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// SHAPES :: https://github.com/prideout/par
// Simple C library for creation and manipulation of triangle meshes.
//
// The API is divided into three sections:
//
// - Generators. Create parametric surfaces, platonic solids, etc.
// - Queries. Ask a mesh for its axis-aligned bounding box, etc.
// - Transforms. Rotate a mesh, merge it with another, add normals, etc.
//
// In addition to the comment block above each function declaration, the API
// has informal documentation here:
//
// http://github.prideout.net/shapes/
//
// For our purposes, a "mesh" is a list of points and a list of triangles; the
// former is a flattened list of three-tuples (32-bit floats) and the latter is
// also a flattened list of three-tuples (16-bit uints). Triangles are always
// oriented such that their front face winds counter-clockwise.
//
// Optionally, meshes can contain 3D normals (one per vertex), and 2D texture
// coordinates (one per vertex). That's it! If you need something fancier,
// look elsewhere.
//
// The MIT License
// Copyright (c) 2015 Philip Rideout
#ifndef PAR_SHAPES_H
#define PAR_SHAPES_H
#ifdef __cplusplus
extern "C" {
#endif
#include <stdint.h>
#if !defined(_MSC_VER)
# include <stdbool.h>
#else // MSVC
# if _MSC_VER >= 1800
# include <stdbool.h>
# else // stdbool.h missing prior to MSVC++ 12.0 (VS2013)
# define bool int
# define true 1
# define false 0
# endif
#endif
#ifndef PAR_SHAPES_T
#define PAR_SHAPES_T uint16_t
#endif
typedef struct par_shapes_mesh_s {
float* points; // Flat list of 3-tuples (X Y Z X Y Z...)
int npoints; // Number of points
PAR_SHAPES_T* triangles; // Flat list of 3-tuples (I J K I J K...)
int ntriangles; // Number of triangles
float* normals; // Optional list of 3-tuples (X Y Z X Y Z...)
float* tcoords; // Optional list of 2-tuples (U V U V U V...)
} par_shapes_mesh;
void par_shapes_free_mesh(par_shapes_mesh*);
// Generators ------------------------------------------------------------------
// Instance a cylinder that sits on the Z=0 plane using the given tessellation
// levels across the UV domain. Think of "slices" like a number of pizza
// slices, and "stacks" like a number of stacked rings. Height and radius are
// both 1.0, but they can easily be changed with par_shapes_scale.
par_shapes_mesh* par_shapes_create_cylinder(int slices, int stacks);
// Create a donut that sits on the Z=0 plane with the specified inner radius.
// The outer radius can be controlled with par_shapes_scale.
par_shapes_mesh* par_shapes_create_torus(int slices, int stacks, float radius);
// Create a sphere with texture coordinates and small triangles near the poles.
par_shapes_mesh* par_shapes_create_parametric_sphere(int slices, int stacks);
// Approximate a sphere with a subdivided icosahedron, which produces a nice
// distribution of triangles, but no texture coordinates. Each subdivision
// level scales the number of triangles by four, so use a very low number.
par_shapes_mesh* par_shapes_create_subdivided_sphere(int nsubdivisions);
// More parametric surfaces.
par_shapes_mesh* par_shapes_create_klein_bottle(int slices, int stacks);
par_shapes_mesh* par_shapes_create_trefoil_knot(int slices, int stacks,
float radius);
par_shapes_mesh* par_shapes_create_hemisphere(int slices, int stacks);
par_shapes_mesh* par_shapes_create_plane(int slices, int stacks);
// Create a parametric surface from a callback function that consumes a 2D
// point in [0,1] and produces a 3D point.
typedef void (*par_shapes_fn)(float const*, float*, void*);
par_shapes_mesh* par_shapes_create_parametric(par_shapes_fn, int slices,
int stacks, void* userdata);
// Generate points for a 20-sided polyhedron that fits in the unit sphere.
// Texture coordinates and normals are not generated.
par_shapes_mesh* par_shapes_create_icosahedron();
// Generate points for a 12-sided polyhedron that fits in the unit sphere.
// Again, texture coordinates and normals are not generated.
par_shapes_mesh* par_shapes_create_dodecahedron();
// More platonic solids.
par_shapes_mesh* par_shapes_create_octahedron();
par_shapes_mesh* par_shapes_create_tetrahedron();
par_shapes_mesh* par_shapes_create_cube();
// Generate an orientable disk shape in 3-space. Does not include normals or
// texture coordinates.
par_shapes_mesh* par_shapes_create_disk(float radius, int slices,
float const* center, float const* normal);
// Create an empty shape. Useful for building scenes with merge_and_free.
par_shapes_mesh* par_shapes_create_empty();
// Generate a rock shape that sits on the Y=0 plane, and sinks into it a bit.
// This includes smooth normals but no texture coordinates. Each subdivision
// level scales the number of triangles by four, so use a very low number.
par_shapes_mesh* par_shapes_create_rock(int seed, int nsubdivisions);
// Create trees or vegetation by executing a recursive turtle graphics program.
// The program is a list of command-argument pairs. See the unit test for
// an example. Texture coordinates and normals are not generated.
par_shapes_mesh* par_shapes_create_lsystem(char const* program, int slices,
int maxdepth);
// Queries ---------------------------------------------------------------------
// Dump out a text file conforming to the venerable OBJ format.
void par_shapes_export(par_shapes_mesh const*, char const* objfile);
// Take a pointer to 6 floats and set them to min xyz, max xyz.
void par_shapes_compute_aabb(par_shapes_mesh const* mesh, float* aabb);
// Make a deep copy of a mesh. To make a brand new copy, pass null to "target".
// To avoid memory churn, pass an existing mesh to "target".
par_shapes_mesh* par_shapes_clone(par_shapes_mesh const* mesh,
par_shapes_mesh* target);
// Transformations -------------------------------------------------------------
void par_shapes_merge(par_shapes_mesh* dst, par_shapes_mesh const* src);
void par_shapes_translate(par_shapes_mesh*, float x, float y, float z);
void par_shapes_rotate(par_shapes_mesh*, float radians, float const* axis);
void par_shapes_scale(par_shapes_mesh*, float x, float y, float z);
void par_shapes_merge_and_free(par_shapes_mesh* dst, par_shapes_mesh* src);
// Reverse the winding of a run of faces. Useful when drawing the inside of
// a Cornell Box. Pass 0 for nfaces to reverse every face in the mesh.
void par_shapes_invert(par_shapes_mesh*, int startface, int nfaces);
// Remove all triangles whose area is less than minarea.
void par_shapes_remove_degenerate(par_shapes_mesh*, float minarea);
// Dereference the entire index buffer and replace the point list.
// This creates an inefficient structure, but is useful for drawing facets.
// If create_indices is true, a trivial "0 1 2 3..." index buffer is generated.
void par_shapes_unweld(par_shapes_mesh* mesh, bool create_indices);
// Merge colocated verts, build a new index buffer, and return the
// optimized mesh. Epsilon is the maximum distance to consider when
// welding vertices. The mapping argument can be null, or a pointer to
// npoints integers, which gets filled with the mapping from old vertex
// indices to new indices.
par_shapes_mesh* par_shapes_weld(par_shapes_mesh const*, float epsilon,
PAR_SHAPES_T* mapping);
// Compute smooth normals by averaging adjacent facet normals.
