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1864 lines
57 KiB
C++
1864 lines
57 KiB
C++
// This file is part of meshoptimizer library; see meshoptimizer.h for version/license details
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#include "meshoptimizer.h"
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#include <assert.h>
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#include <float.h>
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#include <math.h>
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#include <string.h>
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#ifndef TRACE
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#define TRACE 0
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#endif
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#if TRACE
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#include <stdio.h>
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#endif
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#if TRACE
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#define TRACESTATS(i) stats[i]++;
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#else
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#define TRACESTATS(i) (void)0
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#endif
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#define ATTRIBUTES 3
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// This work is based on:
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// Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. 1997
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// Michael Garland. Quadric-based polygonal surface simplification. 1999
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// Peter Lindstrom. Out-of-Core Simplification of Large Polygonal Models. 2000
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// Matthias Teschner, Bruno Heidelberger, Matthias Mueller, Danat Pomeranets, Markus Gross. Optimized Spatial Hashing for Collision Detection of Deformable Objects. 2003
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// Peter Van Sandt, Yannis Chronis, Jignesh M. Patel. Efficiently Searching In-Memory Sorted Arrays: Revenge of the Interpolation Search? 2019
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namespace meshopt
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{
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struct EdgeAdjacency
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{
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struct Edge
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{
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unsigned int next;
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unsigned int prev;
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};
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unsigned int* counts;
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unsigned int* offsets;
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Edge* data;
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};
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static void prepareEdgeAdjacency(EdgeAdjacency& adjacency, size_t index_count, size_t vertex_count, meshopt_Allocator& allocator)
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{
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adjacency.counts = allocator.allocate<unsigned int>(vertex_count);
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adjacency.offsets = allocator.allocate<unsigned int>(vertex_count);
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adjacency.data = allocator.allocate<EdgeAdjacency::Edge>(index_count);
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}
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static void updateEdgeAdjacency(EdgeAdjacency& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count, const unsigned int* remap)
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{
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size_t face_count = index_count / 3;
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// fill edge counts
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memset(adjacency.counts, 0, vertex_count * sizeof(unsigned int));
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for (size_t i = 0; i < index_count; ++i)
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{
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unsigned int v = remap ? remap[indices[i]] : indices[i];
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assert(v < vertex_count);
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adjacency.counts[v]++;
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}
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// fill offset table
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unsigned int offset = 0;
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for (size_t i = 0; i < vertex_count; ++i)
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{
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adjacency.offsets[i] = offset;
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offset += adjacency.counts[i];
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}
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assert(offset == index_count);
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// fill edge data
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for (size_t i = 0; i < face_count; ++i)
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{
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unsigned int a = indices[i * 3 + 0], b = indices[i * 3 + 1], c = indices[i * 3 + 2];
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if (remap)
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{
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a = remap[a];
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b = remap[b];
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c = remap[c];
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}
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adjacency.data[adjacency.offsets[a]].next = b;
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adjacency.data[adjacency.offsets[a]].prev = c;
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adjacency.offsets[a]++;
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adjacency.data[adjacency.offsets[b]].next = c;
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adjacency.data[adjacency.offsets[b]].prev = a;
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adjacency.offsets[b]++;
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adjacency.data[adjacency.offsets[c]].next = a;
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adjacency.data[adjacency.offsets[c]].prev = b;
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adjacency.offsets[c]++;
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}
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// fix offsets that have been disturbed by the previous pass
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for (size_t i = 0; i < vertex_count; ++i)
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{
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assert(adjacency.offsets[i] >= adjacency.counts[i]);
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adjacency.offsets[i] -= adjacency.counts[i];
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}
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}
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struct PositionHasher
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{
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const float* vertex_positions;
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size_t vertex_stride_float;
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size_t hash(unsigned int index) const
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{
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const unsigned int* key = reinterpret_cast<const unsigned int*>(vertex_positions + index * vertex_stride_float);
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// scramble bits to make sure that integer coordinates have entropy in lower bits
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unsigned int x = key[0] ^ (key[0] >> 17);
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unsigned int y = key[1] ^ (key[1] >> 17);
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unsigned int z = key[2] ^ (key[2] >> 17);
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// Optimized Spatial Hashing for Collision Detection of Deformable Objects
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return (x * 73856093) ^ (y * 19349663) ^ (z * 83492791);
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}
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bool equal(unsigned int lhs, unsigned int rhs) const
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{
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return memcmp(vertex_positions + lhs * vertex_stride_float, vertex_positions + rhs * vertex_stride_float, sizeof(float) * 3) == 0;
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}
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};
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static size_t hashBuckets2(size_t count)
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{
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size_t buckets = 1;
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while (buckets < count + count / 4)
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buckets *= 2;
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return buckets;
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}
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template <typename T, typename Hash>
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static T* hashLookup2(T* table, size_t buckets, const Hash& hash, const T& key, const T& empty)
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{
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assert(buckets > 0);
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assert((buckets & (buckets - 1)) == 0);
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size_t hashmod = buckets - 1;
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size_t bucket = hash.hash(key) & hashmod;
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for (size_t probe = 0; probe <= hashmod; ++probe)
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{
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T& item = table[bucket];
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if (item == empty)
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return &item;
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if (hash.equal(item, key))
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return &item;
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// hash collision, quadratic probing
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bucket = (bucket + probe + 1) & hashmod;
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}
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assert(false && "Hash table is full"); // unreachable
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return 0;
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}
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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)
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{
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PositionHasher hasher = {vertex_positions_data, vertex_positions_stride / sizeof(float)};
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size_t table_size = hashBuckets2(vertex_count);
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unsigned int* table = allocator.allocate<unsigned int>(table_size);
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memset(table, -1, table_size * sizeof(unsigned int));
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// build forward remap: for each vertex, which other (canonical) vertex does it map to?
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// we use position equivalence for this, and remap vertices to other existing vertices
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for (size_t i = 0; i < vertex_count; ++i)
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{
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unsigned int index = unsigned(i);
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unsigned int* entry = hashLookup2(table, table_size, hasher, index, ~0u);
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if (*entry == ~0u)
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*entry = index;
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remap[index] = *entry;
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}
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// build wedge table: for each vertex, which other vertex is the next wedge that also maps to the same vertex?
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// entries in table form a (cyclic) wedge loop per vertex; for manifold vertices, wedge[i] == remap[i] == i
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for (size_t i = 0; i < vertex_count; ++i)
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wedge[i] = unsigned(i);
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for (size_t i = 0; i < vertex_count; ++i)
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if (remap[i] != i)
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{
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unsigned int r = remap[i];
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wedge[i] = wedge[r];
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wedge[r] = unsigned(i);
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}
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}
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enum VertexKind
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{
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Kind_Manifold, // not on an attribute seam, not on any boundary
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Kind_Border, // not on an attribute seam, has exactly two open edges
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Kind_Seam, // on an attribute seam with exactly two attribute seam edges
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Kind_Complex, // none of the above; these vertices can move as long as all wedges move to the target vertex
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Kind_Locked, // none of the above; these vertices can't move
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Kind_Count
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};
