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Update with experimental mesh optimizer. 

Normals being optimized has better quality now.

Test simplify once and then use a slightly less tolerant 
error for the target error.
This commit is contained in:
K. S. Ernest (iFire) Lee 2021-04-09 22:44:36 -07:00
parent 4828667759
commit fc8ea1d828
9 changed files with 486 additions and 48 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

107
editor/import/scene_importer_mesh.cpp
View File

@ -30,6 +30,7 @@
#include "scene_importer_mesh.h"
#include "core/math/math_defs.h"
#include "scene/resources/surface_tool.h"
void EditorSceneImporterMesh::add_blend_shape(const String &p_name) {
@ -141,6 +142,18 @@ void EditorSceneImporterMesh::set_surface_material(int p_surface, const Ref<Mate
surfaces.write[p_surface].material = p_material;
}
Basis EditorSceneImporterMesh::compute_rotation_matrix_from_ortho_6d(Vector3 p_x_raw, Vector3 p_y_raw) {
Vector3 x = p_x_raw.normalized();
Vector3 z = x.cross(p_y_raw);
z = z.normalized();
Vector3 y = z.cross(x);
Basis basis;
basis.set_axis(Vector3::AXIS_X, x);
basis.set_axis(Vector3::AXIS_Y, y);
basis.set_axis(Vector3::AXIS_Z, z);
return basis;
}
void EditorSceneImporterMesh::generate_lods() {
if (!SurfaceTool::simplify_func) {
return;
@ -151,6 +164,9 @@ void EditorSceneImporterMesh::generate_lods() {
if (!SurfaceTool::simplify_sloppy_func) {
return;
}
if (!SurfaceTool::simplify_with_attrib_func) {
return;
}
for (int i = 0; i < surfaces.size(); i++) {
if (surfaces[i].primitive != Mesh::PRIMITIVE_TRIANGLES) {
@ -163,59 +179,62 @@ void EditorSceneImporterMesh::generate_lods() {
if (indices.size() == 0) {
continue; //no lods if no indices
}
Vector<Vector3> normals = surfaces[i].arrays[RS::ARRAY_NORMAL];
uint32_t vertex_count = vertices.size();
const Vector3 *vertices_ptr = vertices.ptr();
int min_indices = 10;
int index_target = indices.size() / 2;
print_line("Total indices: " + itos(indices.size()));
float mesh_scale = SurfaceTool::simplify_scale_func((const float *)vertices_ptr, vertex_count, sizeof(Vector3));
const float target_error = 1e-3f;
float abs_target_error = target_error / mesh_scale;
Vector<float> attributes;
Vector<float> normal_weights;
int32_t attribute_count = 6;
if (normals.size()) {
attributes.resize(normals.size() * attribute_count);
for (int32_t normal_i = 0; normal_i < normals.size(); normal_i++) {
Basis basis;
basis.set_euler(normals[normal_i]);
Vector3 basis_x = basis.get_axis(0);
Vector3 basis_y = basis.get_axis(1);
basis = compute_rotation_matrix_from_ortho_6d(basis_x, basis_y);
basis_x = basis.get_axis(0);
basis_y = basis.get_axis(1);
attributes.write[normal_i * attribute_count + 0] = basis_x.x;
attributes.write[normal_i * attribute_count + 1] = basis_x.y;
attributes.write[normal_i * attribute_count + 2] = basis_x.z;
attributes.write[normal_i * attribute_count + 3] = basis_y.x;
attributes.write[normal_i * attribute_count + 4] = basis_y.y;
attributes.write[normal_i * attribute_count + 5] = basis_y.z;
}
normal_weights.resize(vertex_count);
for (int32_t weight_i = 0; weight_i < normal_weights.size(); weight_i++) {