void par_shapes_compute_normals(par_shapes_mesh* m);
#ifndef PAR_PI
#define PAR_PI (3.14159265359)
#define PAR_MIN(a, b) (a > b ? b : a)
#define PAR_MAX(a, b) (a > b ? a : b)
#define PAR_CLAMP(v, lo, hi) PAR_MAX(lo, PAR_MIN(hi, v))
#define PAR_SWAP(T, A, B) { T tmp = B; B = A; A = tmp; }
#define PAR_SQR(a) ((a) * (a))
#endif
#ifndef PAR_MALLOC
#define PAR_MALLOC(T, N) ((T*) malloc(N * sizeof(T)))
#define PAR_CALLOC(T, N) ((T*) calloc(N * sizeof(T), 1))
#define PAR_REALLOC(T, BUF, N) ((T*) realloc(BUF, sizeof(T) * (N)))
#define PAR_FREE(BUF) free(BUF)
#endif
#ifdef __cplusplus
}
#endif
// -----------------------------------------------------------------------------
// END PUBLIC API
// -----------------------------------------------------------------------------
#ifdef PAR_SHAPES_IMPLEMENTATION
#include <stdlib.h>
#include <stdio.h>
#include <assert.h>
#include <float.h>
#include <string.h>
#include <math.h>
#include <errno.h>
static void par_shapes__sphere(float const* uv, float* xyz, void*);
static void par_shapes__hemisphere(float const* uv, float* xyz, void*);
static void par_shapes__plane(float const* uv, float* xyz, void*);
static void par_shapes__klein(float const* uv, float* xyz, void*);
static void par_shapes__cylinder(float const* uv, float* xyz, void*);
static void par_shapes__torus(float const* uv, float* xyz, void*);
static void par_shapes__trefoil(float const* uv, float* xyz, void*);
struct osn_context;
static int par__simplex_noise(int64_t seed, struct osn_context** ctx);
static void par__simplex_noise_free(struct osn_context* ctx);
static double par__simplex_noise2(struct osn_context* ctx, double x, double y);
static void par_shapes__copy3(float* result, float const* a)
{
result[0] = a[0];
result[1] = a[1];
result[2] = a[2];
}
static float par_shapes__dot3(float const* a, float const* b)
{
return b[0] * a[0] + b[1] * a[1] + b[2] * a[2];
}
static void par_shapes__transform3(float* p, float const* x, float const* y,
float const* z)
{
float px = par_shapes__dot3(p, x);
float py = par_shapes__dot3(p, y);
float pz = par_shapes__dot3(p, z);
p[0] = px;
p[1] = py;
p[2] = pz;
}
static void par_shapes__cross3(float* result, float const* a, float const* b)
{
float x = (a[1] * b[2]) - (a[2] * b[1]);
float y = (a[2] * b[0]) - (a[0] * b[2]);
float z = (a[0] * b[1]) - (a[1] * b[0]);
result[0] = x;
result[1] = y;
result[2] = z;
}
static void par_shapes__mix3(float* d, float const* a, float const* b, float t)
{
float x = b[0] * t + a[0] * (1 - t);
float y = b[1] * t + a[1] * (1 - t);
float z = b[2] * t + a[2] * (1 - t);
d[0] = x;
d[1] = y;
d[2] = z;
}
static void par_shapes__scale3(float* result, float a)
{
result[0] *= a;
result[1] *= a;
result[2] *= a;
}
static void par_shapes__normalize3(float* v)
{
float lsqr = sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
if (lsqr > 0) {
par_shapes__scale3(v, 1.0f / lsqr);
}
}
static void par_shapes__subtract3(float* result, float const* a)
{
result[0] -= a[0];
result[1] -= a[1];
result[2] -= a[2];
}
static void par_shapes__add3(float* result, float const* a)
{
result[0] += a[0];
result[1] += a[1];
result[2] += a[2];
}
static float par_shapes__sqrdist3(float const* a, float const* b)
{
float dx = a[0] - b[0];
float dy = a[1] - b[1];
float dz = a[2] - b[2];
return dx * dx + dy * dy + dz * dz;
}
static void par_shapes__compute_welded_normals(par_shapes_mesh* m)
{
m->normals = PAR_MALLOC(float, m->npoints * 3);
PAR_SHAPES_T* weldmap = PAR_MALLOC(PAR_SHAPES_T, m->npoints);
par_shapes_mesh* welded = par_shapes_weld(m, 0.01, weldmap);
par_shapes_compute_normals(welded);
float* pdst = m->normals;
for (int i = 0; i < m->npoints; i++, pdst += 3) {
int d = weldmap[i];
float const* pnormal = welded->normals + d * 3;
pdst[0] = pnormal[0];
pdst[1] = pnormal[1];
pdst[2] = pnormal[2];
}
PAR_FREE(weldmap);
par_shapes_free_mesh(welded);
}
par_shapes_mesh* par_shapes_create_cylinder(int slices, int stacks)
{
if (slices < 3 || stacks < 1) {
return 0;
}
return par_shapes_create_parametric(par_shapes__cylinder, slices,
stacks, 0);
}
par_shapes_mesh* par_shapes_create_parametric_sphere(int slices, int stacks)
{
if (slices < 3 || stacks < 3) {
return 0;
}
par_shapes_mesh* m = par_shapes_create_parametric(par_shapes__sphere,
slices, stacks, 0);
par_shapes_remove_degenerate(m, 0.0001);
return m;
}
par_shapes_mesh* par_shapes_create_hemisphere(int slices, int stacks)
{
if (slices < 3 || stacks < 3) {
return 0;
}
par_shapes_mesh* m = par_shapes_create_parametric(par_shapes__hemisphere,
slices, stacks, 0);
par_shapes_remove_degenerate(m, 0.0001);
return m;
}
par_shapes_mesh* par_shapes_create_torus(int slices, int stacks, float radius)
{
if (slices < 3 || stacks < 3) {
return 0;
}
assert(radius <= 1.0 && "Use smaller radius to avoid self-intersection.");
assert(radius >= 0.1 && "Use larger radius to avoid self-intersection.");
void* userdata = (void*) &radius;
return par_shapes_create_parametric(par_shapes__torus, slices,
stacks, userdata);
}
par_shapes_mesh* par_shapes_create_klein_bottle(int slices, int stacks)
{
if (slices < 3 || stacks < 3) {
return 0;
}
par_shapes_mesh* mesh = par_shapes_create_parametric(
par_shapes__klein, slices, stacks, 0);
int face = 0;
for (int stack = 0; stack < stacks; stack++) {
for (int slice = 0; slice < slices; slice++, face += 2) {
if (stack < 27 * stacks / 32) {
par_shapes_invert(mesh, face, 2);
}
}
}
par_shapes__compute_welded_normals(mesh);
return mesh;
}
par_shapes_mesh* par_shapes_create_trefoil_knot(int slices, int stacks,
float radius)
{
if (slices < 3 || stacks < 3) {
return 0;
}
assert(radius <= 3.0 && "Use smaller radius to avoid self-intersection.");
assert(radius >= 0.5 && "Use larger radius to avoid self-intersection.");
void* userdata = (void*) &radius;
return par_shapes_create_parametric(par_shapes__trefoil, slices,
stacks, userdata);
}
par_shapes_mesh* par_shapes_create_plane(int slices, int stacks)
{
if (slices < 1 || stacks < 1) {
return 0;
}
return par_shapes_create_parametric(par_shapes__plane, slices,
stacks, 0);
}
par_shapes_mesh* par_shapes_create_parametric(par_shapes_fn fn,
int slices, int stacks, void* userdata)
{
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
// Generate verts.
mesh->npoints = (slices + 1) * (stacks + 1);
mesh->points = PAR_CALLOC(float, 3 * mesh->npoints);
float uv[2];
float xyz[3];
float* points = mesh->points;
for (int stack = 0; stack < stacks + 1; stack++) {
uv[0] = (float) stack / stacks;
for (int slice = 0; slice < slices + 1; slice++) {
uv[1] = (float) slice / slices;
fn(uv, xyz, userdata);
*points++ = xyz[0];
*points++ = xyz[1];
*points++ = xyz[2];
}
}
// Generate texture coordinates.
mesh->tcoords = PAR_CALLOC(float, 2 * mesh->npoints);
float* uvs = mesh->tcoords;
for (int stack = 0; stack < stacks + 1; stack++) {
uv[0] = (float) stack / stacks;
for (int slice = 0; slice < slices + 1; slice++) {
uv[1] = (float) slice / slices;
*uvs++ = uv[0];
*uvs++ = uv[1];
}
}
// Generate faces.