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// manifold vertices can collapse onto anything
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// border/seam vertices can only be collapsed onto border/seam respectively
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// complex vertices can collapse onto complex/locked
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// a rule of thumb is that collapsing kind A into kind B preserves the kind B in the target vertex
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// for example, while we could collapse Complex into Manifold, this would mean the target vertex isn't Manifold anymore
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const unsigned char kCanCollapse[Kind_Count][Kind_Count] = {
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{1, 1, 1, 1, 1},
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{0, 1, 0, 0, 0},
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{0, 0, 1, 0, 0},
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{0, 0, 0, 1, 1},
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{0, 0, 0, 0, 0},
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};
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// if a vertex is manifold or seam, adjoining edges are guaranteed to have an opposite edge
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// note that for seam edges, the opposite edge isn't present in the attribute-based topology
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// but is present if you consider a position-only mesh variant
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const unsigned char kHasOpposite[Kind_Count][Kind_Count] = {
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{1, 1, 1, 0, 1},
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{1, 0, 1, 0, 0},
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{1, 1, 1, 0, 1},
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{0, 0, 0, 0, 0},
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{1, 0, 1, 0, 0},
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};
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static bool hasEdge(const EdgeAdjacency& adjacency, unsigned int a, unsigned int b)
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{
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unsigned int count = adjacency.counts[a];
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const EdgeAdjacency::Edge* edges = adjacency.data + adjacency.offsets[a];
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for (size_t i = 0; i < count; ++i)
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if (edges[i].next == b)
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return true;
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return false;
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}
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static void classifyVertices(unsigned char* result, unsigned int* loop, unsigned int* loopback, size_t vertex_count, const EdgeAdjacency& adjacency, const unsigned int* remap, const unsigned int* wedge, unsigned int options)
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{
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memset(loop, -1, vertex_count * sizeof(unsigned int));
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memset(loopback, -1, vertex_count * sizeof(unsigned int));
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// incoming & outgoing open edges: ~0u if no open edges, i if there are more than 1
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// note that this is the same data as required in loop[] arrays; loop[] data is only valid for border/seam
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// but here it's okay to fill the data out for other types of vertices as well
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unsigned int* openinc = loopback;
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unsigned int* openout = loop;
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for (size_t i = 0; i < vertex_count; ++i)
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{
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unsigned int vertex = unsigned(i);
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unsigned int count = adjacency.counts[vertex];
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const EdgeAdjacency::Edge* edges = adjacency.data + adjacency.offsets[vertex];
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for (size_t j = 0; j < count; ++j)
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{
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unsigned int target = edges[j].next;
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if (target == vertex)
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{
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// degenerate triangles have two distinct edges instead of three, and the self edge
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// is bi-directional by definition; this can break border/seam classification by "closing"
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// the open edge from another triangle and falsely marking the vertex as manifold
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// instead we mark the vertex as having >1 open edges which turns it into locked/complex
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openinc[vertex] = openout[vertex] = vertex;
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}
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else if (!hasEdge(adjacency, target, vertex))
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{
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openinc[target] = (openinc[target] == ~0u) ? vertex : target;
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openout[vertex] = (openout[vertex] == ~0u) ? target : vertex;
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}
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}
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}
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#if TRACE
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size_t stats[4] = {};
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#endif
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for (size_t i = 0; i < vertex_count; ++i)
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{
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if (remap[i] == i)
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{
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if (wedge[i] == i)
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{
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// no attribute seam, need to check if it's manifold
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unsigned int openi = openinc[i], openo = openout[i];
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// note: we classify any vertices with no open edges as manifold
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// this is technically incorrect - if 4 triangles share an edge, we'll classify vertices as manifold
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// it's unclear if this is a problem in practice
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if (openi == ~0u && openo == ~0u)
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{
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result[i] = Kind_Manifold;
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}
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else if (openi != i && openo != i)
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{
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result[i] = Kind_Border;
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}
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else
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{
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result[i] = Kind_Locked;
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TRACESTATS(0);
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}
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}
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else if (wedge[wedge[i]] == i)
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{
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// attribute seam; need to distinguish between Seam and Locked
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unsigned int w = wedge[i];
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unsigned int openiv = openinc[i], openov = openout[i];
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unsigned int openiw = openinc[w], openow = openout[w];
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// seam should have one open half-edge for each vertex, and the edges need to "connect" - point to the same vertex post-remap
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if (openiv != ~0u && openiv != i && openov != ~0u && openov != i &&
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openiw != ~0u && openiw != w && openow != ~0u && openow != w)
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{
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if (remap[openiv] == remap[openow] && remap[openov] == remap[openiw])
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{
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result[i] = Kind_Seam;
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}
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else
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{
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result[i] = Kind_Locked;
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TRACESTATS(1);
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}
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}
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else
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{
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result[i] = Kind_Locked;
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TRACESTATS(2);
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}
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}
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else
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{
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// more than one vertex maps to this one; we don't have classification available
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result[i] = Kind_Locked;
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TRACESTATS(3);
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}
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}
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else
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{
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assert(remap[i] < i);
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result[i] = result[remap[i]];
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}
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}
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if (options & meshopt_SimplifyLockBorder)
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for (size_t i = 0; i < vertex_count; ++i)
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if (result[i] == Kind_Border)
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result[i] = Kind_Locked;
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#if TRACE
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printf("locked: many open edges %d, disconnected seam %d, many seam edges %d, many wedges %d\n",
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int(stats[0]), int(stats[1]), int(stats[2]), int(stats[3]));
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#endif
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}
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struct Vector3
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{
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float x, y, z;
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#if ATTRIBUTES
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float a[ATTRIBUTES];
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#endif
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};
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static float rescalePositions(Vector3* result, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride)
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{
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size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
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float minv[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
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float maxv[3] = {-FLT_MAX, -FLT_MAX, -FLT_MAX};
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for (size_t i = 0; i < vertex_count; ++i)
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{
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const float* v = vertex_positions_data + i * vertex_stride_float;
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if (result)
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{
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result[i].x = v[0];
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result[i].y = v[1];
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result[i].z = v[2];
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}
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for (int j = 0; j < 3; ++j)
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{
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float vj = v[j];
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minv[j] = minv[j] > vj ? vj : minv[j];
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maxv[j] = maxv[j] < vj ? vj : maxv[j];
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}
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}
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float extent = 0.f;
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extent = (maxv[0] - minv[0]) < extent ? extent : (maxv[0] - minv[0]);
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extent = (maxv[1] - minv[1]) < extent ? extent : (maxv[1] - minv[1]);
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extent = (maxv[2] - minv[2]) < extent ? extent : (maxv[2] - minv[2]);
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if (result)
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{
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float scale = extent == 0 ? 0.f : 1.f / extent;
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for (size_t i = 0; i < vertex_count; ++i)
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{
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result[i].x = (result[i].x - minv[0]) * scale;
