virtualx-engine/thirdparty/meshoptimizer/clusterizer.cpp
2021-11-19 14:02:49 +01:00

856 lines
28 KiB
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>
// This work is based on:
// Graham Wihlidal. Optimizing the Graphics Pipeline with Compute. 2016
// Matthaeus Chajdas. GeometryFX 1.2 - Cluster Culling. 2016
// Jack Ritter. An Efficient Bounding Sphere. 1990
namespace meshopt
{
// This must be <= 255 since index 0xff is used internally to indice a vertex that doesn't belong to a meshlet
const size_t kMeshletMaxVertices = 255;
// A reasonable limit is around 2*max_vertices or less
const size_t kMeshletMaxTriangles = 512;
struct TriangleAdjacency2
{
unsigned int* counts;
unsigned int* offsets;
unsigned int* data;
};
static void buildTriangleAdjacency(TriangleAdjacency2& 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 triangle 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 triangle 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]++] = unsigned(i);
adjacency.data[adjacency.offsets[b]++] = unsigned(i);
adjacency.data[adjacency.offsets[c]++] = unsigned(i);
}
// 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];
}
}
static void computeBoundingSphere(float result[4], const float points[][3], size_t count)
{
assert(count > 0);
// find extremum points along all 3 axes; for each axis we get a pair of points with min/max coordinates
size_t pmin[3] = {0, 0, 0};
size_t pmax[3] = {0, 0, 0};
for (size_t i = 0; i < count; ++i)
{
const float* p = points[i];
for (int axis = 0; axis < 3; ++axis)
{
pmin[axis] = (p[axis] < points[pmin[axis]][axis]) ? i : pmin[axis];
pmax[axis] = (p[axis] > points[pmax[axis]][axis]) ? i : pmax[axis];
}
}
// find the pair of points with largest distance
float paxisd2 = 0;
int paxis = 0;
for (int axis = 0; axis < 3; ++axis)
{
const float* p1 = points[pmin[axis]];
const float* p2 = points[pmax[axis]];
float d2 = (p2[0] - p1[0]) * (p2[0] - p1[0]) + (p2[1] - p1[1]) * (p2[1] - p1[1]) + (p2[2] - p1[2]) * (p2[2] - p1[2]);
if (d2 > paxisd2)
{
paxisd2 = d2;
paxis = axis;
}
}
// use the longest segment as the initial sphere diameter
const float* p1 = points[pmin[paxis]];
const float* p2 = points[pmax[paxis]];
float center[3] = {(p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2, (p1[2] + p2[2]) / 2};
float radius = sqrtf(paxisd2) / 2;
// iteratively adjust the sphere up until all points fit
for (size_t i = 0; i < count; ++i)
{
const float* p = points[i];
float d2 = (p[0] - center[0]) * (p[0] - center[0]) + (p[1] - center[1]) * (p[1] - center[1]) + (p[2] - center[2]) * (p[2] - center[2]);
if (d2 > radius * radius)
{
float d = sqrtf(d2);
assert(d > 0);
float k = 0.5f + (radius / d) / 2;
center[0] = center[0] * k + p[0] * (1 - k);
center[1] = center[1] * k + p[1] * (1 - k);
center[2] = center[2] * k + p[2] * (1 - k);
radius = (radius + d) / 2;
}
}
result[0] = center[0];
result[1] = center[1];
result[2] = center[2];
result[3] = radius;
}
struct Cone
{
float px, py, pz;
float nx, ny, nz;
};
static float getMeshletScore(float distance2, float spread, float cone_weight, float expected_radius)
{
float cone = 1.f - spread * cone_weight;
float cone_clamped = cone < 1e-3f ? 1e-3f : cone;
return (1 + sqrtf(distance2) / expected_radius * (1 - cone_weight)) * cone_clamped;
}
static Cone getMeshletCone(const Cone& acc, unsigned int triangle_count)
{
Cone result = acc;
float center_scale = triangle_count == 0 ? 0.f : 1.f / float(triangle_count);
result.px *= center_scale;
result.py *= center_scale;
result.pz *= center_scale;
float axis_length = result.nx * result.nx + result.ny * result.ny + result.nz * result.nz;
float axis_scale = axis_length == 0.f ? 0.f : 1.f / sqrtf(axis_length);