mesh->ntriangles = 2 * slices * stacks;
mesh->triangles = PAR_CALLOC(PAR_SHAPES_T, 3 * mesh->ntriangles);
int v = 0;
PAR_SHAPES_T* face = mesh->triangles;
for (int stack = 0; stack < stacks; stack++) {
for (int slice = 0; slice < slices; slice++) {
int next = slice + 1;
*face++ = v + slice + slices + 1;
*face++ = v + next;
*face++ = v + slice;
*face++ = v + slice + slices + 1;
*face++ = v + next + slices + 1;
*face++ = v + next;
}
v += slices + 1;
}
par_shapes__compute_welded_normals(mesh);
return mesh;
}
void par_shapes_free_mesh(par_shapes_mesh* mesh)
{
PAR_FREE(mesh->points);
PAR_FREE(mesh->triangles);
PAR_FREE(mesh->normals);
PAR_FREE(mesh->tcoords);
PAR_FREE(mesh);
}
void par_shapes_export(par_shapes_mesh const* mesh, char const* filename)
{
FILE* objfile = fopen(filename, "wt");
float const* points = mesh->points;
float const* tcoords = mesh->tcoords;
float const* norms = mesh->normals;
PAR_SHAPES_T const* indices = mesh->triangles;
if (tcoords && norms) {
for (int nvert = 0; nvert < mesh->npoints; nvert++) {
fprintf(objfile, "v %f %f %f\n", points[0], points[1], points[2]);
fprintf(objfile, "vt %f %f\n", tcoords[0], tcoords[1]);
fprintf(objfile, "vn %f %f %f\n", norms[0], norms[1], norms[2]);
points += 3;
norms += 3;
tcoords += 2;
}
for (int nface = 0; nface < mesh->ntriangles; nface++) {
int a = 1 + *indices++;
int b = 1 + *indices++;
int c = 1 + *indices++;
fprintf(objfile, "f %d/%d/%d %d/%d/%d %d/%d/%d\n",
a, a, a, b, b, b, c, c, c);
}
} else if (norms) {
for (int nvert = 0; nvert < mesh->npoints; nvert++) {
fprintf(objfile, "v %f %f %f\n", points[0], points[1], points[2]);
fprintf(objfile, "vn %f %f %f\n", norms[0], norms[1], norms[2]);
points += 3;
norms += 3;
}
for (int nface = 0; nface < mesh->ntriangles; nface++) {
int a = 1 + *indices++;
int b = 1 + *indices++;
int c = 1 + *indices++;
fprintf(objfile, "f %d//%d %d//%d %d//%d\n", a, a, b, b, c, c);
}
} else if (tcoords) {
for (int nvert = 0; nvert < mesh->npoints; nvert++) {
fprintf(objfile, "v %f %f %f\n", points[0], points[1], points[2]);
fprintf(objfile, "vt %f %f\n", tcoords[0], tcoords[1]);
points += 3;
tcoords += 2;
}
for (int nface = 0; nface < mesh->ntriangles; nface++) {
int a = 1 + *indices++;
int b = 1 + *indices++;
int c = 1 + *indices++;
fprintf(objfile, "f %d/%d %d/%d %d/%d\n", a, a, b, b, c, c);
}
} else {
for (int nvert = 0; nvert < mesh->npoints; nvert++) {
fprintf(objfile, "v %f %f %f\n", points[0], points[1], points[2]);
points += 3;
}
for (int nface = 0; nface < mesh->ntriangles; nface++) {
int a = 1 + *indices++;
int b = 1 + *indices++;
int c = 1 + *indices++;
fprintf(objfile, "f %d %d %d\n", a, b, c);
}
}
fclose(objfile);
}
static void par_shapes__sphere(float const* uv, float* xyz, void* userdata)
{
float phi = uv[0] * PAR_PI;
float theta = uv[1] * 2 * PAR_PI;
xyz[0] = cosf(theta) * sinf(phi);
xyz[1] = sinf(theta) * sinf(phi);
xyz[2] = cosf(phi);
}
static void par_shapes__hemisphere(float const* uv, float* xyz, void* userdata)
{
float phi = uv[0] * PAR_PI;
float theta = uv[1] * PAR_PI;
xyz[0] = cosf(theta) * sinf(phi);
xyz[1] = sinf(theta) * sinf(phi);
xyz[2] = cosf(phi);
}
static void par_shapes__plane(float const* uv, float* xyz, void* userdata)
{
xyz[0] = uv[0];
xyz[1] = uv[1];
xyz[2] = 0;
}
static void par_shapes__klein(float const* uv, float* xyz, void* userdata)
{
float u = uv[0] * PAR_PI;
float v = uv[1] * 2 * PAR_PI;
u = u * 2;
if (u < PAR_PI) {
xyz[0] = 3 * cosf(u) * (1 + sinf(u)) + (2 * (1 - cosf(u) / 2)) *
cosf(u) * cosf(v);
xyz[2] = -8 * sinf(u) - 2 * (1 - cosf(u) / 2) * sinf(u) * cosf(v);
} else {
xyz[0] = 3 * cosf(u) * (1 + sinf(u)) + (2 * (1 - cosf(u) / 2)) *
cosf(v + PAR_PI);
xyz[2] = -8 * sinf(u);
}
xyz[1] = -2 * (1 - cosf(u) / 2) * sinf(v);
}
static void par_shapes__cylinder(float const* uv, float* xyz, void* userdata)
{
float theta = uv[1] * 2 * PAR_PI;
xyz[0] = sinf(theta);
xyz[1] = cosf(theta);
xyz[2] = uv[0];
}
static void par_shapes__torus(float const* uv, float* xyz, void* userdata)
{
float major = 1;
float minor = *((float*) userdata);
float theta = uv[0] * 2 * PAR_PI;
float phi = uv[1] * 2 * PAR_PI;
float beta = major + minor * cosf(phi);
xyz[0] = cosf(theta) * beta;
xyz[1] = sinf(theta) * beta;
xyz[2] = sinf(phi) * minor;
}
static void par_shapes__trefoil(float const* uv, float* xyz, void* userdata)
{
float minor = *((float*) userdata);
const float a = 0.5f;
const float b = 0.3f;
const float c = 0.5f;
const float d = minor * 0.1f;
const float u = (1 - uv[0]) * 4 * PAR_PI;
const float v = uv[1] * 2 * PAR_PI;
const float r = a + b * cos(1.5f * u);
const float x = r * cos(u);
const float y = r * sin(u);
const float z = c * sin(1.5f * u);
float q[3];
q[0] =
-1.5f * b * sin(1.5f * u) * cos(u) - (a + b * cos(1.5f * u)) * sin(u);
q[1] =
-1.5f * b * sin(1.5f * u) * sin(u) + (a + b * cos(1.5f * u)) * cos(u);
q[2] = 1.5f * c * cos(1.5f * u);
par_shapes__normalize3(q);
float qvn[3] = {q[1], -q[0], 0};
par_shapes__normalize3(qvn);
float ww[3];
par_shapes__cross3(ww, q, qvn);
xyz[0] = x + d * (qvn[0] * cos(v) + ww[0] * sin(v));
xyz[1] = y + d * (qvn[1] * cos(v) + ww[1] * sin(v));
xyz[2] = z + d * ww[2] * sin(v);
}
void par_shapes_merge(par_shapes_mesh* dst, par_shapes_mesh const* src)
{
PAR_SHAPES_T offset = dst->npoints;
int npoints = dst->npoints + src->npoints;
int vecsize = sizeof(float) * 3;
dst->points = PAR_REALLOC(float, dst->points, 3 * npoints);
memcpy(dst->points + 3 * dst->npoints, src->points, vecsize * src->npoints);
dst->npoints = npoints;
if (src->normals || dst->normals) {
dst->normals = PAR_REALLOC(float, dst->normals, 3 * npoints);
if (src->normals) {
memcpy(dst->normals + 3 * offset, src->normals,
vecsize * src->npoints);
}
}
if (src->tcoords || dst->tcoords) {
int uvsize = sizeof(float) * 2;
dst->tcoords = PAR_REALLOC(float, dst->tcoords, 2 * npoints);
if (src->tcoords) {
memcpy(dst->tcoords + 2 * offset, src->tcoords,
uvsize * src->npoints);
}
}
int ntriangles = dst->ntriangles + src->ntriangles;
dst->triangles = PAR_REALLOC(PAR_SHAPES_T, dst->triangles, 3 * ntriangles);
PAR_SHAPES_T* ptriangles = dst->triangles + 3 * dst->ntriangles;
PAR_SHAPES_T const* striangles = src->triangles;
for (int i = 0; i < src->ntriangles; i++) {
*ptriangles++ = offset + *striangles++;
*ptriangles++ = offset + *striangles++;
*ptriangles++ = offset + *striangles++;
}
dst->ntriangles = ntriangles;
}
par_shapes_mesh* par_shapes_create_disk(float radius, int slices,
float const* center, float const* normal)
{
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
mesh->npoints = slices + 1;
mesh->points = PAR_MALLOC(float, 3 * mesh->npoints);
float* points = mesh->points;
*points++ = 0;
*points++ = 0;
*points++ = 0;
for (int i = 0; i < slices; i++) {
float theta = i * PAR_PI * 2 / slices;
*points++ = radius * cos(theta);
*points++ = radius * sin(theta);
*points++ = 0;
}
float nnormal[3] = {normal[0], normal[1], normal[2]};
par_shapes__normalize3(nnormal);
mesh->normals = PAR_MALLOC(float, 3 * mesh->npoints);
float* norms = mesh->normals;
for (int i = 0; i < mesh->npoints; i++) {
*norms++ = nnormal[0];
*norms++ = nnormal[1];
*norms++ = nnormal[2];
}
mesh->ntriangles = slices;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, 3 * mesh->ntriangles);
PAR_SHAPES_T* triangles = mesh->triangles;
for (int i = 0; i < slices; i++) {
*triangles++ = 0;
*triangles++ = 1 + i;
*triangles++ = 1 + (i + 1) % slices;
}
float k[3] = {0, 0, -1};
float axis[3];
par_shapes__cross3(axis, nnormal, k);
par_shapes__normalize3(axis);
par_shapes_rotate(mesh, acos(nnormal[2]), axis);
par_shapes_translate(mesh, center[0], center[1], center[2]);
return mesh;
}
par_shapes_mesh* par_shapes_create_empty()
{
return PAR_CALLOC(par_shapes_mesh, 1);
}
void par_shapes_translate(par_shapes_mesh* m, float x, float y, float z)
{
float* points = m->points;
for (int i = 0; i < m->npoints; i++) {
*points++ += x;
*points++ += y;
*points++ += z;
}
}
void par_shapes_rotate(par_shapes_mesh* mesh, float radians, float const* axis)
{
float s = sinf(radians);
float c = cosf(radians);
float x = axis[0];
float y = axis[1];
float z = axis[2];
float xy = x * y;
float yz = y * z;
float zx = z * x;
float oneMinusC = 1.0f - c;
float col0[3] = {
(((x * x) * oneMinusC) + c),
((xy * oneMinusC) + (z * s)), ((zx * oneMinusC) - (y * s))
};
float col1[3] = {
((xy * oneMinusC) - (z * s)),
(((y * y) * oneMinusC) + c), ((yz * oneMinusC) + (x * s))
};
float col2[3] = {
((zx * oneMinusC) + (y * s)),
((yz * oneMinusC) - (x * s)), (((z * z) * oneMinusC) + c)
};
float* p = mesh->points;
for (int i = 0; i < mesh->npoints; i++, p += 3) {