normal_weights.write[weight_i] = 1.0;
}
} else {
attribute_count = 0;
}
const int min_indices = 10;
const float error_tolerance = 1.44224'95703; // Cube root of 3
const float threshold = 1.0 / error_tolerance;
int index_target = indices.size() * threshold;
float max_mesh_error_percentage = 1e0f;
float mesh_error = 0.0f;
while (index_target > min_indices) {
float error;
Vector<int> new_indices;
new_indices.resize(indices.size());
size_t new_len = SurfaceTool::simplify_func((unsigned int *)new_indices.ptrw(), (const unsigned int *)indices.ptr(), indices.size(), (const float *)vertices_ptr, vertex_count, sizeof(Vector3), index_target, abs_target_error, &error);
if ((int)new_len > (index_target * 120 / 100)) {
// Attribute discontinuities break normals.
bool is_sloppy = false;
if (is_sloppy) {
abs_target_error = target_error / mesh_scale;
index_target = new_len;
while (index_target > min_indices) {
Vector<int> sloppy_new_indices;
sloppy_new_indices.resize(indices.size());
new_len = SurfaceTool::simplify_sloppy_func((unsigned int *)sloppy_new_indices.ptrw(), (const unsigned int *)indices.ptr(), indices.size(), (const float *)vertices_ptr, vertex_count, sizeof(Vector3), index_target, abs_target_error, &error);
if ((int)new_len > (index_target * 120 / 100)) {
break; // 20 percent tolerance
}
sloppy_new_indices.resize(new_len);
Surface::LOD lod;
lod.distance = error * mesh_scale;
abs_target_error = lod.distance;
if (Math::is_equal_approx(abs_target_error, 0.0f)) {
return;
}
lod.indices = sloppy_new_indices;
print_line("Lod " + itos(surfaces.write[i].lods.size()) + " shoot for " + itos(index_target / 3) + " triangles, got " + itos(new_len / 3) + " triangles. Distance " + rtos(lod.distance) + ". Use simplify sloppy.");
surfaces.write[i].lods.push_back(lod);
index_target /= 2;
}
}
break; // 20 percent tolerance
size_t new_len = SurfaceTool::simplify_with_attrib_func((unsigned int *)new_indices.ptrw(), (const unsigned int *)indices.ptr(), indices.size(), (const float *)vertices_ptr, vertex_count, sizeof(Vector3), index_target, max_mesh_error_percentage, &mesh_error, (float *)attributes.ptrw(), normal_weights.ptrw(), attribute_count);
if ((int)new_len > (index_target * error_tolerance)) {
break;
}
Surface::LOD lod;
lod.distance = mesh_error;
if (Math::is_equal_approx(mesh_error, 0.0f)) {
break;
}
if (new_len <= 0) {
break;
}
new_indices.resize(new_len);
Surface::LOD lod;
lod.distance = error * mesh_scale;
abs_target_error = lod.distance;
if (Math::is_equal_approx(abs_target_error, 0.0f)) {
return;
}
lod.indices = new_indices;
print_line("Lod " + itos(surfaces.write[i].lods.size()) + " shoot for " + itos(index_target / 3) + " triangles, got " + itos(new_len / 3) + " triangles. Distance " + rtos(lod.distance));
print_line("Lod " + itos(surfaces.write[i].lods.size()) + " begin with " + itos(indices.size() / 3) + " triangles and shoot for " + itos(index_target / 3) + " triangles. Got " + itos(new_len / 3) + " triangles. Lod screen ratio " + rtos(lod.distance));
surfaces.write[i].lods.push_back(lod);
index_target /= 2;
index_target *= threshold;
}
}
}