result.nx *= axis_scale;
result.ny *= axis_scale;
result.nz *= axis_scale;
return result;
}
static float computeTriangleCones(Cone* triangles, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
{
(void)vertex_count;
size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
size_t face_count = index_count / 3;
float mesh_area = 0;
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];
assert(a < vertex_count && b < vertex_count && c < vertex_count);
const float* p0 = vertex_positions + vertex_stride_float * a;
const float* p1 = vertex_positions + vertex_stride_float * b;
const float* p2 = vertex_positions + vertex_stride_float * c;
float p10[3] = {p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]};
float p20[3] = {p2[0] - p0[0], p2[1] - p0[1], p2[2] - p0[2]};
float normalx = p10[1] * p20[2] - p10[2] * p20[1];
float normaly = p10[2] * p20[0] - p10[0] * p20[2];
float normalz = p10[0] * p20[1] - p10[1] * p20[0];
float area = sqrtf(normalx * normalx + normaly * normaly + normalz * normalz);
float invarea = (area == 0.f) ? 0.f : 1.f / area;
triangles[i].px = (p0[0] + p1[0] + p2[0]) / 3.f;
triangles[i].py = (p0[1] + p1[1] + p2[1]) / 3.f;
triangles[i].pz = (p0[2] + p1[2] + p2[2]) / 3.f;
triangles[i].nx = normalx * invarea;
triangles[i].ny = normaly * invarea;
triangles[i].nz = normalz * invarea;
mesh_area += area;
}
return mesh_area;
}
static void finishMeshlet(meshopt_Meshlet& meshlet, unsigned char* meshlet_triangles)
{
size_t offset = meshlet.triangle_offset + meshlet.triangle_count * 3;
// fill 4b padding with 0
while (offset & 3)
meshlet_triangles[offset++] = 0;
}
static bool appendMeshlet(meshopt_Meshlet& meshlet, unsigned int a, unsigned int b, unsigned int c, unsigned char* used, meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, size_t meshlet_offset, size_t max_vertices, size_t max_triangles)
{
unsigned char& av = used[a];
unsigned char& bv = used[b];
unsigned char& cv = used[c];
bool result = false;
unsigned int used_extra = (av == 0xff) + (bv == 0xff) + (cv == 0xff);
if (meshlet.vertex_count + used_extra > max_vertices || meshlet.triangle_count >= max_triangles)
{
meshlets[meshlet_offset] = meshlet;
for (size_t j = 0; j < meshlet.vertex_count; ++j)
used[meshlet_vertices[meshlet.vertex_offset + j]] = 0xff;
finishMeshlet(meshlet, meshlet_triangles);
meshlet.vertex_offset += meshlet.vertex_count;
meshlet.triangle_offset += (meshlet.triangle_count * 3 + 3) & ~3; // 4b padding
meshlet.vertex_count = 0;
meshlet.triangle_count = 0;
result = true;
}
if (av == 0xff)
{
av = (unsigned char)meshlet.vertex_count;
meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = a;
}
if (bv == 0xff)
{
bv = (unsigned char)meshlet.vertex_count;
meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = b;
}
if (cv == 0xff)
{
cv = (unsigned char)meshlet.vertex_count;
meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = c;
}
meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 0] = av;
meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 1] = bv;
meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 2] = cv;
meshlet.triangle_count++;
return result;
}
struct KDNode
{
union
{
float split;
unsigned int index;
};
// leaves: axis = 3, children = number of extra points after this one (0 if 'index' is the only point)
// branches: axis != 3, left subtree = skip 1, right subtree = skip 1+children
unsigned int axis : 2;
unsigned int children : 30;
};
static size_t kdtreePartition(unsigned int* indices, size_t count, const float* points, size_t stride, unsigned int axis, float pivot)
{
size_t m = 0;
// invariant: elements in range [0, m) are < pivot, elements in range [m, i) are >= pivot