float x = col0[0] * p[0] + col1[0] * p[1] + col2[0] * p[2];
float y = col0[1] * p[0] + col1[1] * p[1] + col2[1] * p[2];
float z = col0[2] * p[0] + col1[2] * p[1] + col2[2] * p[2];
p[0] = x;
p[1] = y;
p[2] = z;
}
p = mesh->normals;
if (p) {
for (int i = 0; i < mesh->npoints; i++, p += 3) {
float x = col0[0] * p[0] + col1[0] * p[1] + col2[0] * p[2];
float y = col0[1] * p[0] + col1[1] * p[1] + col2[1] * p[2];
float z = col0[2] * p[0] + col1[2] * p[1] + col2[2] * p[2];
p[0] = x;
p[1] = y;
p[2] = z;
}
}
}
void par_shapes_scale(par_shapes_mesh* m, float x, float y, float z)
{
float* points = m->points;
for (int i = 0; i < m->npoints; i++) {
*points++ *= x;
*points++ *= y;
*points++ *= z;
}
}
void par_shapes_merge_and_free(par_shapes_mesh* dst, par_shapes_mesh* src)
{
par_shapes_merge(dst, src);
par_shapes_free_mesh(src);
}
void par_shapes_compute_aabb(par_shapes_mesh const* m, float* aabb)
{
float* points = m->points;
aabb[0] = aabb[3] = points[0];
aabb[1] = aabb[4] = points[1];
aabb[2] = aabb[5] = points[2];
points += 3;
for (int i = 1; i < m->npoints; i++, points += 3) {
aabb[0] = PAR_MIN(points[0], aabb[0]);
aabb[1] = PAR_MIN(points[1], aabb[1]);
aabb[2] = PAR_MIN(points[2], aabb[2]);
aabb[3] = PAR_MAX(points[0], aabb[3]);
aabb[4] = PAR_MAX(points[1], aabb[4]);
aabb[5] = PAR_MAX(points[2], aabb[5]);
}
}
void par_shapes_invert(par_shapes_mesh* m, int face, int nfaces)
{
nfaces = nfaces ? nfaces : m->ntriangles;
PAR_SHAPES_T* tri = m->triangles + face * 3;
for (int i = 0; i < nfaces; i++) {
PAR_SWAP(PAR_SHAPES_T, tri[0], tri[2]);
tri += 3;
}
}
par_shapes_mesh* par_shapes_create_icosahedron()
{
static float verts[] = {
0.000, 0.000, 1.000,
0.894, 0.000, 0.447,
0.276, 0.851, 0.447,
-0.724, 0.526, 0.447,
-0.724, -0.526, 0.447,
0.276, -0.851, 0.447,
0.724, 0.526, -0.447,
-0.276, 0.851, -0.447,
-0.894, 0.000, -0.447,
-0.276, -0.851, -0.447,
0.724, -0.526, -0.447,
0.000, 0.000, -1.000
};
static PAR_SHAPES_T faces[] = {
0,1,2,
0,2,3,
0,3,4,
0,4,5,
0,5,1,
7,6,11,
8,7,11,
9,8,11,
10,9,11,
6,10,11,
6,2,1,
7,3,2,
8,4,3,
9,5,4,
10,1,5,
6,7,2,
7,8,3,
8,9,4,
9,10,5,
10,6,1
};
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
mesh->npoints = sizeof(verts) / sizeof(verts[0]) / 3;
mesh->points = PAR_MALLOC(float, sizeof(verts) / 4);
memcpy(mesh->points, verts, sizeof(verts));
mesh->ntriangles = sizeof(faces) / sizeof(faces[0]) / 3;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, sizeof(faces) / 2);
memcpy(mesh->triangles, faces, sizeof(faces));
return mesh;
}
par_shapes_mesh* par_shapes_create_dodecahedron()
{
static float verts[20 * 3] = {
0.607, 0.000, 0.795,
0.188, 0.577, 0.795,
-0.491, 0.357, 0.795,
-0.491, -0.357, 0.795,
0.188, -0.577, 0.795,
0.982, 0.000, 0.188,
0.304, 0.934, 0.188,
-0.795, 0.577, 0.188,
-0.795, -0.577, 0.188,
0.304, -0.934, 0.188,
0.795, 0.577, -0.188,
-0.304, 0.934, -0.188,
-0.982, 0.000, -0.188,
-0.304, -0.934, -0.188,
0.795, -0.577, -0.188,
0.491, 0.357, -0.795,
-0.188, 0.577, -0.795,
-0.607, 0.000, -0.795,
-0.188, -0.577, -0.795,
0.491, -0.357, -0.795,
};
static PAR_SHAPES_T pentagons[12 * 5] = {
0,1,2,3,4,
5,10,6,1,0,
6,11,7,2,1,
7,12,8,3,2,
8,13,9,4,3,
9,14,5,0,4,
15,16,11,6,10,
16,17,12,7,11,
17,18,13,8,12,
18,19,14,9,13,
19,15,10,5,14,
19,18,17,16,15
};
int npentagons = sizeof(pentagons) / sizeof(pentagons[0]) / 5;
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
int ncorners = sizeof(verts) / sizeof(verts[0]) / 3;
mesh->npoints = ncorners;
mesh->points = PAR_MALLOC(float, mesh->npoints * 3);
memcpy(mesh->points, verts, sizeof(verts));
PAR_SHAPES_T const* pentagon = pentagons;
mesh->ntriangles = npentagons * 3;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* tris = mesh->triangles;
for (int p = 0; p < npentagons; p++, pentagon += 5) {
*tris++ = pentagon[0];
*tris++ = pentagon[1];
*tris++ = pentagon[2];
*tris++ = pentagon[0];
*tris++ = pentagon[2];
*tris++ = pentagon[3];
*tris++ = pentagon[0];
*tris++ = pentagon[3];
*tris++ = pentagon[4];
}
return mesh;
}
par_shapes_mesh* par_shapes_create_octahedron()
{
static float verts[6 * 3] = {
0.000, 0.000, 1.000,
1.000, 0.000, 0.000,
0.000, 1.000, 0.000,
-1.000, 0.000, 0.000,
0.000, -1.000, 0.000,
0.000, 0.000, -1.000
};
static PAR_SHAPES_T triangles[8 * 3] = {
0,1,2,
0,2,3,
0,3,4,
0,4,1,
2,1,5,
3,2,5,
4,3,5,
1,4,5,
};
int ntris = sizeof(triangles) / sizeof(triangles[0]) / 3;
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
int ncorners = sizeof(verts) / sizeof(verts[0]) / 3;
mesh->npoints = ncorners;
mesh->points = PAR_MALLOC(float, mesh->npoints * 3);
memcpy(mesh->points, verts, sizeof(verts));
PAR_SHAPES_T const* triangle = triangles;
mesh->ntriangles = ntris;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* tris = mesh->triangles;
for (int p = 0; p < ntris; p++) {
*tris++ = *triangle++;
*tris++ = *triangle++;
*tris++ = *triangle++;
}
return mesh;
}
par_shapes_mesh* par_shapes_create_tetrahedron()
{
static float verts[4 * 3] = {
0.000, 1.333, 0,
0.943, 0, 0,
-0.471, 0, 0.816,
-0.471, 0, -0.816,
};
static PAR_SHAPES_T triangles[4 * 3] = {
2,1,0,
3,2,0,
1,3,0,
1,2,3,
};
int ntris = sizeof(triangles) / sizeof(triangles[0]) / 3;
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
int ncorners = sizeof(verts) / sizeof(verts[0]) / 3;
mesh->npoints = ncorners;
mesh->points = PAR_MALLOC(float, mesh->npoints * 3);
memcpy(mesh->points, verts, sizeof(verts));
PAR_SHAPES_T const* triangle = triangles;
mesh->ntriangles = ntris;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* tris = mesh->triangles;
for (int p = 0; p < ntris; p++) {
*tris++ = *triangle++;
*tris++ = *triangle++;
*tris++ = *triangle++;
}
return mesh;
}
par_shapes_mesh* par_shapes_create_cube()
{
static float verts[8 * 3] = {
0, 0, 0, // 0
0, 1, 0, // 1
1, 1, 0, // 2
1, 0, 0, // 3
0, 0, 1, // 4
0, 1, 1, // 5
1, 1, 1, // 6
1, 0, 1, // 7
};
static PAR_SHAPES_T quads[6 * 4] = {
7,6,5,4, // front
0,1,2,3, // back
6,7,3,2, // right
5,6,2,1, // top
4,5,1,0, // left
7,4,0,3, // bottom
};
int nquads = sizeof(quads) / sizeof(quads[0]) / 4;
par_shapes_mesh* mesh = PAR_CALLOC(par_shapes_mesh, 1);
int ncorners = sizeof(verts) / sizeof(verts[0]) / 3;
mesh->npoints = ncorners;
mesh->points = PAR_MALLOC(float, mesh->npoints * 3);
memcpy(mesh->points, verts, sizeof(verts));
PAR_SHAPES_T const* quad = quads;
mesh->ntriangles = nquads * 2;
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* tris = mesh->triangles;
for (int p = 0; p < nquads; p++, quad += 4) {
*tris++ = quad[0];
*tris++ = quad[1];
*tris++ = quad[2];
*tris++ = quad[2];
*tris++ = quad[3];
*tris++ = quad[0];
}
return mesh;
}
typedef struct {
char* cmd;
char* arg;
} par_shapes__command;
typedef struct {
char const* name;
int weight;
int ncommands;
par_shapes__command* commands;
} par_shapes__rule;
typedef struct {
int pc;
float position[3];
float scale[3];
par_shapes_mesh* orientation;
par_shapes__rule* rule;
} par_shapes__stackframe;
static par_shapes__rule* par_shapes__pick_rule(const char* name,
par_shapes__rule* rules, int nrules)
{
par_shapes__rule* rule = 0;
int total = 0;
for (int i = 0; i < nrules; i++) {
rule = rules + i;
if (!strcmp(rule->name, name)) {
total += rule->weight;
}
}
float r = (float) rand() / RAND_MAX;
float t = 0;
for (int i = 0; i < nrules; i++) {
rule = rules + i;
if (!strcmp(rule->name, name)) {
t += (float) rule->weight / total;
if (t >= r) {
return rule;
}
}
}
return rule;
}
static par_shapes_mesh* par_shapes__create_turtle()
{
const float xaxis[] = {1, 0, 0};
const float yaxis[] = {0, 1, 0};
const float zaxis[] = {0, 0, 1};
par_shapes_mesh* turtle = PAR_CALLOC(par_shapes_mesh, 1);
turtle->npoints = 3;
turtle->points = PAR_CALLOC(float, turtle->npoints * 3);
par_shapes__copy3(turtle->points + 0, xaxis);
par_shapes__copy3(turtle->points + 3, yaxis);
par_shapes__copy3(turtle->points + 6, zaxis);
return turtle;
}
static par_shapes_mesh* par_shapes__apply_turtle(par_shapes_mesh* mesh,
par_shapes_mesh* turtle, float const* pos, float const* scale)
{
par_shapes_mesh* m = par_shapes_clone(mesh, 0);
for (int p = 0; p < m->npoints; p++) {
float* pt = m->points + p * 3;
pt[0] *= scale[0];
pt[1] *= scale[1];
pt[2] *= scale[2];
par_shapes__transform3(pt,
turtle->points + 0, turtle->points + 3, turtle->points + 6);
pt[0] += pos[0];
pt[1] += pos[1];
pt[2] += pos[2];
}
return m;
}
static void par_shapes__connect(par_shapes_mesh* scene,
par_shapes_mesh* cylinder, int slices)
{
int stacks = 1;
int npoints = (slices + 1) * (stacks + 1);
assert(scene->npoints >= npoints && "Cannot connect to empty scene.");
// Create the new point list.