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result[i].y = (result[i].y - minv[1]) * scale;
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result[i].z = (result[i].z - minv[2]) * scale;
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}
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}
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return extent;
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}
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struct Quadric
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{
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float a00, a11, a22;
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float a10, a20, a21;
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float b0, b1, b2, c;
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float w;
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#if ATTRIBUTES
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float gx[ATTRIBUTES];
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float gy[ATTRIBUTES];
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float gz[ATTRIBUTES];
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float gw[ATTRIBUTES];
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#endif
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};
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struct Collapse
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{
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unsigned int v0;
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unsigned int v1;
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union
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{
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unsigned int bidi;
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float error;
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unsigned int errorui;
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};
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float distance_error;
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};
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static float normalize(Vector3& v)
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{
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float length = sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
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if (length > 0)
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{
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v.x /= length;
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v.y /= length;
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v.z /= length;
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}
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return length;
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}
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static void quadricAdd(Quadric& Q, const Quadric& R)
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{
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Q.a00 += R.a00;
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Q.a11 += R.a11;
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Q.a22 += R.a22;
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Q.a10 += R.a10;
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Q.a20 += R.a20;
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Q.a21 += R.a21;
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Q.b0 += R.b0;
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Q.b1 += R.b1;
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Q.b2 += R.b2;
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Q.c += R.c;
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Q.w += R.w;
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#if ATTRIBUTES
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for (int k = 0; k < ATTRIBUTES; ++k)
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{
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Q.gx[k] += R.gx[k];
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Q.gy[k] += R.gy[k];
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Q.gz[k] += R.gz[k];
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Q.gw[k] += R.gw[k];
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}
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#endif
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}
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static float quadricError(const Quadric& Q, const Vector3& v)
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{
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float rx = Q.b0;
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float ry = Q.b1;
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float rz = Q.b2;
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rx += Q.a10 * v.y;
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ry += Q.a21 * v.z;
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rz += Q.a20 * v.x;
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rx *= 2;
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ry *= 2;
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rz *= 2;
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|
|
rx += Q.a00 * v.x;
|
|
ry += Q.a11 * v.y;
|
|
rz += Q.a22 * v.z;
|
|
|
|
float r = Q.c;
|
|
r += rx * v.x;
|
|
r += ry * v.y;
|
|
r += rz * v.z;
|
|
|
|
#if ATTRIBUTES
|
|
// see quadricUpdateAttributes for general derivation; here we need to add the parts of (eval(pos) - attr)^2 that depend on attr
|
|
for (int k = 0; k < ATTRIBUTES; ++k)
|
|
{
|
|
float a = v.a[k];
|
|
|
|
r += a * a * Q.w;
|
|
r -= 2 * a * (v.x * Q.gx[k] + v.y * Q.gy[k] + v.z * Q.gz[k] + Q.gw[k]);
|
|
}
|
|
#endif
|
|
|
|
float s = Q.w == 0.f ? 0.f : 1.f / Q.w;
|
|
|
|
return fabsf(r) * s;
|
|
}
|
|
|
|
static float quadricErrorNoAttributes(const Quadric& Q, const Vector3& v)
|
|
{
|
|
float rx = Q.b0;
|
|
float ry = Q.b1;
|
|
float rz = Q.b2;
|
|
|
|
rx += Q.a10 * v.y;
|
|
ry += Q.a21 * v.z;
|
|
rz += Q.a20 * v.x;
|
|
|
|
rx *= 2;
|
|
ry *= 2;
|
|
rz *= 2;
|
|
|
|
rx += Q.a00 * v.x;
|
|
ry += Q.a11 * v.y;
|
|
rz += Q.a22 * v.z;
|
|
|
|
float r = Q.c;
|
|
r += rx * v.x;
|
|
r += ry * v.y;
|
|
r += rz * v.z;
|
|
|
|
float s = Q.w == 0.f ? 0.f : 1.f / Q.w;
|
|
|
|
return fabsf(r) * s;
|
|
}
|
|
|
|
static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d, float w)
|
|
{
|
|
float aw = a * w;
|
|
float bw = b * w;
|
|
float cw = c * w;
|
|
float dw = d * w;
|
|
|
|
Q.a00 = a * aw;
|
|
Q.a11 = b * bw;
|
|
Q.a22 = c * cw;
|
|
Q.a10 = a * bw;
|
|
Q.a20 = a * cw;
|
|
Q.a21 = b * cw;
|
|
Q.b0 = a * dw;
|
|
Q.b1 = b * dw;
|
|
Q.b2 = c * dw;
|
|
Q.c = d * dw;
|
|
Q.w = w;
|
|
|
|
#if ATTRIBUTES
|
|
memset(Q.gx, 0, sizeof(Q.gx));
|
|
memset(Q.gy, 0, sizeof(Q.gy));
|
|
memset(Q.gz, 0, sizeof(Q.gz));
|
|
memset(Q.gw, 0, sizeof(Q.gw));
|
|
#endif
|
|
}
|
|
|
|
static void quadricFromPoint(Quadric& Q, float x, float y, float z, float w)
|
|
{
|
|
// we need to encode (x - X) ^ 2 + (y - Y)^2 + (z - Z)^2 into the quadric
|
|
Q.a00 = w;
|
|
Q.a11 = w;
|
|
Q.a22 = w;
|
|
Q.a10 = 0.f;
|
|
Q.a20 = 0.f;
|
|
Q.a21 = 0.f;
|
|
Q.b0 = -2.f * x * w;
|
|
Q.b1 = -2.f * y * w;
|
|
Q.b2 = -2.f * z * w;
|
|
Q.c = (x * x + y * y + z * z) * w;
|
|
Q.w = w;
|
|
}
|
|
|
|
static void quadricFromTriangle(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float weight)
|
|
{
|
|
Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z};
|
|
Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z};
|
|
|
|
// normal = cross(p1 - p0, p2 - p0)
|
|
Vector3 normal = {p10.y * p20.z - p10.z * p20.y, p10.z * p20.x - p10.x * p20.z, p10.x * p20.y - p10.y * p20.x};
|
|
float area = normalize(normal);
|
|
|
|
float distance = normal.x * p0.x + normal.y * p0.y + normal.z * p0.z;
|
|
|
|
// we use sqrtf(area) so that the error is scaled linearly; this tends to improve silhouettes
|
|
quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance, sqrtf(area) * weight);
|
|
}
|
|
|
|
static void quadricFromTriangleEdge(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float weight)
|
|
{
|
|
Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z};
|
|
float length = normalize(p10);
|
|
|
|
// p20p = length of projection of p2-p0 onto normalize(p1 - p0)
|
|
Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z};
|
|
float p20p = p20.x * p10.x + p20.y * p10.y + p20.z * p10.z;
|
|
|
|
// normal = altitude of triangle from point p2 onto edge p1-p0
|
|
Vector3 normal = {p20.x - p10.x * p20p, p20.y - p10.y * p20p, p20.z - p10.z * p20p};
|
|
normalize(normal);
|
|
|
|
float distance = normal.x * p0.x + normal.y * p0.y + normal.z * p0.z;
|
|
|
|
// note: the weight is scaled linearly with edge length; this has to match the triangle weight
|
|
quadricFromPlane(Q, normal.x, normal.y, normal.z, -distance, length * weight);
|
|
}
|
|
|
|
#if ATTRIBUTES
|
|
static void quadricUpdateAttributes(Quadric& Q, const Vector3& p0, const Vector3& p1, const Vector3& p2, float w)
|
|
{
|
|
// for each attribute we want to encode the following function into the quadric:
|
|
// (eval(pos) - attr)^2
|
|
// where eval(pos) interpolates attribute across the triangle like so:
|
|
// eval(pos) = pos.x * gx + pos.y * gy + pos.z * gz + gw
|
|
// where gx/gy/gz/gw are gradients
|
|
Vector3 p10 = {p1.x - p0.x, p1.y - p0.y, p1.z - p0.z};
|
|
Vector3 p20 = {p2.x - p0.x, p2.y - p0.y, p2.z - p0.z};
|
|
|
|
// we compute gradients using barycentric coordinates; barycentric coordinates can be computed as follows:
|
|
// v = (d11 * d20 - d01 * d21) / denom
|
|
// w = (d00 * d21 - d01 * d20) / denom
|
|
// u = 1 - v - w
|
|
// here v0, v1 are triangle edge vectors, v2 is a vector from point to triangle corner, and dij = dot(vi, vj)
|
|
const Vector3& v0 = p10;
|
|
const Vector3& v1 = p20;
|
|
float d00 = v0.x * v0.x + v0.y * v0.y + v0.z * v0.z;
|
|
float d01 = v0.x * v1.x + v0.y * v1.y + v0.z * v1.z;
|
|
float d11 = v1.x * v1.x + v1.y * v1.y + v1.z * v1.z;
|
|
float denom = d00 * d11 - d01 * d01;
|
|
float denomr = denom == 0 ? 0.f : 1.f / denom;
|
|
|
|
// precompute gradient factors
|
|
// these are derived by directly computing derivative of eval(pos) = a0 * u + a1 * v + a2 * w and factoring out common factors that are shared between attributes
|
|
float gx1 = (d11 * v0.x - d01 * v1.x) * denomr;
|
|
float gx2 = (d00 * v1.x - d01 * v0.x) * denomr;
|
|
float gy1 = (d11 * v0.y - d01 * v1.y) * denomr;
|
|
float gy2 = (d00 * v1.y - d01 * v0.y) * denomr;
|
|
float gz1 = (d11 * v0.z - d01 * v1.z) * denomr;
|
|
float gz2 = (d00 * v1.z - d01 * v0.z) * denomr;
|
|
|
|
for (int k = 0; k < ATTRIBUTES; ++k)
|
|
{
|
|
float a0 = p0.a[k], a1 = p1.a[k], a2 = p2.a[k];
|
|
|
|
// compute gradient of eval(pos) for x/y/z/w
|
|
// the formulas below are obtained by directly computing derivative of eval(pos) = a0 * u + a1 * v + a2 * w
|
|
float gx = gx1 * (a1 - a0) + gx2 * (a2 - a0);
|
|
float gy = gy1 * (a1 - a0) + gy2 * (a2 - a0);
|
|
float gz = gz1 * (a1 - a0) + gz2 * (a2 - a0);
|
|
float gw = a0 - p0.x * gx - p0.y * gy - p0.z * gz;
|
|
|
|
// quadric encodes (eval(pos)-attr)^2; this means that the resulting expansion needs to compute, for example, pos.x * pos.y * K
|
|
// since quadrics already encode factors for pos.x * pos.y, we can accumulate almost everything in basic quadric fields
|
|
Q.a00 += w * (gx * gx);
|
|
Q.a11 += w * (gy * gy);
|
|
Q.a22 += w * (gz * gz);
|
|
|
|
Q.a10 += w * (gy * gx);
|
|
Q.a20 += w * (gz * gx);
|
|
Q.a21 += w * (gz * gy);
|
|
|
|
Q.b0 += w * (gx * gw);
|
|
Q.b1 += w * (gy * gw);
|
|
Q.b2 += w * (gz * gw);
|
|
|
|
Q.c += w * (gw * gw);
|
|
|
|
// the only remaining sum components are ones that depend on attr; these will be addded during error evaluation, see quadricError
|
|
Q.gx[k] = w * gx;
|
|
Q.gy[k] = w * gy;
|
|
Q.gz[k] = w * gz;
|
|
Q.gw[k] = w * gw;
|
|
|
|
#if TRACE > 2
|
|
printf("attr%d: %e %e %e\n",
|
|
k,
|
|
(gx * p0.x + gy * p0.y + gz * p0.z + gw - a0),
|
|
(gx * p1.x + gy * p1.y + gz * p1.z + gw - a1),
|
|
(gx * p2.x + gy * p2.y + gz * p2.z + gw - a2)
|
|
);
|
|
#endif
|
|
}
|
|
}
|
|
#endif
|
|
|
|
static void fillFaceQuadrics(Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* remap)
|
|
{
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
unsigned int i0 = indices[i + 0];
|
|
unsigned int i1 = indices[i + 1];
|
|
unsigned int i2 = indices[i + 2];
|
|
|
|
Quadric Q;
|
|
quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], 1.f);
|
|
quadricAdd(vertex_no_attrib_quadrics[remap[i0]], Q);
|
|
quadricAdd(vertex_no_attrib_quadrics[remap[i1]], Q);
|
|
quadricAdd(vertex_no_attrib_quadrics[remap[i2]], Q);
|
|
|
|
#if ATTRIBUTES
|
|
quadricUpdateAttributes(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], Q.w);
|
|
#endif
|
|
quadricAdd(vertex_quadrics[remap[i0]], Q);
|
|
quadricAdd(vertex_quadrics[remap[i1]], Q);
|
|
quadricAdd(vertex_quadrics[remap[i2]], Q);
|
|
}
|
|
}
|
|
|
|
static void fillEdgeQuadrics(Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* remap, const unsigned char* vertex_kind, const unsigned int* loop, const unsigned int* loopback)
|
|
{
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
static const int next[3] = {1, 2, 0};
|
|
|
|
for (int e = 0; e < 3; ++e)
|
|
{
|
|
unsigned int i0 = indices[i + e];
|
|
unsigned int i1 = indices[i + next[e]];
|
|
|
|
unsigned char k0 = vertex_kind[i0];
|
|
unsigned char k1 = vertex_kind[i1];
|
|
|
|
// check that either i0 or i1 are border/seam and are on the same edge loop
|
|
// note that we need to add the error even for edged that connect e.g. border & locked
|
|
// if we don't do that, the adjacent border->border edge won't have correct errors for corners
|
|
if (k0 != Kind_Border && k0 != Kind_Seam && k1 != Kind_Border && k1 != Kind_Seam)
|
|
continue;
|
|
|
|
if ((k0 == Kind_Border || k0 == Kind_Seam) && loop[i0] != i1)
|
|
continue;
|
|
|
|
if ((k1 == Kind_Border || k1 == Kind_Seam) && loopback[i1] != i0)
|
|
continue;
|
|
|
|
// seam edges should occur twice (i0->i1 and i1->i0) - skip redundant edges
|
|
if (kHasOpposite[k0][k1] && remap[i1] > remap[i0])
|
|
continue;
|
|
|
|
unsigned int i2 = indices[i + next[next[e]]];
|
|
|
|
// we try hard to maintain border edge geometry; seam edges can move more freely
|
|
// due to topological restrictions on collapses, seam quadrics slightly improves collapse structure but aren't critical
|
|
const float kEdgeWeightSeam = 1.f;
|
|
const float kEdgeWeightBorder = 10.f;
|
|
|
|
float edgeWeight = (k0 == Kind_Border || k1 == Kind_Border) ? kEdgeWeightBorder : kEdgeWeightSeam;
|
|
|
|
Quadric Q;
|
|
quadricFromTriangleEdge(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], edgeWeight);
|
|
|
|
quadricAdd(vertex_quadrics[remap[i0]], Q);
|
|
quadricAdd(vertex_quadrics[remap[i1]], Q);
|
|
|
|
quadricAdd(vertex_no_attrib_quadrics[remap[i0]], Q);
|
|
quadricAdd(vertex_no_attrib_quadrics[remap[i1]], Q);
|
|
}
|
|
}
|
|
}
|
|
|
|
// does triangle ABC flip when C is replaced with D?