for (size_t i = 0; i < count; ++i)
{
float v = points[indices[i] * stride + axis];
// swap(m, i) unconditionally
unsigned int t = indices[m];
indices[m] = indices[i];
indices[i] = t;
// when v >= pivot, we swap i with m without advancing it, preserving invariants
m += v < pivot;
}
return m;
}
static size_t kdtreeBuildLeaf(size_t offset, KDNode* nodes, size_t node_count, unsigned int* indices, size_t count)
{
assert(offset + count <= node_count);
(void)node_count;
KDNode& result = nodes[offset];
result.index = indices[0];
result.axis = 3;
result.children = unsigned(count - 1);
// all remaining points are stored in nodes immediately following the leaf
for (size_t i = 1; i < count; ++i)
{
KDNode& tail = nodes[offset + i];
tail.index = indices[i];
tail.axis = 3;
tail.children = ~0u >> 2; // bogus value to prevent misuse
}
return offset + count;
}
static size_t kdtreeBuild(size_t offset, KDNode* nodes, size_t node_count, const float* points, size_t stride, unsigned int* indices, size_t count, size_t leaf_size)
{
assert(count > 0);
assert(offset < node_count);
if (count <= leaf_size)
return kdtreeBuildLeaf(offset, nodes, node_count, indices, count);
float mean[3] = {};
float vars[3] = {};
float runc = 1, runs = 1;
// gather statistics on the points in the subtree using Welford's algorithm
for (size_t i = 0; i < count; ++i, runc += 1.f, runs = 1.f / runc)
{
const float* point = points + indices[i] * stride;
for (int k = 0; k < 3; ++k)
{
float delta = point[k] - mean[k];
mean[k] += delta * runs;
vars[k] += delta * (point[k] - mean[k]);
}
}
// split axis is one where the variance is largest
unsigned int axis = vars[0] >= vars[1] && vars[0] >= vars[2] ? 0 : vars[1] >= vars[2] ? 1 : 2;
float split = mean[axis];
size_t middle = kdtreePartition(indices, count, points, stride, axis, split);
// when the partition is degenerate simply consolidate the points into a single node
if (middle <= leaf_size / 2 || middle >= count - leaf_size / 2)
return kdtreeBuildLeaf(offset, nodes, node_count, indices, count);
KDNode& result = nodes[offset];
result.split = split;
result.axis = axis;
// left subtree is right after our node
size_t next_offset = kdtreeBuild(offset + 1, nodes, node_count, points, stride, indices, middle, leaf_size);
// distance to the right subtree is represented explicitly
result.children = unsigned(next_offset - offset - 1);
return kdtreeBuild(next_offset, nodes, node_count, points, stride, indices + middle, count - middle, leaf_size);
}
static void kdtreeNearest(KDNode* nodes, unsigned int root, const float* points, size_t stride, const unsigned char* emitted_flags, const float* position, unsigned int& result, float& limit)
{
const KDNode& node = nodes[root];
if (node.axis == 3)
{
// leaf
for (unsigned int i = 0; i <= node.children; ++i)
{
unsigned int index = nodes[root + i].index;
if (emitted_flags[index])
continue;
const float* point = points + index * stride;
float distance2 =
(point[0] - position[0]) * (point[0] - position[0]) +
(point[1] - position[1]) * (point[1] - position[1]) +
(point[2] - position[2]) * (point[2] - position[2]);
float distance = sqrtf(distance2);
if (distance < limit)
{
result = index;
limit = distance;
}
}
}
else
{
// branch; we order recursion to process the node that search position is in first
float delta = position[node.axis] - node.split;
unsigned int first = (delta <= 0) ? 0 : node.children;
unsigned int second = first ^ node.children;
kdtreeNearest(nodes, root + 1 + first, points, stride, emitted_flags, position, result, limit);
// only process the other node if it can have a match based on closest distance so far
if (fabsf(delta) <= limit)