npoints = scene->npoints + (slices + 1);
float* points = PAR_MALLOC(float, npoints * 3);
memcpy(points, scene->points, sizeof(float) * scene->npoints * 3);
float* newpts = points + scene->npoints * 3;
memcpy(newpts, cylinder->points + (slices + 1) * 3,
sizeof(float) * (slices + 1) * 3);
PAR_FREE(scene->points);
scene->points = points;
// Create the new triangle list.
int ntriangles = scene->ntriangles + 2 * slices * stacks;
PAR_SHAPES_T* triangles = PAR_MALLOC(PAR_SHAPES_T, ntriangles * 3);
memcpy(triangles, scene->triangles, 2 * scene->ntriangles * 3);
int v = scene->npoints - (slices + 1);
PAR_SHAPES_T* face = triangles + scene->ntriangles * 3;
for (int stack = 0; stack < stacks; stack++) {
for (int slice = 0; slice < slices; slice++) {
int next = slice + 1;
*face++ = v + slice + slices + 1;
*face++ = v + next;
*face++ = v + slice;
*face++ = v + slice + slices + 1;
*face++ = v + next + slices + 1;
*face++ = v + next;
}
v += slices + 1;
}
PAR_FREE(scene->triangles);
scene->triangles = triangles;
scene->npoints = npoints;
scene->ntriangles = ntriangles;
}
par_shapes_mesh* par_shapes_create_lsystem(char const* text, int slices,
int maxdepth)
{
char* program;
program = PAR_MALLOC(char, strlen(text) + 1);
// The first pass counts the number of rules and commands.
strcpy(program, text);
char *cmd = strtok(program, " ");
int nrules = 1;
int ncommands = 0;
while (cmd) {
char *arg = strtok(0, " ");
if (!arg) {
puts("lsystem error: unexpected end of program.");
break;
}
if (!strcmp(cmd, "rule")) {
nrules++;
} else {
ncommands++;
}
cmd = strtok(0, " ");
}
// Allocate space.
par_shapes__rule* rules = PAR_MALLOC(par_shapes__rule, nrules);
par_shapes__command* commands = PAR_MALLOC(par_shapes__command, ncommands);
// Initialize the entry rule.
par_shapes__rule* current_rule = &rules[0];
par_shapes__command* current_command = &commands[0];
current_rule->name = "entry";
current_rule->weight = 1;
current_rule->ncommands = 0;
current_rule->commands = current_command;
// The second pass fills in the structures.
strcpy(program, text);
cmd = strtok(program, " ");
while (cmd) {
char *arg = strtok(0, " ");
if (!strcmp(cmd, "rule")) {
current_rule++;
// Split the argument into a rule name and weight.
char* dot = strchr(arg, '.');
if (dot) {
current_rule->weight = atoi(dot + 1);
*dot = 0;
} else {
current_rule->weight = 1;
}
current_rule->name = arg;
current_rule->ncommands = 0;
current_rule->commands = current_command;
} else {
current_rule->ncommands++;
current_command->cmd = cmd;
current_command->arg = arg;
current_command++;
}
cmd = strtok(0, " ");
}
// For testing purposes, dump out the parsed program.
#ifdef TEST_PARSE
for (int i = 0; i < nrules; i++) {
par_shapes__rule rule = rules[i];
printf("rule %s.%d\n", rule.name, rule.weight);
for (int c = 0; c < rule.ncommands; c++) {
par_shapes__command cmd = rule.commands[c];
printf("\t%s %s\n", cmd.cmd, cmd.arg);
}
}
#endif
// Instantiate the aggregated shape and the template shapes.
par_shapes_mesh* scene = PAR_CALLOC(par_shapes_mesh, 1);
par_shapes_mesh* tube = par_shapes_create_cylinder(slices, 1);
par_shapes_mesh* turtle = par_shapes__create_turtle();
// We're not attempting to support texture coordinates and normals
// with L-systems, so remove them from the template shape.
PAR_FREE(tube->normals);
PAR_FREE(tube->tcoords);
tube->normals = 0;
tube->tcoords = 0;
const float xaxis[] = {1, 0, 0};
const float yaxis[] = {0, 1, 0};
const float zaxis[] = {0, 0, 1};
const float units[] = {1, 1, 1};
// Execute the L-system program until the stack size is 0.
par_shapes__stackframe* stack =
PAR_CALLOC(par_shapes__stackframe, maxdepth);
int stackptr = 0;
stack[0].orientation = turtle;
stack[0].rule = &rules[0];
par_shapes__copy3(stack[0].scale, units);
while (stackptr >= 0) {
par_shapes__stackframe* frame = &stack[stackptr];
par_shapes__rule* rule = frame->rule;
par_shapes_mesh* turtle = frame->orientation;
float* position = frame->position;
float* scale = frame->scale;
if (frame->pc >= rule->ncommands) {
par_shapes_free_mesh(turtle);
stackptr--;
continue;
}
par_shapes__command* cmd = rule->commands + (frame->pc++);
#ifdef DUMP_TRACE
printf("%5s %5s %5s:%d %03d\n", cmd->cmd, cmd->arg, rule->name,
frame->pc - 1, stackptr);
#endif
float value;
if (!strcmp(cmd->cmd, "shape")) {
par_shapes_mesh* m = par_shapes__apply_turtle(tube, turtle,
position, scale);
if (!strcmp(cmd->arg, "connect")) {
par_shapes__connect(scene, m, slices);
} else {
par_shapes_merge(scene, m);
}
par_shapes_free_mesh(m);
} else if (!strcmp(cmd->cmd, "call") && stackptr < maxdepth - 1) {
rule = par_shapes__pick_rule(cmd->arg, rules, nrules);
frame = &stack[++stackptr];
frame->rule = rule;
frame->orientation = par_shapes_clone(turtle, 0);
frame->pc = 0;
par_shapes__copy3(frame->scale, scale);
par_shapes__copy3(frame->position, position);
continue;
} else {
value = atof(cmd->arg);
if (!strcmp(cmd->cmd, "rx")) {
par_shapes_rotate(turtle, value * PAR_PI / 180.0, xaxis);
} else if (!strcmp(cmd->cmd, "ry")) {
par_shapes_rotate(turtle, value * PAR_PI / 180.0, yaxis);
} else if (!strcmp(cmd->cmd, "rz")) {
par_shapes_rotate(turtle, value * PAR_PI / 180.0, zaxis);
} else if (!strcmp(cmd->cmd, "tx")) {
float vec[3] = {value, 0, 0};
float t[3] = {
par_shapes__dot3(turtle->points + 0, vec),
par_shapes__dot3(turtle->points + 3, vec),
par_shapes__dot3(turtle->points + 6, vec)
};
par_shapes__add3(position, t);
} else if (!strcmp(cmd->cmd, "ty")) {
float vec[3] = {0, value, 0};
float t[3] = {
par_shapes__dot3(turtle->points + 0, vec),
par_shapes__dot3(turtle->points + 3, vec),
par_shapes__dot3(turtle->points + 6, vec)
};
par_shapes__add3(position, t);
} else if (!strcmp(cmd->cmd, "tz")) {
float vec[3] = {0, 0, value};
float t[3] = {
par_shapes__dot3(turtle->points + 0, vec),
par_shapes__dot3(turtle->points + 3, vec),
par_shapes__dot3(turtle->points + 6, vec)
};
par_shapes__add3(position, t);
} else if (!strcmp(cmd->cmd, "sx")) {
scale[0] *= value;
} else if (!strcmp(cmd->cmd, "sy")) {
scale[1] *= value;
} else if (!strcmp(cmd->cmd, "sz")) {
scale[2] *= value;
} else if (!strcmp(cmd->cmd, "sa")) {
scale[0] *= value;
scale[1] *= value;
scale[2] *= value;
}
}
}
PAR_FREE(stack);
PAR_FREE(program);
PAR_FREE(rules);
PAR_FREE(commands);
return scene;
}
void par_shapes_unweld(par_shapes_mesh* mesh, bool create_indices)
{
int npoints = mesh->ntriangles * 3;
float* points = PAR_MALLOC(float, 3 * npoints);
float* dst = points;
PAR_SHAPES_T const* index = mesh->triangles;
for (int i = 0; i < npoints; i++) {
float const* src = mesh->points + 3 * (*index++);
