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simplifier.c
// 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;
}
Raw
simplifier.cpp
// 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;
}
Raw
simplifierb.cpp
// 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;