have classification available | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| assert(remap[i] < i); | |
| result[i] = result[remap[i]]; | |
| } | |
| } | |
| } | |
| struct Vector3 | |
| { | |
| float x, y, z; | |
| }; | |
| static void rescalePositions(meshopt_Buffer<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; | |
| 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]); | |
| 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; | |
| } | |
| } | |
| struct Quadric | |
| { | |
| float a00; | |
| float a10, a11; | |
| float a20, a21, a22; | |
| float b0, b1, b2, c; | |
| }; | |
| struct Collapse | |
| { | |
| unsigned int v0; | |
| unsigned int v1; | |
| union { | |
| unsigned int bidi; | |
| float error; | |
| unsigned int errorui; | |
| }; | |
| }; | |
| 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.a10 += R.a10; | |
| Q.a11 += R.a11; | |
| Q.a20 += R.a20; | |
| Q.a21 += R.a21; | |
| Q.a22 += R.a22; | |
| Q.b0 += R.b0; | |
| Q.b1 += R.b1; | |
| Q.b2 += R.b2; | |
| Q.c += R.c; | |
| } | |
| static void quadricMul(Quadric& Q, float s) | |
| { | |
| Q.a00 *= s; | |
| Q.a10 *= s; | |
| Q.a11 *= s; | |
| Q.a20 *= s; | |
| Q.a21 *= s; | |
| Q.a22 *= s; | |
| Q.b0 *= s; | |
| Q.b1 *= s; | |
| Q.b2 *= s; | |
| Q.c *= s; | |
| } | |
| 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; | |
| return fabsf(r); | |
| } | |
| static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d) | |
| { | |
| Q.a00 = a * a; | |
| Q.a10 = b * a; | |
| Q.a11 = b * b; | |
| Q.a20 = c * a; | |
| Q.a21 = c * b; | |
| Q.a22 = c * c; | |
| Q.b0 = d * a; | |
| Q.b1 = d * b; | |
| Q.b2 = d * c; | |
| Q.c = d * d; | |
| } | |
| static void quadricFromTriangle(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2) | |
| { | |
| 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}; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, area); | |
| } | |
| 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); | |
| 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; | |
| 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; | |
| quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance); | |
| quadricMul(Q, length * length * weight); | |
| } | |
| static void fillFaceQuadrics(meshopt_Buffer<Quadric>& vertex_quadrics, const unsigned int* indices, size_t index_count, const meshopt_Buffer<Vector3>& vertex_positions, const meshopt_Buffer<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]); | |
| quadricAdd(vertex_quadrics[remap[i0]], Q); | |
| quadricAdd(vertex_quadrics[remap[i1]], Q); | |
| quadricAdd(vertex_quadrics[remap[i2]], Q); | |
| } | |
| } | |
| static void fillEdgeQuadrics(meshopt_Buffer<Quadric>& vertex_quadrics, const unsigned int* indices, size_t index_count, const meshopt_Buffer<Vector3>& vertex_positions, const meshopt_Buffer<unsigned int>& remap, const meshopt_Buffer<unsigned char>& vertex_kind, const meshopt_Buffer<unsigned int>& loop) | |
| { | |
| 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 i0 and i1 are border/seam and are on the same edge loop | |
| // 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; | |
| 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_Seam) ? kEdgeWeightSeam : kEdgeWeightBorder; | |
| 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); | |
| } | |
| } | |
| } | |
| static size_t pickEdgeCollapses(meshopt_Buffer<Collapse>& collapses, const unsigned int* indices, size_t index_count, const meshopt_Buffer<unsigned int>& remap, const meshopt_Buffer<unsigned char>& vertex_kind, const meshopt_Buffer<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(meshopt_Buffer<Collapse>& collapses, size_t collapse_count, const meshopt_Buffer<Vector3>& vertex_positions, const meshopt_Buffer<Quadric>& vertex_quadrics, const meshopt_Buffer<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; | |
| float ei = quadricError(vertex_quadrics[remap[i0]], vertex_positions[i1]); | |
| float ej = quadricError(vertex_quadrics[remap[j0]], vertex_positions[j1]); | |
| // pick edge direction with minimal error | |
| c.v0 = ei <= ej ? i0 : j0; | |
| c.v1 = ei <= ej ? i1 : j1; | |
| c.error = ei <= ej ? ei : ej; | |
| } | |
| } | |
| #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]), cerrors[k0][k1]); | |
| } | |