|
|
static bool hasTriangleFlip(const Vector3& a, const Vector3& b, const Vector3& c, const Vector3& d)
|
|
{
|
|
Vector3 eb = {b.x - a.x, b.y - a.y, b.z - a.z};
|
|
Vector3 ec = {c.x - a.x, c.y - a.y, c.z - a.z};
|
|
Vector3 ed = {d.x - a.x, d.y - a.y, d.z - a.z};
|
|
|
|
Vector3 nbc = {eb.y * ec.z - eb.z * ec.y, eb.z * ec.x - eb.x * ec.z, eb.x * ec.y - eb.y * ec.x};
|
|
Vector3 nbd = {eb.y * ed.z - eb.z * ed.y, eb.z * ed.x - eb.x * ed.z, eb.x * ed.y - eb.y * ed.x};
|
|
|
|
return nbc.x * nbd.x + nbc.y * nbd.y + nbc.z * nbd.z < 0;
|
|
}
|
|
|
|
static bool hasTriangleFlips(const EdgeAdjacency& adjacency, const Vector3* vertex_positions, const unsigned int* collapse_remap, unsigned int i0, unsigned int i1)
|
|
{
|
|
assert(collapse_remap[i0] == i0);
|
|
assert(collapse_remap[i1] == i1);
|
|
|
|
const Vector3& v0 = vertex_positions[i0];
|
|
const Vector3& v1 = vertex_positions[i1];
|
|
|
|
const EdgeAdjacency::Edge* edges = &adjacency.data[adjacency.offsets[i0]];
|
|
size_t count = adjacency.counts[i0];
|
|
|
|
for (size_t i = 0; i < count; ++i)
|
|
{
|
|
unsigned int a = collapse_remap[edges[i].next];
|
|
unsigned int b = collapse_remap[edges[i].prev];
|
|
|
|
// skip triangles that get collapsed
|
|
// note: this is mathematically redundant as if either of these is true, the dot product in hasTriangleFlip should be 0
|
|
if (a == i1 || b == i1)
|
|
continue;
|
|
|
|
// early-out when at least one triangle flips due to a collapse
|
|
if (hasTriangleFlip(vertex_positions[a], vertex_positions[b], v0, v1))
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
static size_t pickEdgeCollapses(Collapse* collapses, const unsigned int* indices, size_t index_count, const unsigned int* remap, const unsigned char* vertex_kind, const unsigned int* loop)
|
|
{
|
|
size_t collapse_count = 0;
|
|
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
static const int next[3] = {1, 2, 0};
|
|
|
|
for (int e = 0; e < 3; ++e)
|
|
{
|
|
unsigned int i0 = indices[i + e];
|
|
unsigned int i1 = indices[i + next[e]];
|
|
|
|
// this can happen either when input has a zero-length edge, or when we perform collapses for complex
|
|
// topology w/seams and collapse a manifold vertex that connects to both wedges onto one of them
|
|
// we leave edges like this alone since they may be important for preserving mesh integrity
|
|
if (remap[i0] == remap[i1])
|
|
continue;
|
|
|
|
unsigned char k0 = vertex_kind[i0];
|
|
unsigned char k1 = vertex_kind[i1];
|
|
|
|
// the edge has to be collapsible in at least one direction
|
|
if (!(kCanCollapse[k0][k1] | kCanCollapse[k1][k0]))
|
|
continue;
|
|
|
|
// manifold and seam edges should occur twice (i0->i1 and i1->i0) - skip redundant edges
|
|
if (kHasOpposite[k0][k1] && remap[i1] > remap[i0])
|
|
continue;
|
|
|
|
// two vertices are on a border or a seam, but there's no direct edge between them
|
|
// this indicates that they belong to two different edge loops and we should not collapse this edge
|
|
// loop[] tracks half edges so we only need to check i0->i1
|
|
if (k0 == k1 && (k0 == Kind_Border || k0 == Kind_Seam) && loop[i0] != i1)
|
|
continue;
|
|
|
|
// edge can be collapsed in either direction - we will pick the one with minimum error
|
|
// note: we evaluate error later during collapse ranking, here we just tag the edge as bidirectional
|
|
if (kCanCollapse[k0][k1] & kCanCollapse[k1][k0])
|
|
{
|
|
Collapse c = {i0, i1, {/* bidi= */ 1}};
|
|
collapses[collapse_count++] = c;
|
|
}
|
|
else
|
|
{
|
|
// edge can only be collapsed in one direction
|
|
unsigned int e0 = kCanCollapse[k0][k1] ? i0 : i1;
|
|
unsigned int e1 = kCanCollapse[k0][k1] ? i1 : i0;
|
|
|
|
Collapse c = {e0, e1, {/* bidi= */ 0}};
|
|
collapses[collapse_count++] = c;
|
|
}
|
|
}
|
|
}
|
|
|
|
return collapse_count;
|
|
}
|
|
|
|
static void rankEdgeCollapses(Collapse* collapses, size_t collapse_count, const Vector3* vertex_positions, const Quadric* vertex_quadrics, const Quadric* vertex_no_attrib_quadrics, const unsigned int* remap)
|
|
{
|
|
for (size_t i = 0; i < collapse_count; ++i)
|
|
{
|
|
Collapse& c = collapses[i];
|
|
|
|
unsigned int i0 = c.v0;
|
|
unsigned int i1 = c.v1;
|
|
|
|
// most edges are bidirectional which means we need to evaluate errors for two collapses
|
|
// to keep this code branchless we just use the same edge for unidirectional edges
|
|
unsigned int j0 = c.bidi ? i1 : i0;
|
|
unsigned int j1 = c.bidi ? i0 : i1;
|
|
|
|
const Quadric& qi = vertex_quadrics[remap[i0]];
|
|
const Quadric& qj = vertex_quadrics[remap[j0]];
|
|
|
|
float ei = quadricError(qi, vertex_positions[i1]);
|
|
float ej = quadricError(qj, vertex_positions[j1]);
|
|
|
|
const Quadric& naqi = vertex_no_attrib_quadrics[remap[i0]];
|
|
const Quadric& naqj = vertex_no_attrib_quadrics[remap[j0]];
|
|
|
|
// pick edge direction with minimal error
|
|
c.v0 = ei <= ej ? i0 : j0;
|
|
c.v1 = ei <= ej ? i1 : j1;
|
|
c.error = ei <= ej ? ei : ej;
|
|
c.distance_error = ei <= ej ? quadricErrorNoAttributes(naqi, vertex_positions[i1]) : quadricErrorNoAttributes(naqj, vertex_positions[j1]);
|
|
}
|
|
}
|
|
|
|
#if TRACE > 1
|
|
static void dumpEdgeCollapses(const Collapse* collapses, size_t collapse_count, const unsigned char* vertex_kind)
|
|
{
|
|
size_t ckinds[Kind_Count][Kind_Count] = {};
|
|
float cerrors[Kind_Count][Kind_Count] = {};
|
|
|
|
for (int k0 = 0; k0 < Kind_Count; ++k0)
|
|
for (int k1 = 0; k1 < Kind_Count; ++k1)
|
|
cerrors[k0][k1] = FLT_MAX;
|
|
|
|
for (size_t i = 0; i < collapse_count; ++i)
|
|
{
|
|
unsigned int i0 = collapses[i].v0;
|
|
unsigned int i1 = collapses[i].v1;
|
|
|
|
unsigned char k0 = vertex_kind[i0];
|
|
unsigned char k1 = vertex_kind[i1];
|
|
|
|
ckinds[k0][k1]++;
|
|
cerrors[k0][k1] = (collapses[i].error < cerrors[k0][k1]) ? collapses[i].error : cerrors[k0][k1];
|
|
}
|
|
|
|
for (int k0 = 0; k0 < Kind_Count; ++k0)
|
|
for (int k1 = 0; k1 < Kind_Count; ++k1)
|
|
if (ckinds[k0][k1])
|
|
printf("collapses %d -> %d: %d, min error %e\n", k0, k1, int(ckinds[k0][k1]), ckinds[k0][k1] ? sqrtf(cerrors[k0][k1]) : 0.f);
|
|
}
|
|
|
|
static void dumpLockedCollapses(const unsigned int* indices, size_t index_count, const unsigned char* vertex_kind)
|
|
{
|
|
size_t locked_collapses[Kind_Count][Kind_Count] = {};
|
|
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
static const int next[3] = {1, 2, 0};
|
|
|
|
for (int e = 0; e < 3; ++e)
|
|
{
|
|
unsigned int i0 = indices[i + e];
|
|
unsigned int i1 = indices[i + next[e]];
|
|
|
|
unsigned char k0 = vertex_kind[i0];
|
|
unsigned char k1 = vertex_kind[i1];
|
|
|
|
locked_collapses[k0][k1] += !kCanCollapse[k0][k1] && !kCanCollapse[k1][k0];
|
|
}
|
|
}
|
|
|
|
for (int k0 = 0; k0 < Kind_Count; ++k0)
|
|
for (int k1 = 0; k1 < Kind_Count; ++k1)
|
|
if (locked_collapses[k0][k1])
|
|
printf("locked collapses %d -> %d: %d\n", k0, k1, int(locked_collapses[k0][k1]));
|
|
}
|
|
#endif
|
|
|
|
static void sortEdgeCollapses(unsigned int* sort_order, const Collapse* collapses, size_t collapse_count)
|
|
{
|
|
const int sort_bits = 11;
|
|
|
|
// fill histogram for counting sort
|
|
unsigned int histogram[1 << sort_bits];
|
|
memset(histogram, 0, sizeof(histogram));
|
|
|
|
for (size_t i = 0; i < collapse_count; ++i)
|
|
{
|
|
// skip sign bit since error is non-negative
|
|
unsigned int key = (collapses[i].errorui << 1) >> (32 - sort_bits);
|
|
|