kdtreeNearest(nodes, root + 1 + second, points, stride, emitted_flags, position, result, limit);
}
}
} // namespace meshopt
size_t meshopt_buildMeshletsBound(size_t index_count, size_t max_vertices, size_t max_triangles)
{
using namespace meshopt;
assert(index_count % 3 == 0);
assert(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
(void)kMeshletMaxVertices;
(void)kMeshletMaxTriangles;
// meshlet construction is limited by max vertices and max triangles per meshlet
// the worst case is that the input is an unindexed stream since this equally stresses both limits
// note that we assume that in the worst case, we leave 2 vertices unpacked in each meshlet - if we have space for 3 we can pack any triangle
size_t max_vertices_conservative = max_vertices - 2;
size_t meshlet_limit_vertices = (index_count + max_vertices_conservative - 1) / max_vertices_conservative;
size_t meshlet_limit_triangles = (index_count / 3 + max_triangles - 1) / max_triangles;
return meshlet_limit_vertices > meshlet_limit_triangles ? meshlet_limit_vertices : meshlet_limit_triangles;
}
size_t meshopt_buildMeshlets(meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t max_vertices, size_t max_triangles, float cone_weight)
{
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(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
meshopt_Allocator allocator;
TriangleAdjacency2 adjacency = {};
buildTriangleAdjacency(adjacency, indices, index_count, vertex_count, allocator);
unsigned int* live_triangles = allocator.allocate<unsigned int>(vertex_count);
memcpy(live_triangles, adjacency.counts, vertex_count * sizeof(unsigned int));
size_t face_count = index_count / 3;
unsigned char* emitted_flags = allocator.allocate<unsigned char>(face_count);
memset(emitted_flags, 0, face_count);
// for each triangle, precompute centroid & normal to use for scoring
Cone* triangles = allocator.allocate<Cone>(face_count);
float mesh_area = computeTriangleCones(triangles, indices, index_count, vertex_positions, vertex_count, vertex_positions_stride);
// assuming each meshlet is a square patch, expected radius is sqrt(expected area)
float triangle_area_avg = face_count == 0 ? 0.f : mesh_area / float(face_count) * 0.5f;
float meshlet_expected_radius = sqrtf(triangle_area_avg * max_triangles) * 0.5f;
// build a kd-tree for nearest neighbor lookup
unsigned int* kdindices = allocator.allocate<unsigned int>(face_count);
for (size_t i = 0; i < face_count; ++i)
kdindices[i] = unsigned(i);
KDNode* nodes = allocator.allocate<KDNode>(face_count * 2);
kdtreeBuild(0, nodes, face_count * 2, &triangles[0].px, sizeof(Cone) / sizeof(float), kdindices, face_count, /* leaf_size= */ 8);
// index of the vertex in the meshlet, 0xff if the vertex isn't used
unsigned char* used = allocator.allocate<unsigned char>(vertex_count);
memset(used, -1, vertex_count);
meshopt_Meshlet meshlet = {};
size_t meshlet_offset = 0;
Cone meshlet_cone_acc = {};
for (;;)
{
unsigned int best_triangle = ~0u;
unsigned int best_extra = 5;
float best_score = FLT_MAX;
Cone meshlet_cone = getMeshletCone(meshlet_cone_acc, meshlet.triangle_count);
for (size_t i = 0; i < meshlet.vertex_count; ++i)
{
unsigned int index = meshlet_vertices[meshlet.vertex_offset + i];
unsigned int* neighbours = &adjacency.data[0] + adjacency.offsets[index];
size_t neighbours_size = adjacency.counts[index];
for (size_t j = 0; j < neighbours_size; ++j)
{
unsigned int triangle = neighbours[j];
assert(!emitted_flags[triangle]);
unsigned int a = indices[triangle * 3 + 0], b = indices[triangle * 3 + 1], c = indices[triangle * 3 + 2];
assert(a < vertex_count && b < vertex_count && c < vertex_count);
unsigned int extra = (used[a] == 0xff) + (used[b] == 0xff) + (used[c] == 0xff);