1
editor/import/scene_importer_mesh.h
View File

@ -67,6 +67,7 @@ class EditorSceneImporterMesh : public Resource {
Ref<EditorSceneImporterMesh> shadow_mesh;
Size2i lightmap_size_hint;
Basis compute_rotation_matrix_from_ortho_6d(Vector3 p_x_raw, Vector3 y_raw);
protected:
void _set_data(const Dictionary &p_data);

1
modules/meshoptimizer/register_types.cpp
View File

@ -35,6 +35,7 @@
void register_meshoptimizer_types() {
SurfaceTool::optimize_vertex_cache_func = meshopt_optimizeVertexCache;
SurfaceTool::simplify_func = meshopt_simplify;
SurfaceTool::simplify_with_attrib_func = meshopt_simplifyWithAttributes;
SurfaceTool::simplify_scale_func = meshopt_simplifyScale;
SurfaceTool::simplify_sloppy_func = meshopt_simplifySloppy;
}

1
scene/resources/surface_tool.cpp
View File

@ -35,6 +35,7 @@
SurfaceTool::OptimizeVertexCacheFunc SurfaceTool::optimize_vertex_cache_func = nullptr;
SurfaceTool::SimplifyFunc SurfaceTool::simplify_func = nullptr;
SurfaceTool::SimplifyWithAttribFunc SurfaceTool::simplify_with_attrib_func = nullptr;
SurfaceTool::SimplifyScaleFunc SurfaceTool::simplify_scale_func = nullptr;
SurfaceTool::SimplifySloppyFunc SurfaceTool::simplify_sloppy_func = nullptr;

2
scene/resources/surface_tool.h
View File

@ -78,6 +78,8 @@ public:
static OptimizeVertexCacheFunc optimize_vertex_cache_func;
typedef size_t (*SimplifyFunc)(unsigned int *destination, const unsigned int *indices, size_t index_count, const float *vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float *r_error);
static SimplifyFunc simplify_func;
typedef size_t (*SimplifyWithAttribFunc)(unsigned int *destination, const unsigned int *indices, size_t index_count, const float *vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float *result_error, const float *attributes, const float *attribute_weights, size_t attribute_count);
static SimplifyWithAttribFunc simplify_with_attrib_func;
typedef float (*SimplifyScaleFunc)(const float *vertex_positions, size_t vertex_count, size_t vertex_positions_stride);
static SimplifyScaleFunc simplify_scale_func;
typedef size_t (*SimplifySloppyFunc)(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);

3
thirdparty/README.md vendored
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@ -375,6 +375,9 @@ Files extracted from upstream repository:
- All files in `src/`.
- `LICENSE.md`.
An [experimental upstream feature](https://github.com/zeux/meshoptimizer/tree/simplify-attr),
has been backported, see patch in `patches` directory.
## miniupnpc

5
thirdparty/meshoptimizer/meshoptimizer.h vendored
View File

@ -298,6 +298,11 @@ MESHOPTIMIZER_EXPERIMENTAL void meshopt_decodeFilterExp(void* buffer, size_t ver
*/
MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error);
/**
* Experimental: Mesh simplifier with attribute metric; attributes follow xyz position data atm (vertex data must contain 3 + attribute_count floats per vertex)
*/
MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float* result_error, const float* attributes, const float* attribute_weights, size_t attribute_count);
/**
* Experimental: Mesh simplifier (sloppy)
* Reduces the number of triangles in the mesh, sacrificing mesh apperance for simplification performance