| 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(meshopt_Buffer<unsigned int>& sort_order, const meshopt_Buffer<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(meshopt_Buffer<unsigned int>& collapse_remap, meshopt_Buffer<unsigned char>& collapse_locked, meshopt_Buffer<Quadric>& vertex_quadrics, const meshopt_Buffer<Collapse>& collapses, size_t collapse_count, const meshopt_Buffer<unsigned int>& collapse_order, const meshopt_Buffer<unsigned int>& remap, const meshopt_Buffer<unsigned int>& wedge, const meshopt_Buffer<unsigned char>& vertex_kind, size_t triangle_collapse_goal, float error_limit) | |
| { | |
| size_t edge_collapses = 0; | |
| size_t triangle_collapses = 0; | |
| for (size_t i = 0; i < collapse_count; ++i) | |
| { | |
| const Collapse& c = collapses[collapse_order[i]]; | |
| if (c.error > error_limit) | |
| break; | |
| if (triangle_collapses >= triangle_collapse_goal) | |
| break; | |
| unsigned int r0 = remap[c.v0]; | |
| unsigned int r1 = remap[c.v1]; | |
| // 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]) | |
| continue; | |
| assert(collapse_remap[r0] == r0); | |
| assert(collapse_remap[r1] == r1); | |
| quadricAdd(vertex_quadrics[r1], vertex_quadrics[r0]); | |
| if (vertex_kind[c.v0] == Kind_Seam) | |
| { | |
| // remap v0 to v1 and seam pair of v0 to seam pair of v1 | |
| unsigned int s0 = wedge[c.v0]; | |
| unsigned int s1 = wedge[c.v1]; | |
| assert(s0 != c.v0 && s1 != c.v1); | |
| assert(wedge[s0] == c.v0 && wedge[s1] == c.v1); | |
| collapse_remap[c.v0] = c.v1; | |
| collapse_remap[s0] = s1; | |
| } | |
| else | |
| { | |
| assert(wedge[c.v0] == c.v0); | |
| collapse_remap[c.v0] = c.v1; | |
| } | |
| collapse_locked[r0] = 1; | |
| collapse_locked[r1] = 1; | |
| // border edges collapse 1 triangle, other edges collapse 2 or more | |
| triangle_collapses += (vertex_kind[c.v0] == Kind_Border) ? 1 : 2; | |
| edge_collapses++; | |
| } | |
| return edge_collapses; | |
| } | |
| static size_t remapIndexBuffer(unsigned int* indices, size_t index_count, const meshopt_Buffer<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(meshopt_Buffer<unsigned int>& loop, size_t vertex_count, const meshopt_Buffer<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; | |
| } | |
| } | |
| } | |
| } // namespace meshopt | |
| #if TRACE | |
| unsigned char* meshopt_simplifyDebugKind = 0; | |
| unsigned int* meshopt_simplifyDebugLoop = 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) | |
| { | |
| 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); | |
| meshopt_Allocator allocator; | |
| unsigned int* result = destination; | |
| // build adjacency information | |
| EdgeAdjacency adjacency = {}; | |
| buildEdgeAdjacency(adjacency, indices, index_count, vertex_count); | |
| // build position remap that maps each vertex to the one with identical position | |
| meshopt_Buffer<unsigned int> remap(vertex_count); | |
| meshopt_Buffer<unsigned int> wedge(vertex_count); | |
| buildPositionRemap(remap, wedge, vertex_positions_data, vertex_count, vertex_positions_stride); | |
| // classify vertices; vertex kind determines collapse rules, see kCanCollapse | |
| meshopt_Buffer<unsigned char> vertex_kind(vertex_count); | |
| meshopt_Buffer<unsigned int> loop(vertex_count); | |
| classifyVertices(vertex_kind, loop, 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, locked %d\n", | |
| int(kinds[Kind_Manifold]), int(kinds[Kind_Border]), int(kinds[Kind_Seam]), int(kinds[Kind_Locked])); | |
| #endif | |
| meshopt_Buffer<Vector3> vertex_positions(vertex_count); | |
| rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride); | |
| meshopt_Buffer<Quadric> vertex_quadrics(vertex_count); | |
| memset(&vertex_quadrics[0], 0, vertex_count * sizeof(Quadric)); | |
| fillFaceQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap); | |
| fillEdgeQuadrics(vertex_quadrics, indices, index_count, vertex_positions, remap, vertex_kind, loop); | |
| if (result != indices) | |
| memcpy(result, indices, index_count * sizeof(unsigned int)); | |
| #if TRACE | |
| size_t pass_count = 0; | |
| float worst_error = 0; | |
| #endif | |
| meshopt_Buffer<Collapse> edge_collapses(index_count); | |
| meshopt_Buffer<unsigned int> collapse_order(index_count); | |
| meshopt_Buffer<unsigned int> collapse_remap(vertex_count); | |
| meshopt_Buffer<unsigned char> collapse_locked(vertex_count); | |
| size_t result_count = index_count; | |