// triangles that don't add new vertices to meshlets are max. priority
if (extra != 0)
{
// artificially increase the priority of dangling triangles as they're expensive to add to new meshlets
if (live_triangles[a] == 1 || live_triangles[b] == 1 || live_triangles[c] == 1)
extra = 0;
extra++;
}
// since topology-based priority is always more important than the score, we can skip scoring in some cases
if (extra > best_extra)
continue;
const Cone& tri_cone = triangles[triangle];
float distance2 =
(tri_cone.px - meshlet_cone.px) * (tri_cone.px - meshlet_cone.px) +
(tri_cone.py - meshlet_cone.py) * (tri_cone.py - meshlet_cone.py) +
(tri_cone.pz - meshlet_cone.pz) * (tri_cone.pz - meshlet_cone.pz);
float spread = tri_cone.nx * meshlet_cone.nx + tri_cone.ny * meshlet_cone.ny + tri_cone.nz * meshlet_cone.nz;
float score = getMeshletScore(distance2, spread, cone_weight, meshlet_expected_radius);
// note that topology-based priority is always more important than the score
// this helps maintain reasonable effectiveness of meshlet data and reduces scoring cost
if (extra < best_extra || score < best_score)
{
best_triangle = triangle;
best_extra = extra;
best_score = score;
}
}
}
if (best_triangle == ~0u)
{
float position[3] = {meshlet_cone.px, meshlet_cone.py, meshlet_cone.pz};
unsigned int index = ~0u;
float limit = FLT_MAX;
kdtreeNearest(nodes, 0, &triangles[0].px, sizeof(Cone) / sizeof(float), emitted_flags, position, index, limit);
best_triangle = index;
}
if (best_triangle == ~0u)
break;
unsigned int a = indices[best_triangle * 3 + 0], b = indices[best_triangle * 3 + 1], c = indices[best_triangle * 3 + 2];
assert(a < vertex_count && b < vertex_count && c < vertex_count);
// add meshlet to the output; when the current meshlet is full we reset the accumulated bounds
if (appendMeshlet(meshlet, a, b, c, used, meshlets, meshlet_vertices, meshlet_triangles, meshlet_offset, max_vertices, max_triangles))
{
meshlet_offset++;
memset(&meshlet_cone_acc, 0, sizeof(meshlet_cone_acc));
}
live_triangles[a]--;
live_triangles[b]--;
live_triangles[c]--;
// remove emitted triangle from adjacency data
// this makes sure that we spend less time traversing these lists on subsequent iterations
for (size_t k = 0; k < 3; ++k)
{
unsigned int index = indices[best_triangle * 3 + k];
unsigned int* neighbours = &adjacency.data[0] + adjacency.offsets[index];
size_t neighbours_size = adjacency.counts[index];
for (size_t i = 0; i < neighbours_size; ++i)
{
unsigned int tri = neighbours[i];
if (tri == best_triangle)
{
neighbours[i] = neighbours[neighbours_size - 1];
adjacency.counts[index]--;
break;
}
}
}
// update aggregated meshlet cone data for scoring subsequent triangles
meshlet_cone_acc.px += triangles[best_triangle].px;
meshlet_cone_acc.py += triangles[best_triangle].py;
meshlet_cone_acc.pz += triangles[best_triangle].pz;
meshlet_cone_acc.nx += triangles[best_triangle].nx;
meshlet_cone_acc.ny += triangles[best_triangle].ny;
meshlet_cone_acc.nz += triangles[best_triangle].nz;
emitted_flags[best_triangle] = 1;
}
if (meshlet.triangle_count)
{
finishMeshlet(meshlet, meshlet_triangles);
meshlets[meshlet_offset++] = meshlet;
}
assert(meshlet_offset <= meshopt_buildMeshletsBound(index_count, max_vertices, max_triangles));
return meshlet_offset;
}
size_t meshopt_buildMeshletsScan(meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, const unsigned int* indices, size_t index_count, size_t vertex_count, size_t max_vertices, size_t max_triangles)
{
using namespace meshopt;
assert(index_count % 3 == 0);
assert(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
meshopt_Allocator allocator;
// index of the vertex in the meshlet, 0xff if the vertex isn't used