|
histogram[key]++;
|
|
}
|
|
|
|
// compute offsets based on histogram data
|
|
size_t histogram_sum = 0;
|
|
|
|
for (size_t i = 0; i < 1 << sort_bits; ++i)
|
|
{
|
|
size_t count = histogram[i];
|
|
histogram[i] = unsigned(histogram_sum);
|
|
histogram_sum += count;
|
|
}
|
|
|
|
assert(histogram_sum == collapse_count);
|
|
|
|
// compute sort order based on offsets
|
|
for (size_t i = 0; i < collapse_count; ++i)
|
|
{
|
|
// skip sign bit since error is non-negative
|
|
unsigned int key = (collapses[i].errorui << 1) >> (32 - sort_bits);
|
|
|
|
sort_order[histogram[key]++] = unsigned(i);
|
|
}
|
|
}
|
|
|
|
static size_t performEdgeCollapses(unsigned int* collapse_remap, unsigned char* collapse_locked, Quadric* vertex_quadrics, Quadric* vertex_no_attrib_quadrics, const Collapse* collapses, size_t collapse_count, const unsigned int* collapse_order, const unsigned int* remap, const unsigned int* wedge, const unsigned char* vertex_kind, const Vector3* vertex_positions, const EdgeAdjacency& adjacency, size_t triangle_collapse_goal, float error_limit, float& result_error)
|
|
{
|
|
size_t edge_collapses = 0;
|
|
size_t triangle_collapses = 0;
|
|
|
|
// most collapses remove 2 triangles; use this to establish a bound on the pass in terms of error limit
|
|
// note that edge_collapse_goal is an estimate; triangle_collapse_goal will be used to actually limit collapses
|
|
size_t edge_collapse_goal = triangle_collapse_goal / 2;
|
|
|
|
#if TRACE
|
|
size_t stats[4] = {};
|
|
#endif
|
|
|
|
for (size_t i = 0; i < collapse_count; ++i)
|
|
{
|
|
const Collapse& c = collapses[collapse_order[i]];
|
|
|
|
TRACESTATS(0);
|
|
|
|
if (c.error > error_limit)
|
|
break;
|
|
|
|
if (triangle_collapses >= triangle_collapse_goal)
|
|
break;
|
|
|
|
// we limit the error in each pass based on the error of optimal last collapse; since many collapses will be locked
|
|
// as they will share vertices with other successfull collapses, we need to increase the acceptable error by some factor
|
|
float error_goal = edge_collapse_goal < collapse_count ? 1.5f * collapses[collapse_order[edge_collapse_goal]].error : FLT_MAX;
|
|
|
|
// on average, each collapse is expected to lock 6 other collapses; to avoid degenerate passes on meshes with odd
|
|
// topology, we only abort if we got over 1/6 collapses accordingly.
|
|
if (c.error > error_goal && triangle_collapses > triangle_collapse_goal / 6)
|
|
break;
|
|
|
|
unsigned int i0 = c.v0;
|
|
unsigned int i1 = c.v1;
|
|
|
|
unsigned int r0 = remap[i0];
|
|
unsigned int r1 = remap[i1];
|
|
|
|
// we don't collapse vertices that had source or target vertex involved in a collapse
|
|
// it's important to not move the vertices twice since it complicates the tracking/remapping logic
|
|
// it's important to not move other vertices towards a moved vertex to preserve error since we don't re-rank collapses mid-pass
|
|
if (collapse_locked[r0] | collapse_locked[r1])
|
|
{
|
|
TRACESTATS(1);
|
|
continue;
|
|
}
|
|
|
|
if (hasTriangleFlips(adjacency, vertex_positions, collapse_remap, r0, r1))
|
|
{
|
|
// adjust collapse goal since this collapse is invalid and shouldn't factor into error goal
|
|
edge_collapse_goal++;
|
|
|
|
TRACESTATS(2);
|
|
continue;
|
|
}
|
|
|
|
assert(collapse_remap[r0] == r0);
|
|
assert(collapse_remap[r1] == r1);
|
|
|
|
quadricAdd(vertex_quadrics[r1], vertex_quadrics[r0]);
|
|
quadricAdd(vertex_no_attrib_quadrics[r1], vertex_no_attrib_quadrics[r0]);
|
|
|
|
if (vertex_kind[i0] == Kind_Complex)
|
|
{
|
|
unsigned int v = i0;
|
|
|
|
do
|
|
{
|
|
collapse_remap[v] = r1;
|
|
v = wedge[v];
|
|
} while (v != i0);
|
|
}
|
|
else if (vertex_kind[i0] == Kind_Seam)
|
|
{
|
|
// remap v0 to v1 and seam pair of v0 to seam pair of v1
|
|
unsigned int s0 = wedge[i0];
|
|
unsigned int s1 = wedge[i1];
|
|
|
|
assert(s0 != i0 && s1 != i1);
|
|
assert(wedge[s0] == i0 && wedge[s1] == i1);
|
|
|
|
collapse_remap[i0] = i1;
|
|
collapse_remap[s0] = s1;
|
|
}
|
|
else
|
|
{
|
|
assert(wedge[i0] == i0);
|
|
|
|
collapse_remap[i0] = i1;
|
|
}
|
|
|
|
collapse_locked[r0] = 1;
|
|
collapse_locked[r1] = 1;
|
|
|
|
// border edges collapse 1 triangle, other edges collapse 2 or more
|
|
triangle_collapses += (vertex_kind[i0] == Kind_Border) ? 1 : 2;
|
|
edge_collapses++;
|
|
|
|
result_error = result_error < c.distance_error ? c.distance_error : result_error;
|
|
}
|
|
|
|
#if TRACE
|
|
float error_goal_perfect = edge_collapse_goal < collapse_count ? collapses[collapse_order[edge_collapse_goal]].error : 0.f;
|
|
|
|
printf("removed %d triangles, error %e (goal %e); evaluated %d/%d collapses (done %d, skipped %d, invalid %d)\n",
|
|
int(triangle_collapses), sqrtf(result_error), sqrtf(error_goal_perfect),
|
|
int(stats[0]), int(collapse_count), int(edge_collapses), int(stats[1]), int(stats[2]));
|
|
#endif
|
|
|
|
return edge_collapses;
|
|
}
|
|
|
|
static size_t remapIndexBuffer(unsigned int* indices, size_t index_count, const unsigned int* collapse_remap)
|
|
{
|
|
size_t write = 0;
|
|
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
unsigned int v0 = collapse_remap[indices[i + 0]];
|
|
unsigned int v1 = collapse_remap[indices[i + 1]];
|
|
unsigned int v2 = collapse_remap[indices[i + 2]];
|
|
|
|
// we never move the vertex twice during a single pass
|
|
assert(collapse_remap[v0] == v0);
|
|
assert(collapse_remap[v1] == v1);
|
|
assert(collapse_remap[v2] == v2);
|
|
|
|
if (v0 != v1 && v0 != v2 && v1 != v2)
|
|
{
|
|
indices[write + 0] = v0;
|
|
indices[write + 1] = v1;
|
|
indices[write + 2] = v2;
|
|
write += 3;
|
|
}
|
|
}
|
|
|
|
return write;
|
|
}
|
|
|
|
static void remapEdgeLoops(unsigned int* loop, size_t vertex_count, const unsigned int* collapse_remap)
|
|
{
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
if (loop[i] != ~0u)
|
|
{
|
|
unsigned int l = loop[i];
|
|
unsigned int r = collapse_remap[l];
|
|
|
|
// i == r is a special case when the seam edge is collapsed in a direction opposite to where loop goes
|
|
loop[i] = (i == r) ? loop[l] : r;
|
|
}
|
|
}
|
|
}
|
|
|
|
struct CellHasher
|
|
{
|
|
const unsigned int* vertex_ids;
|
|
|
|
size_t hash(unsigned int i) const
|
|
{
|
|
unsigned int h = vertex_ids[i];
|
|
|
|
// MurmurHash2 finalizer
|
|
h ^= h >> 13;
|
|
h *= 0x5bd1e995;
|
|
h ^= h >> 15;
|
|
return h;
|
|
}
|
|
|
|
bool equal(unsigned int lhs, unsigned int rhs) const
|
|
{
|
|
return vertex_ids[lhs] == vertex_ids[rhs];
|
|
}
|
|
};
|
|
|
|
struct IdHasher
|
|
{
|
|
size_t hash(unsigned int id) const
|
|
{
|
|
unsigned int h = id;
|
|
|
|
// MurmurHash2 finalizer
|
|
h ^= h >> 13;
|
|
h *= 0x5bd1e995;
|
|
h ^= h >> 15;
|
|
return h;
|
|
}
|
|
|
|
bool equal(unsigned int lhs, unsigned int rhs) const
|
|
{
|
|
return lhs == rhs;
|
|
}
|
|
};
|
|
|
|
struct TriangleHasher
|
|
{
|
|
const unsigned int* indices;
|
|
|
|
size_t hash(unsigned int i) const
|
|
{
|
|
const unsigned int* tri = indices + i * 3;
|
|
|
|
// Optimized Spatial Hashing for Collision Detection of Deformable Objects
|
|
return (tri[0] * 73856093) ^ (tri[1] * 19349663) ^ (tri[2] * 83492791);
|
|
}
|
|
|
|
bool equal(unsigned int lhs, unsigned int rhs) const
|
|
{
|
|
const unsigned int* lt = indices + lhs * 3;
|
|
const unsigned int* rt = indices + rhs * 3;
|
|
|
|
return lt[0] == rt[0] && lt[1] == rt[1] && lt[2] == rt[2];
|
|
}
|
|
};
|
|
|
|