*dst++ = src[0];
*dst++ = src[1];
*dst++ = src[2];
}
PAR_FREE(mesh->points);
mesh->points = points;
mesh->npoints = npoints;
if (create_indices) {
PAR_SHAPES_T* tris = PAR_MALLOC(PAR_SHAPES_T, 3 * mesh->ntriangles);
PAR_SHAPES_T* index = tris;
for (int i = 0; i < mesh->ntriangles * 3; i++) {
*index++ = i;
}
PAR_FREE(mesh->triangles);
mesh->triangles = tris;
}
}
void par_shapes_compute_normals(par_shapes_mesh* m)
{
PAR_FREE(m->normals);
m->normals = PAR_CALLOC(float, m->npoints * 3);
PAR_SHAPES_T const* triangle = m->triangles;
float next[3], prev[3], cp[3];
for (int f = 0; f < m->ntriangles; f++, triangle += 3) {
float const* pa = m->points + 3 * triangle[0];
float const* pb = m->points + 3 * triangle[1];
float const* pc = m->points + 3 * triangle[2];
par_shapes__copy3(next, pb);
par_shapes__subtract3(next, pa);
par_shapes__copy3(prev, pc);
par_shapes__subtract3(prev, pa);
par_shapes__cross3(cp, next, prev);
par_shapes__add3(m->normals + 3 * triangle[0], cp);
par_shapes__copy3(next, pc);
par_shapes__subtract3(next, pb);
par_shapes__copy3(prev, pa);
par_shapes__subtract3(prev, pb);
par_shapes__cross3(cp, next, prev);
par_shapes__add3(m->normals + 3 * triangle[1], cp);
par_shapes__copy3(next, pa);
par_shapes__subtract3(next, pc);
par_shapes__copy3(prev, pb);
par_shapes__subtract3(prev, pc);
par_shapes__cross3(cp, next, prev);
par_shapes__add3(m->normals + 3 * triangle[2], cp);
}
float* normal = m->normals;
for (int p = 0; p < m->npoints; p++, normal += 3) {
par_shapes__normalize3(normal);
}
}
static void par_shapes__subdivide(par_shapes_mesh* mesh)
{
assert(mesh->npoints == mesh->ntriangles * 3 && "Must be unwelded.");
int ntriangles = mesh->ntriangles * 4;
int npoints = ntriangles * 3;
float* points = PAR_CALLOC(float, npoints * 3);
float* dpoint = points;
float const* spoint = mesh->points;
for (int t = 0; t < mesh->ntriangles; t++, spoint += 9, dpoint += 3) {
float const* a = spoint;
float const* b = spoint + 3;
float const* c = spoint + 6;
float const* p0 = dpoint;
float const* p1 = dpoint + 3;
float const* p2 = dpoint + 6;
par_shapes__mix3(dpoint, a, b, 0.5);
par_shapes__mix3(dpoint += 3, b, c, 0.5);
par_shapes__mix3(dpoint += 3, a, c, 0.5);
par_shapes__add3(dpoint += 3, a);
par_shapes__add3(dpoint += 3, p0);
par_shapes__add3(dpoint += 3, p2);
par_shapes__add3(dpoint += 3, p0);
par_shapes__add3(dpoint += 3, b);
par_shapes__add3(dpoint += 3, p1);
par_shapes__add3(dpoint += 3, p2);
par_shapes__add3(dpoint += 3, p1);
par_shapes__add3(dpoint += 3, c);
}
PAR_FREE(mesh->points);
mesh->points = points;
mesh->npoints = npoints;
mesh->ntriangles = ntriangles;
}
par_shapes_mesh* par_shapes_create_subdivided_sphere(int nsubd)
{
par_shapes_mesh* mesh = par_shapes_create_icosahedron();
par_shapes_unweld(mesh, false);
PAR_FREE(mesh->triangles);
mesh->triangles = 0;
while (nsubd--) {
par_shapes__subdivide(mesh);
}
for (int i = 0; i < mesh->npoints; i++) {
par_shapes__normalize3(mesh->points + i * 3);
}
mesh->triangles = PAR_MALLOC(PAR_SHAPES_T, 3 * mesh->ntriangles);
for (int i = 0; i < mesh->ntriangles * 3; i++) {
mesh->triangles[i] = i;
}
par_shapes_mesh* tmp = mesh;
mesh = par_shapes_weld(mesh, 0.01, 0);
par_shapes_free_mesh(tmp);
par_shapes_compute_normals(mesh);
return mesh;
}
par_shapes_mesh* par_shapes_create_rock(int seed, int subd)
{
par_shapes_mesh* mesh = par_shapes_create_subdivided_sphere(subd);
struct osn_context* ctx;
par__simplex_noise(seed, &ctx);
for (int p = 0; p < mesh->npoints; p++) {
float* pt = mesh->points + p * 3;
float a = 0.25, f = 1.0;
double n = a * par__simplex_noise2(ctx, f * pt[0], f * pt[2]);
a *= 0.5; f *= 2;
n += a * par__simplex_noise2(ctx, f * pt[0], f * pt[2]);
pt[0] *= 1 + 2 * n;
pt[1] *= 1 + n;
pt[2] *= 1 + 2 * n;
if (pt[1] < 0) {
pt[1] = -pow(-pt[1], 0.5) / 2;
}
}
par__simplex_noise_free(ctx);
par_shapes_compute_normals(mesh);
return mesh;
}
par_shapes_mesh* par_shapes_clone(par_shapes_mesh const* mesh,
par_shapes_mesh* clone)
{
if (!clone) {
clone = PAR_CALLOC(par_shapes_mesh, 1);
}
clone->npoints = mesh->npoints;
clone->points = PAR_REALLOC(float, clone->points, 3 * clone->npoints);
memcpy(clone->points, mesh->points, sizeof(float) * 3 * clone->npoints);
clone->ntriangles = mesh->ntriangles;
clone->triangles = PAR_REALLOC(PAR_SHAPES_T, clone->triangles, 3 *
clone->ntriangles);
memcpy(clone->triangles, mesh->triangles,
sizeof(PAR_SHAPES_T) * 3 * clone->ntriangles);
if (mesh->normals) {
clone->normals = PAR_REALLOC(float, clone->normals, 3 * clone->npoints);
memcpy(clone->normals, mesh->normals,
sizeof(float) * 3 * clone->npoints);
}
if (mesh->tcoords) {
clone->tcoords = PAR_REALLOC(float, clone->tcoords, 2 * clone->npoints);
memcpy(clone->tcoords, mesh->tcoords,
sizeof(float) * 2 * clone->npoints);
}
return clone;
}
static struct {
float const* points;
int gridsize;
} par_shapes__sort_context;
static int par_shapes__cmp1(const void *arg0, const void *arg1)
{
const int g = par_shapes__sort_context.gridsize;
// Convert arg0 into a flattened grid index.
PAR_SHAPES_T d0 = *(const PAR_SHAPES_T*) arg0;
float const* p0 = par_shapes__sort_context.points + d0 * 3;
int i0 = (int) p0[0];
int j0 = (int) p0[1];
int k0 = (int) p0[2];
int index0 = i0 + g * j0 + g * g * k0;
// Convert arg1 into a flattened grid index.
PAR_SHAPES_T d1 = *(const PAR_SHAPES_T*) arg1;
float const* p1 = par_shapes__sort_context.points + d1 * 3;
int i1 = (int) p1[0];
int j1 = (int) p1[1];
int k1 = (int) p1[2];
int index1 = i1 + g * j1 + g * g * k1;
// Return the ordering.
if (index0 < index1) return -1;
if (index0 > index1) return 1;
return 0;
}
static void par_shapes__sort_points(par_shapes_mesh* mesh, int gridsize,
PAR_SHAPES_T* sortmap)
{
// Run qsort over a list of consecutive integers that get deferenced
// within the comparator function; this creates a reorder mapping.
for (int i = 0; i < mesh->npoints; i++) {
sortmap[i] = i;
}
par_shapes__sort_context.gridsize = gridsize;
par_shapes__sort_context.points = mesh->points;
qsort(sortmap, mesh->npoints, sizeof(PAR_SHAPES_T), par_shapes__cmp1);
// Apply the reorder mapping to the XYZ coordinate data.
float* newpts = PAR_MALLOC(float, mesh->npoints * 3);
PAR_SHAPES_T* invmap = PAR_MALLOC(PAR_SHAPES_T, mesh->npoints);
float* dstpt = newpts;
for (int i = 0; i < mesh->npoints; i++) {
invmap[sortmap[i]] = i;
float const* srcpt = mesh->points + 3 * sortmap[i];
*dstpt++ = *srcpt++;
*dstpt++ = *srcpt++;
*dstpt++ = *srcpt++;
}
PAR_FREE(mesh->points);
mesh->points = newpts;
// Apply the inverse reorder mapping to the triangle indices.