unsigned char* used = allocator.allocate<unsigned char>(vertex_count);
memset(used, -1, vertex_count);
meshopt_Meshlet meshlet = {};
size_t meshlet_offset = 0;
for (size_t i = 0; i < index_count; i += 3)
{
unsigned int a = indices[i + 0], b = indices[i + 1], c = indices[i + 2];
assert(a < vertex_count && b < vertex_count && c < vertex_count);
// appends triangle to the meshlet and writes previous meshlet to the output if full
meshlet_offset += appendMeshlet(meshlet, a, b, c, used, meshlets, meshlet_vertices, meshlet_triangles, meshlet_offset, max_vertices, max_triangles);
}
if (meshlet.triangle_count)
{
finishMeshlet(meshlet, meshlet_triangles);
meshlets[meshlet_offset++] = meshlet;
}
assert(meshlet_offset <= meshopt_buildMeshletsBound(index_count, max_vertices, max_triangles));
return meshlet_offset;
}
meshopt_Bounds meshopt_computeClusterBounds(const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
{
using namespace meshopt;
assert(index_count % 3 == 0);
assert(index_count / 3 <= kMeshletMaxTriangles);
assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
assert(vertex_positions_stride % sizeof(float) == 0);
(void)vertex_count;
size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
// compute triangle normals and gather triangle corners
float normals[kMeshletMaxTriangles][3];
float corners[kMeshletMaxTriangles][3][3];
size_t triangles = 0;
for (size_t i = 0; i < index_count; i += 3)
{
unsigned int a = indices[i + 0], b = indices[i + 1], c = indices[i + 2];
assert(a < vertex_count && b < vertex_count && c < vertex_count);
const float* p0 = vertex_positions + vertex_stride_float * a;
const float* p1 = vertex_positions + vertex_stride_float * b;
const float* p2 = vertex_positions + vertex_stride_float * c;
float p10[3] = {p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]};
float p20[3] = {p2[0] - p0[0], p2[1] - p0[1], p2[2] - p0[2]};
float normalx = p10[1] * p20[2] - p10[2] * p20[1];
float normaly = p10[2] * p20[0] - p10[0] * p20[2];
float normalz = p10[0] * p20[1] - p10[1] * p20[0];
float area = sqrtf(normalx * normalx + normaly * normaly + normalz * normalz);
// no need to include degenerate triangles - they will be invisible anyway
if (area == 0.f)
continue;
// record triangle normals & corners for future use; normal and corner 0 define a plane equation
normals[triangles][0] = normalx / area;
normals[triangles][1] = normaly / area;
normals[triangles][2] = normalz / area;
memcpy(corners[triangles][0], p0, 3 * sizeof(float));
memcpy(corners[triangles][1], p1, 3 * sizeof(float));
memcpy(corners[triangles][2], p2, 3 * sizeof(float));
triangles++;
}
meshopt_Bounds bounds = {};
// degenerate cluster, no valid triangles => trivial reject (cone data is 0)
if (triangles == 0)
return bounds;
// compute cluster bounding sphere; we'll use the center to determine normal cone apex as well
float psphere[4] = {};
computeBoundingSphere(psphere, corners[0], triangles * 3);
float center[3] = {psphere[0], psphere[1], psphere[2]};
// treating triangle normals as points, find the bounding sphere - the sphere center determines the optimal cone axis
float nsphere[4] = {};
computeBoundingSphere(nsphere, normals, triangles);
float axis[3] = {nsphere[0], nsphere[1], nsphere[2]};
float axislength = sqrtf(axis[0] * axis[0] + axis[1] * axis[1] + axis[2] * axis[2]);
float invaxislength = axislength == 0.f ? 0.f : 1.f / axislength;
axis[0] *= invaxislength;
axis[1] *= invaxislength;
axis[2] *= invaxislength;
// compute a tight cone around all normals, mindp = cos(angle/2)
float mindp = 1.f;
for (size_t i = 0; i < triangles; ++i)
{
float dp = normals[i][0] * axis[0] + normals[i][1] * axis[1] + normals[i][2] * axis[2];