| while (result_count > target_index_count) | |
| { | |
| 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, remap); | |
| #if TRACE > 1 | |
| dumpEdgeCollapses(edge_collapses, edge_collapse_count, vertex_kind); | |
| #endif | |
| sortEdgeCollapses(collapse_order, edge_collapses, edge_collapse_count); | |
| // 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 triangle_collapse_goal = (result_count - target_index_count) / 3; | |
| size_t edge_collapse_goal = triangle_collapse_goal / 2; | |
| // 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 this factor | |
| const float kPassErrorBound = 1.5f; | |
| float error_goal = edge_collapse_goal < edge_collapse_count ? edge_collapses[collapse_order[edge_collapse_goal]].error * kPassErrorBound : FLT_MAX; | |
| float error_limit = error_goal > target_error ? target_error : error_goal; | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| collapse_remap[i] = unsigned(i); | |
| memset(&collapse_locked[0], 0, vertex_count); | |
| size_t collapses = performEdgeCollapses(collapse_remap, collapse_locked, vertex_quadrics, edge_collapses, edge_collapse_count, collapse_order, remap, wedge, vertex_kind, triangle_collapse_goal, error_limit); | |
| // 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); | |
| size_t new_count = remapIndexBuffer(result, result_count, collapse_remap); | |
| assert(new_count < result_count); | |
| #if TRACE | |
| float pass_error = 0.f; | |
| for (size_t i = 0; i < edge_collapse_count; ++i) | |
| { | |
| Collapse& c = edge_collapses[collapse_order[i]]; | |
| if (collapse_remap[c.v0] == c.v1) | |
| pass_error = c.error; | |
| } | |
| pass_count++; | |
| worst_error = (worst_error < pass_error) ? pass_error : worst_error; | |
| printf("pass %d: triangles: %d -> %d, collapses: %d/%d (goal: %d), error: %e (limit %e goal %e)\n", int(pass_count), int(result_count / 3), int(new_count / 3), int(collapses), int(edge_collapse_count), int(edge_collapse_goal), pass_error, error_limit, error_goal); | |
| #endif | |
| result_count = new_count; | |
| } | |
| #if TRACE | |
| printf("passes: %d, worst error: %e\n", int(pass_count), worst_error); | |
| #endif | |
| #if TRACE > 1 | |
| dumpLockedCollapses(result, result_count, vertex_kind); | |
| #endif | |
| #if TRACE | |
| if (meshopt_simplifyDebugKind) | |
| memcpy(meshopt_simplifyDebugKind, vertex_kind, vertex_count); | |
| if (meshopt_simplifyDebugLoop) | |
| memcpy(meshopt_simplifyDebugLoop, loop, vertex_count * sizeof(unsigned int)); | |
| #endif | |
| return result_count; | |
| } |
| // This file is part of meshoptimizer library; see meshoptimizer.h for version/license details | |
| #include "meshoptimizer.h" | |
| #include <cassert> | |
| #include <cfloat> | |
| #include <cmath> | |
| #include <cstring> | |
| #include <vector> | |
| #ifndef TRACE | |
| #define TRACE 0 | |
| #endif | |
| #if TRACE | |
| #include <stdio.h> | |
| #endif | |
| // 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 | |
| namespace meshopt | |
| { | |
| struct EdgeAdjacency | |
| { | |
| std::vector<unsigned int> counts; | |
| std::vector<unsigned int> offsets; | |
| std::vector<unsigned int> data; | |
| }; | |
| static void buildEdgeAdjacency(EdgeAdjacency& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count) | |
| { | |
| size_t face_count = index_count / 3; | |
| // allocate arrays | |
| adjacency.counts.resize(vertex_count); | |
| adjacency.offsets.resize(vertex_count); | |
| adjacency.data.resize(index_count); | |
| // fill edge counts | |
| for (size_t i = 0; i < index_count; ++i) | |
| { | |
| assert(indices[i] < vertex_count); | |
| adjacency.counts[indices[i]]++; | |
| } | |
| // 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]; | |
| adjacency.data[adjacency.offsets[a]++] = b; | |
| adjacency.data[adjacency.offsets[b]++] = c; | |
| adjacency.data[adjacency.offsets[c]++] = a; | |
| } | |
| // 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 | |
| { | |
| // MurmurHash2 | |
| const unsigned int m = 0x5bd1e995; | |
| const int r = 24; | |
| unsigned int h = 0; | |
| const unsigned int* key = reinterpret_cast<const unsigned int*>(vertex_positions + index * vertex_stride_float); | |
| for (size_t i = 0; i < 3; ++i) | |
| { | |
| unsigned int k = key[i]; | |
| k *= m; | |
| k ^= k >> r; | |
| k *= m; | |