PAR_SHAPES_T* newinds = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* dstind = newinds;
PAR_SHAPES_T const* srcind = mesh->triangles;
for (int i = 0; i < mesh->ntriangles * 3; i++) {
*dstind++ = invmap[*srcind++];
}
PAR_FREE(mesh->triangles);
mesh->triangles = newinds;
// Cleanup.
memcpy(sortmap, invmap, sizeof(PAR_SHAPES_T) * mesh->npoints);
PAR_FREE(invmap);
}
static void par_shapes__weld_points(par_shapes_mesh* mesh, int gridsize,
float epsilon, PAR_SHAPES_T* weldmap)
{
// Each bin contains a "pointer" (really an index) to its first point.
// We add 1 because 0 is reserved to mean that the bin is empty.
// Since the points are spatially sorted, there's no need to store
// a point count in each bin.
PAR_SHAPES_T* bins = PAR_CALLOC(PAR_SHAPES_T,
gridsize * gridsize * gridsize);
int prev_binindex = -1;
for (int p = 0; p < mesh->npoints; p++) {
float const* pt = mesh->points + p * 3;
int i = (int) pt[0];
int j = (int) pt[1];
int k = (int) pt[2];
int this_binindex = i + gridsize * j + gridsize * gridsize * k;
if (this_binindex != prev_binindex) {
bins[this_binindex] = 1 + p;
}
prev_binindex = this_binindex;
}
// Examine all bins that intersect the epsilon-sized cube centered at each
// point, and check for colocated points within those bins.
float const* pt = mesh->points;
int nremoved = 0;
for (int p = 0; p < mesh->npoints; p++, pt += 3) {
// Skip if this point has already been welded.
if (weldmap[p] != p) {
continue;
}
// Build a list of bins that intersect the epsilon-sized cube.
int nearby[8];
int nbins = 0;
int minp[3], maxp[3];
for (int c = 0; c < 3; c++) {
minp[c] = (int) (pt[c] - epsilon);
maxp[c] = (int) (pt[c] + epsilon);
}
for (int i = minp[0]; i <= maxp[0]; i++) {
for (int j = minp[1]; j <= maxp[1]; j++) {
for (int k = minp[2]; k <= maxp[2]; k++) {
int binindex = i + gridsize * j + gridsize * gridsize * k;
PAR_SHAPES_T binvalue = *(bins + binindex);
if (binvalue > 0) {
if (nbins == 8) {
printf("Epsilon value is too large.\n");
break;
}
nearby[nbins++] = binindex;
}
}
}
}
// Check for colocated points in each nearby bin.
for (int b = 0; b < nbins; b++) {
int binindex = nearby[b];
PAR_SHAPES_T binvalue = *(bins + binindex);
PAR_SHAPES_T nindex = binvalue - 1;
while (true) {
// If this isn't "self" and it's colocated, then weld it!
if (nindex != p && weldmap[nindex] == nindex) {
float const* thatpt = mesh->points + nindex * 3;
float dist2 = par_shapes__sqrdist3(thatpt, pt);
if (dist2 < epsilon) {
weldmap[nindex] = p;
nremoved++;
}
}
// Advance to the next point if possible.
if (++nindex >= mesh->npoints) {
break;
}
// If the next point is outside the bin, then we're done.
float const* nextpt = mesh->points + nindex * 3;
int i = (int) nextpt[0];
int j = (int) nextpt[1];
int k = (int) nextpt[2];
int nextbinindex = i + gridsize * j + gridsize * gridsize * k;
if (nextbinindex != binindex) {
break;
}
}
}
}
PAR_FREE(bins);
// Apply the weldmap to the vertices.
int npoints = mesh->npoints - nremoved;
float* newpts = PAR_MALLOC(float, 3 * npoints);
float* dst = newpts;
PAR_SHAPES_T* condensed_map = PAR_MALLOC(PAR_SHAPES_T, mesh->npoints);
PAR_SHAPES_T* cmap = condensed_map;
float const* src = mesh->points;
int ci = 0;
for (int p = 0; p < mesh->npoints; p++, src += 3) {
if (weldmap[p] == p) {
*dst++ = src[0];
*dst++ = src[1];
*dst++ = src[2];
*cmap++ = ci++;
} else {
*cmap++ = condensed_map[weldmap[p]];
}
}
assert(ci == npoints);
PAR_FREE(mesh->points);
memcpy(weldmap, condensed_map, mesh->npoints * sizeof(PAR_SHAPES_T));
PAR_FREE(condensed_map);
mesh->points = newpts;
mesh->npoints = npoints;
// Apply the weldmap to the triangle indices and skip the degenerates.
PAR_SHAPES_T const* tsrc = mesh->triangles;
PAR_SHAPES_T* tdst = mesh->triangles;
int ntriangles = 0;
for (int i = 0; i < mesh->ntriangles; i++, tsrc += 3) {
PAR_SHAPES_T a = weldmap[tsrc[0]];
PAR_SHAPES_T b = weldmap[tsrc[1]];
PAR_SHAPES_T c = weldmap[tsrc[2]];
if (a != b && a != c && b != c) {
*tdst++ = a;
*tdst++ = b;
*tdst++ = c;
ntriangles++;
}
}
mesh->ntriangles = ntriangles;
}
par_shapes_mesh* par_shapes_weld(par_shapes_mesh const* mesh, float epsilon,
PAR_SHAPES_T* weldmap)
{
par_shapes_mesh* clone = par_shapes_clone(mesh, 0);
float aabb[6];
int gridsize = 20;
float maxcell = gridsize - 1;
par_shapes_compute_aabb(clone, aabb);
float scale[3] = {
aabb[3] == aabb[0] ? 1.0f : maxcell / (aabb[3] - aabb[0]),
aabb[4] == aabb[1] ? 1.0f : maxcell / (aabb[4] - aabb[1]),
aabb[5] == aabb[2] ? 1.0f : maxcell / (aabb[5] - aabb[2]),
};
par_shapes_translate(clone, -aabb[0], -aabb[1], -aabb[2]);
par_shapes_scale(clone, scale[0], scale[1], scale[2]);
PAR_SHAPES_T* sortmap = PAR_MALLOC(PAR_SHAPES_T, mesh->npoints);
par_shapes__sort_points(clone, gridsize, sortmap);
bool owner = false;
if (!weldmap) {
owner = true;
weldmap = PAR_MALLOC(PAR_SHAPES_T, mesh->npoints);
}
for (int i = 0; i < mesh->npoints; i++) {
weldmap[i] = i;
}
par_shapes__weld_points(clone, gridsize, epsilon, weldmap);
if (owner) {
PAR_FREE(weldmap);
} else {
PAR_SHAPES_T* newmap = PAR_MALLOC(PAR_SHAPES_T, mesh->npoints);
for (int i = 0; i < mesh->npoints; i++) {
newmap[i] = weldmap[sortmap[i]];
}
memcpy(weldmap, newmap, sizeof(PAR_SHAPES_T) * mesh->npoints);
PAR_FREE(newmap);
}
PAR_FREE(sortmap);
par_shapes_scale(clone, 1.0 / scale[0], 1.0 / scale[1], 1.0 / scale[2]);
par_shapes_translate(clone, aabb[0], aabb[1], aabb[2]);
return clone;
}
// -----------------------------------------------------------------------------
// BEGIN OPEN SIMPLEX NOISE
// -----------------------------------------------------------------------------
#define STRETCH_CONSTANT_2D (-0.211324865405187) // (1 / sqrt(2 + 1) - 1 ) / 2;
#define SQUISH_CONSTANT_2D (0.366025403784439) // (sqrt(2 + 1) -1) / 2;
#define STRETCH_CONSTANT_3D (-1.0 / 6.0) // (1 / sqrt(3 + 1) - 1) / 3;
#define SQUISH_CONSTANT_3D (1.0 / 3.0) // (sqrt(3+1)-1)/3;
#define STRETCH_CONSTANT_4D (-0.138196601125011) // (1 / sqrt(4 + 1) - 1) / 4;
#define SQUISH_CONSTANT_4D (0.309016994374947) // (sqrt(4 + 1) - 1) / 4;
#define NORM_CONSTANT_2D (47.0)
#define NORM_CONSTANT_3D (103.0)
#define NORM_CONSTANT_4D (30.0)
#define DEFAULT_SEED (0LL)
struct osn_context {
int16_t* perm;
int16_t* permGradIndex3D;
};
#define ARRAYSIZE(x) (sizeof((x)) / sizeof((x)[0]))
/*
* Gradients for 2D. They approximate the directions to the
* vertices of an octagon from the center.