mindp = (dp < mindp) ? dp : mindp;
}
// fill bounding sphere info; note that below we can return bounds without cone information for degenerate cones
bounds.center[0] = center[0];
bounds.center[1] = center[1];
bounds.center[2] = center[2];
bounds.radius = psphere[3];
// degenerate cluster, normal cone is larger than a hemisphere => trivial accept
// note that if mindp is positive but close to 0, the triangle intersection code below gets less stable
// we arbitrarily decide that if a normal cone is ~168 degrees wide or more, the cone isn't useful
if (mindp <= 0.1f)
{
bounds.cone_cutoff = 1;
bounds.cone_cutoff_s8 = 127;
return bounds;
}
float maxt = 0;
// we need to find the point on center-t*axis ray that lies in negative half-space of all triangles
for (size_t i = 0; i < triangles; ++i)
{
// dot(center-t*axis-corner, trinormal) = 0
// dot(center-corner, trinormal) - t * dot(axis, trinormal) = 0
float cx = center[0] - corners[i][0][0];
float cy = center[1] - corners[i][0][1];
float cz = center[2] - corners[i][0][2];
float dc = cx * normals[i][0] + cy * normals[i][1] + cz * normals[i][2];
float dn = axis[0] * normals[i][0] + axis[1] * normals[i][1] + axis[2] * normals[i][2];
// dn should be larger than mindp cutoff above
assert(dn > 0.f);
float t = dc / dn;
maxt = (t > maxt) ? t : maxt;
}
// cone apex should be in the negative half-space of all cluster triangles by construction
bounds.cone_apex[0] = center[0] - axis[0] * maxt;
bounds.cone_apex[1] = center[1] - axis[1] * maxt;
bounds.cone_apex[2] = center[2] - axis[2] * maxt;
// note: this axis is the axis of the normal cone, but our test for perspective camera effectively negates the axis
bounds.cone_axis[0] = axis[0];
bounds.cone_axis[1] = axis[1];
bounds.cone_axis[2] = axis[2];
// cos(a) for normal cone is mindp; we need to add 90 degrees on both sides and invert the cone
// which gives us -cos(a+90) = -(-sin(a)) = sin(a) = sqrt(1 - cos^2(a))
bounds.cone_cutoff = sqrtf(1 - mindp * mindp);
// quantize axis & cutoff to 8-bit SNORM format
bounds.cone_axis_s8[0] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[0], 8));
bounds.cone_axis_s8[1] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[1], 8));
bounds.cone_axis_s8[2] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[2], 8));
// for the 8-bit test to be conservative, we need to adjust the cutoff by measuring the max. error
float cone_axis_s8_e0 = fabsf(bounds.cone_axis_s8[0] / 127.f - bounds.cone_axis[0]);
float cone_axis_s8_e1 = fabsf(bounds.cone_axis_s8[1] / 127.f - bounds.cone_axis[1]);
float cone_axis_s8_e2 = fabsf(bounds.cone_axis_s8[2] / 127.f - bounds.cone_axis[2]);
// note that we need to round this up instead of rounding to nearest, hence +1
int cone_cutoff_s8 = int(127 * (bounds.cone_cutoff + cone_axis_s8_e0 + cone_axis_s8_e1 + cone_axis_s8_e2) + 1);
bounds.cone_cutoff_s8 = (cone_cutoff_s8 > 127) ? 127 : (signed char)(cone_cutoff_s8);
return bounds;
}
meshopt_Bounds meshopt_computeMeshletBounds(const unsigned int* meshlet_vertices, const unsigned char* meshlet_triangles, size_t triangle_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
{
using namespace meshopt;
assert(triangle_count <= kMeshletMaxTriangles);
assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
assert(vertex_positions_stride % sizeof(float) == 0);
unsigned int indices[kMeshletMaxTriangles * 3];
for (size_t i = 0; i < triangle_count * 3; ++i)
{
unsigned int index = meshlet_vertices[meshlet_triangles[i]];
assert(index < vertex_count);
indices[i] = index;
}
return meshopt_computeClusterBounds(indices, triangle_count * 3, vertex_positions, vertex_count, vertex_positions_stride);
}