262
thirdparty/meshoptimizer/patches/attribute-aware-simplify.patch vendored Normal file
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@ -0,0 +1,262 @@
diff --git a/thirdparty/meshoptimizer/meshoptimizer.h b/thirdparty/meshoptimizer/meshoptimizer.h
index fe8d349731..e44b99ce52 100644
--- a/thirdparty/meshoptimizer/meshoptimizer.h
+++ b/thirdparty/meshoptimizer/meshoptimizer.h
@@ -298,6 +298,11 @@ MESHOPTIMIZER_EXPERIMENTAL void meshopt_decodeFilterExp(void* buffer, size_t ver
*/
MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* result_error);
+/**
+ * Experimental: Mesh simplifier with attribute metric; attributes follow xyz position data atm (vertex data must contain 3 + attribute_count floats per vertex)
+ */
+MESHOPTIMIZER_EXPERIMENTAL size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float* result_error, const float* attributes, const float* attribute_weights, size_t attribute_count);
+
/**
* Experimental: Mesh simplifier (sloppy)
* Reduces the number of triangles in the mesh, sacrificing mesh apperance for simplification performance
diff --git a/thirdparty/meshoptimizer/simplifier.cpp b/thirdparty/meshoptimizer/simplifier.cpp
index b2cb589462..059cabb055 100644
--- a/thirdparty/meshoptimizer/simplifier.cpp
+++ b/thirdparty/meshoptimizer/simplifier.cpp
@@ -20,6 +20,8 @@
#define TRACESTATS(i) (void)0
#endif
+#define ATTRIBUTES 8
+
// This work is based on:
// Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. 1997
// Michael Garland. Quadric-based polygonal surface simplification. 1999
@@ -358,6 +360,10 @@ static void classifyVertices(unsigned char* result, unsigned int* loop, unsigned
struct Vector3
{
float x, y, z;
+
+#if ATTRIBUTES
+ float a[ATTRIBUTES];
+#endif
};
static float rescalePositions(Vector3* result, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride)
@@ -414,6 +420,13 @@ struct Quadric
float a10, a20, a21;
float b0, b1, b2, c;
float w;
+
+#if ATTRIBUTES
+ float gx[ATTRIBUTES];
+ float gy[ATTRIBUTES];
+ float gz[ATTRIBUTES];
+ float gw[ATTRIBUTES];
+#endif
};
struct Collapse
@@ -456,6 +469,16 @@ static void quadricAdd(Quadric& Q, const Quadric& R)
Q.b2 += R.b2;
Q.c += R.c;
Q.w += R.w;
+
+#if ATTRIBUTES
+ for (int k = 0; k < ATTRIBUTES; ++k)
+ {
+ Q.gx[k] += R.gx[k];
+ Q.gy[k] += R.gy[k];
+ Q.gz[k] += R.gz[k];
+ Q.gw[k] += R.gw[k];
+ }
+#endif
}
static float quadricError(const Quadric& Q, const Vector3& v)
@@ -481,6 +504,17 @@ static float quadricError(const Quadric& Q, const Vector3& v)
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;
@@ -504,6 +538,13 @@ static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d, flo
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)
@@ -556,6 +597,84 @@ static void quadricFromTriangleEdge(Quadric& Q, const Vector3& p0, const Vector3
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, 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)
@@ -567,6 +686,9 @@ static void fillFaceQuadrics(Quadric* vertex_quadrics, const unsigned int* indic
Quadric Q;
quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], 1.f);
+#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);
@@ -1259,13 +1381,19 @@ unsigned int* meshopt_simplifyDebugLoopBack = 0;
#endif
size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* out_result_error)
+{
+ return meshopt_simplifyWithAttributes(destination, indices, index_count, vertex_positions_data, vertex_count, vertex_positions_stride, target_index_count, target_error, out_result_error, 0, 0, 0);
+}
+
+size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float* out_result_error, const float* attributes, const float* attribute_weights, size_t attribute_count)
{
using namespace meshopt;
assert(index_count % 3 == 0);
- assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
- assert(vertex_positions_stride % sizeof(float) == 0);
+ assert(vertex_stride > 0 && vertex_stride <= 256);
+ assert(vertex_stride % sizeof(float) == 0);
assert(target_index_count <= index_count);
+ assert(attribute_count <= ATTRIBUTES);
meshopt_Allocator allocator;
@@ -1279,7 +1407,7 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
// build position remap that maps each vertex to the one with identical position
unsigned int* remap = allocator.allocate<unsigned int>(vertex_count);
unsigned int* wedge = allocator.allocate<unsigned int>(vertex_count);
- buildPositionRemap(remap, wedge, vertex_positions_data, vertex_count, vertex_positions_stride, allocator);
+ 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);
@@ -1303,7 +1431,21 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
#endif
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
- rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride);
+ 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));
@@ -1395,7 +1537,9 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
// 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;
}