static void computeVertexIds(unsigned int* vertex_ids, const Vector3* vertex_positions, size_t vertex_count, int grid_size)
|
|
{
|
|
assert(grid_size >= 1 && grid_size <= 1024);
|
|
float cell_scale = float(grid_size - 1);
|
|
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
const Vector3& v = vertex_positions[i];
|
|
|
|
int xi = int(v.x * cell_scale + 0.5f);
|
|
int yi = int(v.y * cell_scale + 0.5f);
|
|
int zi = int(v.z * cell_scale + 0.5f);
|
|
|
|
vertex_ids[i] = (xi << 20) | (yi << 10) | zi;
|
|
}
|
|
}
|
|
|
|
static size_t countTriangles(const unsigned int* vertex_ids, const unsigned int* indices, size_t index_count)
|
|
{
|
|
size_t result = 0;
|
|
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
unsigned int id0 = vertex_ids[indices[i + 0]];
|
|
unsigned int id1 = vertex_ids[indices[i + 1]];
|
|
unsigned int id2 = vertex_ids[indices[i + 2]];
|
|
|
|
result += (id0 != id1) & (id0 != id2) & (id1 != id2);
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
static size_t fillVertexCells(unsigned int* table, size_t table_size, unsigned int* vertex_cells, const unsigned int* vertex_ids, size_t vertex_count)
|
|
{
|
|
CellHasher hasher = {vertex_ids};
|
|
|
|
memset(table, -1, table_size * sizeof(unsigned int));
|
|
|
|
size_t result = 0;
|
|
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
unsigned int* entry = hashLookup2(table, table_size, hasher, unsigned(i), ~0u);
|
|
|
|
if (*entry == ~0u)
|
|
{
|
|
*entry = unsigned(i);
|
|
vertex_cells[i] = unsigned(result++);
|
|
}
|
|
else
|
|
{
|
|
vertex_cells[i] = vertex_cells[*entry];
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
static size_t countVertexCells(unsigned int* table, size_t table_size, const unsigned int* vertex_ids, size_t vertex_count)
|
|
{
|
|
IdHasher hasher;
|
|
|
|
memset(table, -1, table_size * sizeof(unsigned int));
|
|
|
|
size_t result = 0;
|
|
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
unsigned int id = vertex_ids[i];
|
|
unsigned int* entry = hashLookup2(table, table_size, hasher, id, ~0u);
|
|
|
|
result += (*entry == ~0u);
|
|
*entry = id;
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
static void fillCellQuadrics(Quadric* cell_quadrics, const unsigned int* indices, size_t index_count, const Vector3* vertex_positions, const unsigned int* vertex_cells)
|
|
{
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
unsigned int i0 = indices[i + 0];
|
|
unsigned int i1 = indices[i + 1];
|
|
unsigned int i2 = indices[i + 2];
|
|
|
|
unsigned int c0 = vertex_cells[i0];
|
|
unsigned int c1 = vertex_cells[i1];
|
|
unsigned int c2 = vertex_cells[i2];
|
|
|
|
bool single_cell = (c0 == c1) & (c0 == c2);
|
|
|
|
Quadric Q;
|
|
quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], single_cell ? 3.f : 1.f);
|
|
|
|
if (single_cell)
|
|
{
|
|
quadricAdd(cell_quadrics[c0], Q);
|
|
}
|
|
else
|
|
{
|
|
quadricAdd(cell_quadrics[c0], Q);
|
|
quadricAdd(cell_quadrics[c1], Q);
|
|
quadricAdd(cell_quadrics[c2], Q);
|
|
}
|
|
}
|
|
}
|
|
|
|
static void fillCellQuadrics(Quadric* cell_quadrics, const Vector3* vertex_positions, size_t vertex_count, const unsigned int* vertex_cells)
|
|
{
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
unsigned int c = vertex_cells[i];
|
|
const Vector3& v = vertex_positions[i];
|
|
|
|
Quadric Q;
|
|
quadricFromPoint(Q, v.x, v.y, v.z, 1.f);
|
|
|
|
quadricAdd(cell_quadrics[c], Q);
|
|
}
|
|
}
|
|
|
|
static void fillCellRemap(unsigned int* cell_remap, float* cell_errors, size_t cell_count, const unsigned int* vertex_cells, const Quadric* cell_quadrics, const Vector3* vertex_positions, size_t vertex_count)
|
|
{
|
|
memset(cell_remap, -1, cell_count * sizeof(unsigned int));
|
|
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
unsigned int cell = vertex_cells[i];
|
|
float error = quadricError(cell_quadrics[cell], vertex_positions[i]);
|
|
|
|
if (cell_remap[cell] == ~0u || cell_errors[cell] > error)
|
|
{
|
|
cell_remap[cell] = unsigned(i);
|
|
cell_errors[cell] = error;
|
|
}
|
|
}
|
|
}
|
|
|
|
static size_t filterTriangles(unsigned int* destination, unsigned int* tritable, size_t tritable_size, const unsigned int* indices, size_t index_count, const unsigned int* vertex_cells, const unsigned int* cell_remap)
|
|
{
|
|
TriangleHasher hasher = {destination};
|
|
|
|
memset(tritable, -1, tritable_size * sizeof(unsigned int));
|
|
|
|
size_t result = 0;
|
|
|
|
for (size_t i = 0; i < index_count; i += 3)
|
|
{
|
|
unsigned int c0 = vertex_cells[indices[i + 0]];
|
|
unsigned int c1 = vertex_cells[indices[i + 1]];
|
|
unsigned int c2 = vertex_cells[indices[i + 2]];
|
|
|
|
if (c0 != c1 && c0 != c2 && c1 != c2)
|
|
{
|
|
unsigned int a = cell_remap[c0];
|
|
unsigned int b = cell_remap[c1];
|
|
unsigned int c = cell_remap[c2];
|
|
|
|
if (b < a && b < c)
|
|
{
|
|
unsigned int t = a;
|
|
a = b, b = c, c = t;
|
|
}
|
|
else if (c < a && c < b)
|
|
{
|
|
unsigned int t = c;
|
|
c = b, b = a, a = t;
|
|
}
|
|
|
|
destination[result * 3 + 0] = a;
|
|
destination[result * 3 + 1] = b;
|
|
destination[result * 3 + 2] = c;
|
|
|
|
unsigned int* entry = hashLookup2(tritable, tritable_size, hasher, unsigned(result), ~0u);
|
|
|
|
if (*entry == ~0u)
|
|
*entry = unsigned(result++);
|
|
}
|
|
}
|
|
|
|
return result * 3;
|
|
}
|
|
|
|
static float interpolate(float y, float x0, float y0, float x1, float y1, float x2, float y2)
|
|
{
|
|
// three point interpolation from "revenge of interpolation search" paper
|
|
float num = (y1 - y) * (x1 - x2) * (x1 - x0) * (y2 - y0);
|
|
float den = (y2 - y) * (x1 - x2) * (y0 - y1) + (y0 - y) * (x1 - x0) * (y1 - y2);
|
|
return x1 + num / den;
|
|
}
|
|
|
|
} // namespace meshopt
|
|
|
|
#ifndef NDEBUG
|
|
// Note: this is only exposed for debug visualization purposes; do *not* use these in debug builds
|
|
MESHOPTIMIZER_API unsigned char* meshopt_simplifyDebugKind = 0;
|
|
MESHOPTIMIZER_API unsigned int* meshopt_simplifyDebugLoop = 0;
|
|
MESHOPTIMIZER_API unsigned int* meshopt_simplifyDebugLoopBack = 0;
|
|
#endif
|
|
|
|
size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, unsigned int options, float* out_result_error)
|
|
{
|
|
return meshopt_simplifyWithAttributes(destination, indices, index_count, vertex_positions_data, vertex_count, vertex_positions_stride, target_index_count, target_error, options, out_result_error, 0, 0, 0);
|
|
}
|
|
|
|
size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, unsigned int options, float* out_result_error, const float* attributes, const float* attribute_weights, size_t attribute_count)
|
|
{
|
|
using namespace meshopt;
|
|
|
|
assert(index_count % 3 == 0);
|
|
assert(vertex_stride >= 12 && vertex_stride <= 256);
|
|
assert(vertex_stride % sizeof(float) == 0);
|
|
assert(target_index_count <= index_count);
|
|
assert((options & ~(meshopt_SimplifyLockBorder)) == 0);
|
|
assert(attribute_count <= ATTRIBUTES);
|
|
|
|
meshopt_Allocator allocator;
|
|
|
|
unsigned int* result = destination;
|
|
|
|
// build adjacency information
|
|
EdgeAdjacency adjacency = {};
|
|
prepareEdgeAdjacency(adjacency, index_count, vertex_count, allocator);
|
|
updateEdgeAdjacency(adjacency, indices, index_count, vertex_count, NULL);
|
|
|
|
// build position remap that maps each vertex to the one with identical position
|
|
unsigned int* remap = allocator.allocate<unsigned int>(vertex_count);
|
|