*/
static const int8_t gradients2D[] = {
5, 2, 2, 5, -5, 2, -2, 5, 5, -2, 2, -5, -5, -2, -2, -5,
};
/*
* Gradients for 3D. They approximate the directions to the
* vertices of a rhombicuboctahedron from the center, skewed so
* that the triangular and square facets can be inscribed inside
* circles of the same radius.
*/
static const signed char gradients3D[] = {
-11, 4, 4, -4, 11, 4, -4, 4, 11, 11, 4, 4, 4, 11, 4, 4, 4, 11, -11, -4, 4,
-4, -11, 4, -4, -4, 11, 11, -4, 4, 4, -11, 4, 4, -4, 11, -11, 4, -4, -4, 11,
-4, -4, 4, -11, 11, 4, -4, 4, 11, -4, 4, 4, -11, -11, -4, -4, -4, -11, -4,
-4, -4, -11, 11, -4, -4, 4, -11, -4, 4, -4, -11,
};
/*
* Gradients for 4D. They approximate the directions to the
* vertices of a disprismatotesseractihexadecachoron from the center,
* skewed so that the tetrahedral and cubic facets can be inscribed inside
* spheres of the same radius.
*/
static const signed char gradients4D[] = {
3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, -3, 1, 1, 1, -1, 3, 1, 1,
-1, 1, 3, 1, -1, 1, 1, 3, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1,
3, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, 3, 1, -1, 1, 1,
3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3,
1, -1, 1, -1, 3, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, -3,
-1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, 3, 1, 1, -1, 1, 3,
1, -1, 1, 1, 3, -1, 1, 1, 1, -3, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1,
-1, 1, 1, -3, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, -3,
-1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, 3, 1, -1, -1, 1, 3,
-1, -1, 1, 1, -3, -1, 1, 1, -1, -3, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3,
-1, -1, 1, -1, -3, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1,
-3, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3,
};
static double extrapolate2(
struct osn_context* ctx, int xsb, int ysb, double dx, double dy)
{
int16_t* perm = ctx->perm;
int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
return gradients2D[index] * dx + gradients2D[index + 1] * dy;
}
static inline int fastFloor(double x)
{
int xi = (int) x;
return x < xi ? xi - 1 : xi;
}
static int allocate_perm(struct osn_context* ctx, int nperm, int ngrad)
{
PAR_FREE(ctx->perm);
PAR_FREE(ctx->permGradIndex3D);
ctx->perm = PAR_MALLOC(int16_t, nperm);
if (!ctx->perm) {
return -ENOMEM;
}
ctx->permGradIndex3D = PAR_MALLOC(int16_t, ngrad);
if (!ctx->permGradIndex3D) {
PAR_FREE(ctx->perm);
return -ENOMEM;
}
return 0;
}
static int par__simplex_noise(int64_t seed, struct osn_context** ctx)
{
int rc;
int16_t source[256];
int i;
int16_t* perm;
int16_t* permGradIndex3D;
*ctx = PAR_MALLOC(struct osn_context, 1);
if (!(*ctx)) {
return -ENOMEM;
}
(*ctx)->perm = NULL;
(*ctx)->permGradIndex3D = NULL;
rc = allocate_perm(*ctx, 256, 256);
if (rc) {
PAR_FREE(*ctx);
return rc;
}
perm = (*ctx)->perm;
permGradIndex3D = (*ctx)->permGradIndex3D;
for (i = 0; i < 256; i++) {
source[i] = (int16_t) i;
}
seed = seed * 6364136223846793005LL + 1442695040888963407LL;
seed = seed * 6364136223846793005LL + 1442695040888963407LL;
seed = seed * 6364136223846793005LL + 1442695040888963407LL;
for (i = 255; i >= 0; i--) {
seed = seed * 6364136223846793005LL + 1442695040888963407LL;
int r = (int) ((seed + 31) % (i + 1));
if (r < 0)
r += (i + 1);
perm[i] = source[r];
permGradIndex3D[i] =
(short) ((perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3);
source[r] = source[i];
}
return 0;
}
static void par__simplex_noise_free(struct osn_context* ctx)
{
if (!ctx)
return;
if (ctx->perm) {
PAR_FREE(ctx->perm);
ctx->perm = NULL;
}
if (ctx->permGradIndex3D) {
PAR_FREE(ctx->permGradIndex3D);
ctx->permGradIndex3D = NULL;
}
PAR_FREE(ctx);
}
static double par__simplex_noise2(struct osn_context* ctx, double x, double y)
{
// Place input coordinates onto grid.
double stretchOffset = (x + y) * STRETCH_CONSTANT_2D;
double xs = x + stretchOffset;
double ys = y + stretchOffset;
// Floor to get grid coordinates of rhombus (stretched square) super-cell
// origin.
int xsb = fastFloor(xs);
int ysb = fastFloor(ys);
// Skew out to get actual coordinates of rhombus origin. We'll need these
// later.
double squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D;
double xb = xsb + squishOffset;
double yb = ysb + squishOffset;
// Compute grid coordinates relative to rhombus origin.
double xins = xs - xsb;
double yins = ys - ysb;
// Sum those together to get a value that determines which region we're in.
double inSum = xins + yins;
// Positions relative to origin point.
double dx0 = x - xb;
double dy0 = y - yb;
// We'll be defining these inside the next block and using them afterwards.
double dx_ext, dy_ext;
int xsv_ext, ysv_ext;
double value = 0;
// Contribution (1,0)
double dx1 = dx0 - 1 - SQUISH_CONSTANT_2D;
double dy1 = dy0 - 0 - SQUISH_CONSTANT_2D;
double attn1 = 2 - dx1 * dx1 - dy1 * dy1;
if (attn1 > 0) {
attn1 *= attn1;
value += attn1 * attn1 * extrapolate2(ctx, xsb + 1, ysb + 0, dx1, dy1);
}
// Contribution (0,1)
double dx2 = dx0 - 0 - SQUISH_CONSTANT_2D;
double dy2 = dy0 - 1 - SQUISH_CONSTANT_2D;
double attn2 = 2 - dx2 * dx2 - dy2 * dy2;
if (attn2 > 0) {
attn2 *= attn2;
value += attn2 * attn2 * extrapolate2(ctx, xsb + 0, ysb + 1, dx2, dy2);
}
if (inSum <= 1) { // We're inside the triangle (2-Simplex) at (0,0)
double zins = 1 - inSum;
if (zins > xins || zins > yins) {
if (xins > yins) {
xsv_ext = xsb + 1;
ysv_ext = ysb - 1;
dx_ext = dx0 - 1;
dy_ext = dy0 + 1;
} else {
xsv_ext = xsb - 1;
ysv_ext = ysb + 1;
dx_ext = dx0 + 1;
dy_ext = dy0 - 1;
}
} else { //(1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1;
ysv_ext = ysb + 1;
dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
}
} else { // We're inside the triangle (2-Simplex) at (1,1)
double zins = 2 - inSum;
if (zins < xins || zins < yins) {
if (xins > yins) {
xsv_ext = xsb + 2;
ysv_ext = ysb + 0;
dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D;
dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D;
} else {
xsv_ext = xsb + 0;
ysv_ext = ysb + 2;
dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D;
dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D;
}
} else { //(1,0) and (0,1) are the closest two vertices.
dx_ext = dx0;
dy_ext = dy0;
xsv_ext = xsb;
ysv_ext = ysb;
}
xsb += 1;
ysb += 1;
dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
}
// Contribution (0,0) or (1,1)
double attn0 = 2 - dx0 * dx0 - dy0 * dy0;
if (attn0 > 0) {
attn0 *= attn0;
value += attn0 * attn0 * extrapolate2(ctx, xsb, ysb, dx0, dy0);
}
// Extra Vertex
double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
if (attn_ext > 0) {
attn_ext *= attn_ext;
value += attn_ext * attn_ext *
extrapolate2(ctx, xsv_ext, ysv_ext, dx_ext, dy_ext);
}
return value / NORM_CONSTANT_2D;
}
void par_shapes_remove_degenerate(par_shapes_mesh* mesh, float mintriarea)
{
int ntriangles = 0;
PAR_SHAPES_T* triangles = PAR_MALLOC(PAR_SHAPES_T, mesh->ntriangles * 3);
PAR_SHAPES_T* dst = triangles;
PAR_SHAPES_T const* src = mesh->triangles;
float next[3], prev[3], cp[3];
float mincplen2 = (mintriarea * 2) * (mintriarea * 2);
for (int f = 0; f < mesh->ntriangles; f++, src += 3) {
float const* pa = mesh->points + 3 * src[0];
float const* pb = mesh->points + 3 * src[1];
float const* pc = mesh->points + 3 * src[2];
par_shapes__copy3(next, pb);
par_shapes__subtract3(next, pa);
par_shapes__copy3(prev, pc);
par_shapes__subtract3(prev, pa);
par_shapes__cross3(cp, next, prev);
float cplen2 = par_shapes__dot3(cp, cp);
if (cplen2 >= mincplen2) {
*dst++ = src[0];
*dst++ = src[1];
*dst++ = src[2];
ntriangles++;
}
}
mesh->ntriangles = ntriangles;
PAR_FREE(mesh->triangles);
mesh->triangles = triangles;
}
#endif // PAR_SHAPES_IMPLEMENTATION
#endif // PAR_SHAPES_H