152
thirdparty/meshoptimizer/simplifier.cpp vendored
View File

@ -20,6 +20,8 @@
#define TRACESTATS(i) (void)0
#endif
#define ATTRIBUTES 8
// This work is based on:
// Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. 1997
// Michael Garland. Quadric-based polygonal surface simplification. 1999
@ -358,6 +360,10 @@ static void classifyVertices(unsigned char* result, unsigned int* loop, unsigned
struct Vector3
{
float x, y, z;
#if ATTRIBUTES
float a[ATTRIBUTES];
#endif
};
static float rescalePositions(Vector3* result, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride)
@ -414,6 +420,13 @@ struct Quadric
float a10, a20, a21;
float b0, b1, b2, c;
float w;
#if ATTRIBUTES
float gx[ATTRIBUTES];
float gy[ATTRIBUTES];
float gz[ATTRIBUTES];
float gw[ATTRIBUTES];
#endif
};
struct Collapse
@ -456,6 +469,16 @@ static void quadricAdd(Quadric& Q, const Quadric& R)
Q.b2 += R.b2;
Q.c += R.c;
Q.w += R.w;
#if ATTRIBUTES
for (int k = 0; k < ATTRIBUTES; ++k)
{
Q.gx[k] += R.gx[k];
Q.gy[k] += R.gy[k];
Q.gz[k] += R.gz[k];
Q.gw[k] += R.gw[k];
}
#endif
}
static float quadricError(const Quadric& Q, const Vector3& v)
@ -481,6 +504,17 @@ static float quadricError(const Quadric& Q, const Vector3& v)
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;
@ -504,6 +538,13 @@ static void quadricFromPlane(Quadric& Q, float a, float b, float c, float d, flo
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)
@ -556,6 +597,84 @@ static void quadricFromTriangleEdge(Quadric& Q, const Vector3& p0, const Vector3
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, 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)
@ -567,6 +686,9 @@ static void fillFaceQuadrics(Quadric* vertex_quadrics, const unsigned int* indic
Quadric Q;
quadricFromTriangle(Q, vertex_positions[i0], vertex_positions[i1], vertex_positions[i2], 1.f);
#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);
@ -1259,13 +1381,19 @@ unsigned int* meshopt_simplifyDebugLoopBack = 0;
#endif
size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions_data, size_t vertex_count, size_t vertex_positions_stride, size_t target_index_count, float target_error, float* out_result_error)
{
return meshopt_simplifyWithAttributes(destination, indices, index_count, vertex_positions_data, vertex_count, vertex_positions_stride, target_index_count, target_error, out_result_error, 0, 0, 0);
}
size_t meshopt_simplifyWithAttributes(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_data, size_t vertex_count, size_t vertex_stride, size_t target_index_count, float target_error, float* out_result_error, const float* attributes, const float* attribute_weights, size_t attribute_count)
{
using namespace meshopt;
assert(index_count % 3 == 0);
assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
assert(vertex_positions_stride % sizeof(float) == 0);
assert(vertex_stride > 0 && vertex_stride <= 256);
assert(vertex_stride % sizeof(float) == 0);
assert(target_index_count <= index_count);
assert(attribute_count <= ATTRIBUTES);
meshopt_Allocator allocator;
@ -1279,7 +1407,7 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
// build position remap that maps each vertex to the one with identical position
unsigned int* remap = allocator.allocate<unsigned int>(vertex_count);
unsigned int* wedge = allocator.allocate<unsigned int>(vertex_count);
buildPositionRemap(remap, wedge, vertex_positions_data, vertex_count, vertex_positions_stride, allocator);
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);
@ -1303,7 +1431,21 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
#endif
Vector3* vertex_positions = allocator.allocate<Vector3>(vertex_count);
rescalePositions(vertex_positions, vertex_positions_data, vertex_count, vertex_positions_stride);
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));
@ -1395,7 +1537,9 @@ size_t meshopt_simplify(unsigned int* destination, const unsigned int* indices,
// 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;
}