unsigned int* wedge = allocator.allocate<unsigned int>(vertex_count);
|
|
buildPositionRemap(remap, wedge, vertex_data, vertex_count, vertex_stride, allocator);
|
|
|
|
// classify vertices; vertex kind determines collapse rules, see kCanCollapse
|
|
unsigned char* vertex_kind = allocator.allocate<unsigned char>(vertex_count);
|
|
unsigned int* loop = allocator.allocate<unsigned int>(vertex_count);
|
|
unsigned int* loopback = allocator.allocate<unsigned int>(vertex_count);
|
|
classifyVertices(vertex_kind, loop, loopback, vertex_count, adjacency, remap, wedge, options);
|
|
|
|
#if TRACE
|
|
size_t unique_positions = 0;
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
unique_positions += remap[i] == i;
|
|
|
|
printf("position remap: %d vertices => %d positions\n", int(vertex_count), int(unique_positions));
|
|
|
|
size_t kinds[Kind_Count] = {};
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
kinds[vertex_kind[i]] += remap[i] == i;
|
|
|
|
printf("kinds: manifold %d, border %d, seam %d, complex %d, locked %d\n",
|
|
int(kinds[Kind_Manifold]), int(kinds[Kind_Border]), int(kinds[Kind_Seam]), int(kinds[Kind_Complex]), int(kinds[Kind_Locked]));
|
|
#endif
|
|
|
|
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
|
|
rescalePositions(vertex_positions, vertex_data, vertex_count, vertex_stride);
|
|
|
|
#if ATTRIBUTES
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
{
|
|
memset(vertex_positions[i].a, 0, sizeof(vertex_positions[i].a));
|
|
|
|
for (size_t k = 0; k < attribute_count; ++k)
|
|
{
|
|
float a = attributes[i * attribute_count + k];
|
|
|
|
vertex_positions[i].a[k] = a * attribute_weights[k];
|
|
}
|
|
}
|
|
#endif
|
|
|
|
Quadric* vertex_quadrics = allocator.allocate<Quadric>(vertex_count);
|
|
memset(vertex_quadrics, 0, vertex_count * sizeof(Quadric));
|
|
Quadric* vertex_no_attrib_quadrics = allocator.allocate<Quadric>(vertex_count);
|
|
memset(vertex_no_attrib_quadrics, 0, vertex_count * sizeof(Quadric));
|
|
|
|
fillFaceQuadrics(vertex_quadrics, vertex_no_attrib_quadrics, indices, index_count, vertex_positions, remap);
|
|
fillEdgeQuadrics(vertex_quadrics, vertex_no_attrib_quadrics, indices, index_count, vertex_positions, remap, vertex_kind, loop, loopback);
|
|
|
|
if (result != indices)
|
|
memcpy(result, indices, index_count * sizeof(unsigned int));
|
|
|
|
#if TRACE
|
|
size_t pass_count = 0;
|
|
#endif
|
|
|
|
Collapse* edge_collapses = allocator.allocate<Collapse>(index_count);
|
|
unsigned int* collapse_order = allocator.allocate<unsigned int>(index_count);
|
|
unsigned int* collapse_remap = allocator.allocate<unsigned int>(vertex_count);
|
|
unsigned char* collapse_locked = allocator.allocate<unsigned char>(vertex_count);
|
|
|
|
size_t result_count = index_count;
|
|
float result_error = 0;
|
|
|
|
// target_error input is linear; we need to adjust it to match quadricError units
|
|
float error_limit = target_error * target_error;
|
|
|
|
while (result_count > target_index_count)
|
|
{
|
|
// note: throughout the simplification process adjacency structure reflects welded topology for result-in-progress
|
|
updateEdgeAdjacency(adjacency, result, result_count, vertex_count, remap);
|
|
|
|
size_t edge_collapse_count = pickEdgeCollapses(edge_collapses, result, result_count, remap, vertex_kind, loop);
|
|
|
|
// no edges can be collapsed any more due to topology restrictions
|
|
if (edge_collapse_count == 0)
|
|
break;
|
|
|
|
rankEdgeCollapses(edge_collapses, edge_collapse_count, vertex_positions, vertex_quadrics, vertex_no_attrib_quadrics, remap);
|
|
|
|
#if TRACE > 1
|
|
dumpEdgeCollapses(edge_collapses, edge_collapse_count, vertex_kind);
|
|
#endif
|
|
|
|
sortEdgeCollapses(collapse_order, edge_collapses, edge_collapse_count);
|
|
|
|
size_t triangle_collapse_goal = (result_count - target_index_count) / 3;
|
|
|
|
for (size_t i = 0; i < vertex_count; ++i)
|
|
collapse_remap[i] = unsigned(i);
|
|
|
|
memset(collapse_locked, 0, vertex_count);
|
|
|
|
#if TRACE
|
|
printf("pass %d: ", int(pass_count++));
|
|
#endif
|
|
|
|
size_t collapses = performEdgeCollapses(collapse_remap, collapse_locked, vertex_quadrics, vertex_no_attrib_quadrics, edge_collapses, edge_collapse_count, collapse_order, remap, wedge, vertex_kind, vertex_positions, adjacency, triangle_collapse_goal, error_limit, result_error);
|
|
|
|
// no edges can be collapsed any more due to hitting the error limit or triangle collapse limit
|
|
if (collapses == 0)
|
|
break;
|
|
|
|
remapEdgeLoops(loop, vertex_count, collapse_remap);
|
|
remapEdgeLoops(loopback, vertex_count, collapse_remap);
|
|
|
|
size_t new_count = remapIndexBuffer(result, result_count, collapse_remap);
|
|
assert(new_count < result_count);
|
|
|
|
result_count = new_count;
|
|
}
|
|
|
|
#if TRACE
|
|
printf("result: %d triangles, error: %e; total %d passes\n", int(result_count), sqrtf(result_error), int(pass_count));
|
|
#endif
|
|
|
|
#if TRACE > 1
|
|
dumpLockedCollapses(result, result_count, vertex_kind);
|
|
#endif
|
|
|
|
#ifndef NDEBUG
|
|
if (meshopt_simplifyDebugKind)
|
|
memcpy(meshopt_simplifyDebugKind, vertex_kind, vertex_count);
|
|
|
|
if (meshopt_simplifyDebugLoop)
|
|
memcpy(meshopt_simplifyDebugLoop, loop, vertex_count * sizeof(unsigned int));
|
|
|
|
if (meshopt_simplifyDebugLoopBack)
|
|
memcpy(meshopt_simplifyDebugLoopBack, loopback, vertex_count * sizeof(unsigned int));
|
|
#endif
|
|
|
|
// result_error is quadratic; we need to remap it back to linear
|
|
if (out_result_error)
|
|
{
|
|
*out_result_error = sqrtf(result_error);
|
|
}
|
|
|
|
return result_count;
|
|
}
|
|
|
|
size_t meshopt_simplifySloppy(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* out_result_error)
|
|
{
|
|
using namespace meshopt;
|
|
|
|
assert(index_count % 3 == 0);
|
|
assert(vertex_positions_stride >= 12 && vertex_positions_stride <= 256);
|
|
assert(vertex_positions_stride % sizeof(float) == 0);
|
|
assert(target_index_count <= index_count);
|
|
|
|
// we expect to get ~2 triangles/vertex in the output
|
|
size_t target_cell_count = target_index_count / 6;
|
|
|
|
meshopt_Allocator allocator;
|
|
|
|
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
|
|
rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride);
|
|
|
|
// find the optimal grid size using guided binary search
|
|
#if TRACE
|
|
printf("source: %d vertices, %d triangles\n", int(vertex_count), int(index_count / 3));
|
|
printf("target: %d cells, %d triangles\n", int(target_cell_count), int(target_index_count / 3));
|
|
#endif
|
|
|
|
unsigned int* vertex_ids = allocator.allocate<unsigned int>(vertex_count);
|
|
|
|
const int kInterpolationPasses = 5;
|
|
|
|
// invariant: # of triangles in min_grid <= target_count
|
|
int min_grid = int(1.f / (target_error < 1e-3f ? 1e-3f : target_error));
|
|
int max_grid = 1025;
|
|
size_t min_triangles = 0;
|
|
size_t max_triangles = index_count / 3;
|
|
|
|
// when we're error-limited, we compute the triangle count for the min. size; this accelerates convergence and provides the correct answer when we can't use a larger grid
|
|
if (min_grid > 1)
|
|
{
|
|
computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid);
|
|
min_triangles = countTriangles(vertex_ids, indices, index_count);
|
|
}
|
|
|
|
// instead of starting in the middle, let's guess as to what the answer might be! triangle count usually grows as a square of grid size...