| h *= m; | |
| h ^= k; | |
| } | |
| return h; | |
| } | |
| 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) | |
| buckets *= 2; | |
| return buckets; | |
| } | |
| template <typename T, typename Hash> | |
| static T* hashLookup2(std::vector<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"); | |
| return 0; | |
| } | |
| static void buildPositionRemap(std::vector<unsigned int>& remap, std::vector<unsigned int>& wedge, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride) | |
| { | |
| PositionHasher hasher = {vertex_positions_data, vertex_positions_stride / sizeof(float)}; | |
| size_t table_size = hashBuckets2(vertex_count); | |
| std::vector<unsigned int> table(table_size); | |
| memset(&table[0], -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_Locked, // none of the above; these vertices can't move | |
| Kind_Count | |
| }; | |
| // manifold vertices can collapse on anything except locked | |
| // border/seam vertices can only be collapsed onto border/seam respectively | |
| const unsigned char kCanCollapse[Kind_Count][Kind_Count] = { | |
| {1, 1, 1, 1}, | |
| {0, 1, 0, 0}, | |
| {0, 0, 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, 1}, | |
| {1, 0, 1, 0}, | |
| {1, 1, 1, 1}, | |
| {1, 0, 1, 0}, | |
| }; | |
| static bool hasEdge(const EdgeAdjacency& adjacency, unsigned int a, unsigned int b) | |
| { | |
| unsigned int count = adjacency.counts[a]; | |
| const unsigned int* data = &adjacency.data[adjacency.offsets[a]]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (data[i] == b) | |
| return true; | |
| return false; | |
| } | |
| static unsigned int findWedgeEdge(const EdgeAdjacency& adjacency, const std::vector<unsigned int>& wedge, unsigned int a, unsigned int b) | |
| { | |
| unsigned int v = a; | |
| do | |
| { | |
| if (hasEdge(adjacency, v, b)) | |
| return v; | |
| v = wedge[v]; | |
| } while (v != a); | |
| return ~0u; | |
| } | |
| static size_t countOpenEdges(const EdgeAdjacency& adjacency, unsigned int vertex, unsigned int* last = 0) | |
| { | |
| size_t result = 0; | |
| unsigned int count = adjacency.counts[vertex]; | |
| const unsigned int* data = &adjacency.data[adjacency.offsets[vertex]]; | |
| for (size_t i = 0; i < count; ++i) | |
| if (!hasEdge(adjacency, data[i], vertex)) | |
| { | |
| result++; | |
| if (last) | |
| *last = data[i]; | |
| } | |
| return result; | |
| } | |
| static void classifyVertices(std::vector<unsigned char>& result, std::vector<unsigned int>& loop, size_t vertex_count, const EdgeAdjacency& adjacency, const std::vector<unsigned int>& remap, const std::vector<unsigned int>& wedge) | |
| { | |
| for (size_t i = 0; i < vertex_count; ++i) | |
| loop[i] = ~0u; | |
| 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 v = 0; | |
| size_t edges = countOpenEdges(adjacency, unsigned(i), &v); | |
| // 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 | |
| // also note that we classify vertices as border if they have *one* open edge, not two | |
| // this is because we only have half-edges - so a border vertex would have one incoming and one outgoing edge | |
| if (edges == 0) | |
| { | |
| result[i] = Kind_Manifold; | |
| } | |
| else if (edges == 1) | |
| { | |
| result[i] = Kind_Border; | |
| loop[i] = v; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else if (wedge[wedge[i]] == i) | |
| { | |
| // attribute seam; need to distinguish between Seam and Locked | |
| unsigned int a = 0; | |
| size_t a_count = countOpenEdges(adjacency, unsigned(i), &a); | |
| unsigned int b = 0; | |
| size_t b_count = countOpenEdges(adjacency, wedge[i], &b); | |
| // seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap | |
| if (a_count == 1 && b_count == 1) | |
| { | |
| unsigned int ao = findWedgeEdge(adjacency, wedge, a, wedge[i]); | |
| unsigned int bo = findWedgeEdge(adjacency, wedge, b, unsigned(i)); | |
| if (ao != ~0u && bo != ~0u) | |
| { | |
| result[i] = Kind_Seam; | |
| loop[i] = a; | |
| loop[wedge[i]] = b; | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| // more than one vertex maps to this one; we don't have classification available | |
| result[i] = Kind_Locked; | |
| } | |
| } | |
| else | |
| { | |
| assert(remap[i] < i); | |
| result[i] = result[remap[i]]; | |
| } | |
| } | |
| } | |
| struct Vector3 | |
| { | |
| float x, y, z; | |
| }; | |
| static |