|
|
int next_grid_size = int(sqrtf(float(target_cell_count)) + 0.5f);
|
|
|
|
for (int pass = 0; pass < 10 + kInterpolationPasses; ++pass)
|
|
{
|
|
if (min_triangles >= target_index_count / 3 || max_grid - min_grid <= 1)
|
|
break;
|
|
|
|
// we clamp the prediction of the grid size to make sure that the search converges
|
|
int grid_size = next_grid_size;
|
|
grid_size = (grid_size <= min_grid) ? min_grid + 1 : (grid_size >= max_grid) ? max_grid - 1 : grid_size;
|
|
|
|
computeVertexIds(vertex_ids, vertex_positions, vertex_count, grid_size);
|
|
size_t triangles = countTriangles(vertex_ids, indices, index_count);
|
|
|
|
#if TRACE
|
|
printf("pass %d (%s): grid size %d, triangles %d, %s\n",
|
|
pass, (pass == 0) ? "guess" : (pass <= kInterpolationPasses) ? "lerp" : "binary",
|
|
grid_size, int(triangles),
|
|
(triangles <= target_index_count / 3) ? "under" : "over");
|
|
#endif
|
|
|
|
float tip = interpolate(float(target_index_count / 3), float(min_grid), float(min_triangles), float(grid_size), float(triangles), float(max_grid), float(max_triangles));
|
|
|
|
if (triangles <= target_index_count / 3)
|
|
{
|
|
min_grid = grid_size;
|
|
min_triangles = triangles;
|
|
}
|
|
else
|
|
{
|
|
max_grid = grid_size;
|
|
max_triangles = triangles;
|
|
}
|
|
|
|
// we start by using interpolation search - it usually converges faster
|
|
// however, interpolation search has a worst case of O(N) so we switch to binary search after a few iterations which converges in O(logN)
|
|
next_grid_size = (pass < kInterpolationPasses) ? int(tip + 0.5f) : (min_grid + max_grid) / 2;
|
|
}
|
|
|
|
if (min_triangles == 0)
|
|
{
|
|
if (out_result_error)
|
|
*out_result_error = 1.f;
|
|
|
|
return 0;
|
|
}
|
|
|
|
// build vertex->cell association by mapping all vertices with the same quantized position to the same cell
|
|
size_t table_size = hashBuckets2(vertex_count);
|
|
unsigned int* table = allocator.allocate<unsigned int>(table_size);
|
|
|
|
unsigned int* vertex_cells = allocator.allocate<unsigned int>(vertex_count);
|
|
|
|
computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid);
|
|
size_t cell_count = fillVertexCells(table, table_size, vertex_cells, vertex_ids, vertex_count);
|
|
|
|
// build a quadric for each target cell
|
|
Quadric* cell_quadrics = allocator.allocate<Quadric>(cell_count);
|
|
memset(cell_quadrics, 0, cell_count * sizeof(Quadric));
|
|
|
|
fillCellQuadrics(cell_quadrics, indices, index_count, vertex_positions, vertex_cells);
|
|
|
|
// for each target cell, find the vertex with the minimal error
|
|
unsigned int* cell_remap = allocator.allocate<unsigned int>(cell_count);
|
|
float* cell_errors = allocator.allocate<float>(cell_count);
|
|
|
|
fillCellRemap(cell_remap, cell_errors, cell_count, vertex_cells, cell_quadrics, vertex_positions, vertex_count);
|
|
|
|
// compute error
|
|
float result_error = 0.f;
|
|
|
|
for (size_t i = 0; i < cell_count; ++i)
|
|
result_error = result_error < cell_errors[i] ? cell_errors[i] : result_error;
|
|
|
|
// collapse triangles!
|
|
// note that we need to filter out triangles that we've already output because we very frequently generate redundant triangles between cells :(
|
|
size_t tritable_size = hashBuckets2(min_triangles);
|
|
unsigned int* tritable = allocator.allocate<unsigned int>(tritable_size);
|
|
|
|
size_t write = filterTriangles(destination, tritable, tritable_size, indices, index_count, vertex_cells, cell_remap);
|
|
|
|
#if TRACE
|
|
printf("result: %d cells, %d triangles (%d unfiltered), error %e\n", int(cell_count), int(write / 3), int(min_triangles), sqrtf(result_error));
|
|
#endif
|
|
|
|
if (out_result_error)
|
|
*out_result_error = sqrtf(result_error);
|
|
|
|
return write;
|
|
}
|
|
|
|
size_t meshopt_simplifyPoints(unsigned int* destination, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_vertex_count)
|
|
{
|
|
using namespace meshopt;
|
|
|
|
assert(vertex_positions_stride >= 12 && vertex_positions_stride <= 256);
|
|
assert(vertex_positions_stride % sizeof(float) == 0);
|
|
assert(target_vertex_count <= vertex_count);
|
|
|
|
size_t target_cell_count = target_vertex_count;
|
|
|
|
if (target_cell_count == 0)
|
|
return 0;
|
|
|
|
meshopt_Allocator allocator;
|
|
|
|
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
|
|
rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride);
|
|
|
|
// find the optimal grid size using guided binary search
|
|
#if TRACE
|
|
printf("source: %d vertices\n", int(vertex_count));
|
|
printf("target: %d cells\n", int(target_cell_count));
|
|
#endif
|
|
|
|
unsigned int* vertex_ids = allocator.allocate<unsigned int>(vertex_count);
|
|
|
|
size_t table_size = hashBuckets2(vertex_count);
|
|
unsigned int* table = allocator.allocate<unsigned int>(table_size);
|
|
|
|
const int kInterpolationPasses = 5;
|
|
|
|
// invariant: # of vertices in min_grid <= target_count
|
|
int min_grid = 0;
|
|
int max_grid = 1025;
|
|
size_t min_vertices = 0;
|
|
size_t max_vertices = vertex_count;
|
|
|
|
// instead of starting in the middle, let's guess as to what the answer might be! triangle count usually grows as a square of grid size...
|
|
int next_grid_size = int(sqrtf(float(target_cell_count)) + 0.5f);
|
|
|
|
for (int pass = 0; pass < 10 + kInterpolationPasses; ++pass)
|
|
{
|
|
assert(min_vertices < target_vertex_count);
|
|
assert(max_grid - min_grid > 1);
|
|
|
|
// we clamp the prediction of the grid size to make sure that the search converges
|
|
int grid_size = next_grid_size;
|
|
grid_size = (grid_size <= min_grid) ? min_grid + 1 : (grid_size >= max_grid) ? max_grid - 1 : grid_size;
|
|
|
|
computeVertexIds(vertex_ids, vertex_positions, vertex_count, grid_size);
|
|
size_t vertices = countVertexCells(table, table_size, vertex_ids, vertex_count);
|
|
|
|
#if TRACE
|
|
printf("pass %d (%s): grid size %d, vertices %d, %s\n",
|
|
pass, (pass == 0) ? "guess" : (pass <= kInterpolationPasses) ? "lerp" : "binary",
|
|
grid_size, int(vertices),
|
|
(vertices <= target_vertex_count) ? "under" : "over");
|
|
#endif
|
|
|
|
float tip = interpolate(float(target_vertex_count), float(min_grid), float(min_vertices), float(grid_size), float(vertices), float(max_grid), float(max_vertices));
|
|
|
|
if (vertices <= target_vertex_count)
|
|
{
|
|
min_grid = grid_size;
|
|
min_vertices = vertices;
|
|
}
|
|
else
|
|
{
|
|
max_grid = grid_size;
|
|
max_vertices = vertices;
|
|
}
|
|
|
|
if (vertices == target_vertex_count || max_grid - min_grid <= 1)
|
|
break;
|
|
|
|
// we start by using interpolation search - it usually converges faster
|
|
// however, interpolation search has a worst case of O(N) so we switch to binary search after a few iterations which converges in O(logN)
|
|
next_grid_size = (pass < kInterpolationPasses) ? int(tip + 0.5f) : (min_grid + max_grid) / 2;
|
|
}
|
|
|
|
if (min_vertices == 0)
|
|
return 0;
|
|
|
|
// build vertex->cell association by mapping all vertices with the same quantized position to the same cell
|
|
unsigned int* vertex_cells = allocator.allocate<unsigned int>(vertex_count);
|
|
|
|
computeVertexIds(vertex_ids, vertex_positions, vertex_count, min_grid);
|
|
size_t cell_count = fillVertexCells(table, table_size, vertex_cells, vertex_ids, vertex_count);
|
|
|
|
// build a quadric for each target cell
|
|
Quadric* cell_quadrics = allocator.allocate<Quadric>(cell_count);
|
|
memset(cell_quadrics, 0, cell_count * sizeof(Quadric));
|
|
|
|
fillCellQuadrics(cell_quadrics, vertex_positions, vertex_count, vertex_cells);
|
|
|
|
// for each target cell, find the vertex with the minimal error
|
|
unsigned int* cell_remap = allocator.allocate<unsigned int>(cell_count);
|
|
float* cell_errors = allocator.allocate<float>(cell_count);
|
|
|
|
fillCellRemap(cell_remap, cell_errors, cell_count, vertex_cells, cell_quadrics, vertex_positions, vertex_count);
|
|
|
|
// copy results to the output
|
|
assert(cell_count <= target_vertex_count);
|
|
memcpy(destination, cell_remap, sizeof(unsigned int) * cell_count);
|
|
|
|
#if TRACE
|
|
printf("result: %d cells\n", int(cell_count));
|
|
#endif
|
|
|
|
return cell_count;
|
|
}
|
|
|
|
float meshopt_simplifyScale(const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
|
|
{
|
|
using namespace meshopt;
|
|
|
|
assert(vertex_positions_stride >= 12 && vertex_positions_stride <= 256);
|
|
assert(vertex_positions_stride % sizeof(float) == 0);
|
|
|
|
float extent = rescalePositions(NULL, vertex_positions, vertex_count, vertex_positions_stride);
|
|
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return extent;
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}
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