minesweeper

par_shapes.h (72865B)

---

 // 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:
 //
 //     https://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.
 //
 // Distributed under the MIT License, see bottom of file.
 
 #ifndef PAR_SHAPES_H
 #define PAR_SHAPES_H
 
 #ifdef __cplusplus
 extern "C" {
 #endif
 
 #include <stdint.h>
 // Ray (@raysan5): Commented to avoid conflict with raylib bool
 /*
 #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);
 
 // Cone is similar to cylinder but the radius diminishes to zero as Z increases.
 // Again, height and radius are 1.0, but can be changed with par_shapes_scale.
 par_shapes_mesh* par_shapes_create_cone(int slices, int stacks);
 
 // Create a disk of radius 1.0 with texture coordinates and normals by squashing
 // a cone flat on the Z=0 plane.
 par_shapes_mesh* par_shapes_create_parametric_disk(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);
 
 // Global Config ---------------------------------------------------------------
 
 void par_shapes_set_epsilon_welded_normals(float epsilon);
 void par_shapes_set_epsilon_degenerate_sphere(float epsilon);
 
 // Advanced --------------------------------------------------------------------
 
 void par_shapes__compute_welded_normals(par_shapes_mesh* m);
 void par_shapes__connect(par_shapes_mesh* scene, par_shapes_mesh* cylinder,
     int slices);
 
 #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 float par_shapes__epsilon_welded_normals = 0.001;
 static float par_shapes__epsilon_degenerate_sphere = 0.0001;
 
 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__cone(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;
 }
 
 void par_shapes__compute_welded_normals(par_shapes_mesh* m)
 {
     const float epsilon = par_shapes__epsilon_welded_normals;
     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, epsilon, 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_cone(int slices, int stacks)
 {
     if (slices < 3 || stacks < 1) {
         return 0;
     }
     return par_shapes_create_parametric(par_shapes__cone, slices,
         stacks, 0);
 }
 
 par_shapes_mesh* par_shapes_create_parametric_disk(int slices, int stacks)
 {
     par_shapes_mesh* m = par_shapes_create_cone(slices, stacks);
     if (m) {
         par_shapes_scale(m, 1.0f, 1.0f, 0.0f);
     }
     return m;
 }
 
 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, par_shapes__epsilon_degenerate_sphere);
     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, par_shapes__epsilon_degenerate_sphere);
     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__cone(float const* uv, float* xyz, void* userdata)
 {
     float r = 1.0f - uv[0];
     float theta = uv[1] * 2 * PAR_PI;
     xyz[0] = r * sinf(theta);
     xyz[1] = r * 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_set_epsilon_welded_normals(float epsilon) {
     par_shapes__epsilon_welded_normals = epsilon;
 }
 
 void par_shapes_set_epsilon_degenerate_sphere(float epsilon) {
     par_shapes__epsilon_degenerate_sphere = epsilon;
 }
 
 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;
     }
     float* n = mesh->normals;
     if (n) {
         for (int i = 0; i < mesh->npoints; i++, n += 3) {
             float x = col0[0] * n[0] + col1[0] * n[1] + col2[0] * n[2];
             float y = col0[1] * n[0] + col1[1] * n[1] + col2[1] * n[2];
             float z = col0[2] * n[0] + col1[2] * n[1] + col2[2] * n[2];
             n[0] = x;
             n[1] = y;
             n[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;
     }
     float* n = m->normals;
     if (n && !(x == y && y == z)) {
         bool x_zero = x == 0;
         bool y_zero = y == 0;
         bool z_zero = z == 0;
         if (!x_zero && !y_zero && !z_zero) {
             x = 1.0f / x;
             y = 1.0f / y;
             z = 1.0f / z;
         } else {
             x = x_zero && !y_zero && !z_zero;
             y = y_zero && !x_zero && !z_zero;
             z = z_zero && !x_zero && !y_zero;
         }
         for (int i = 0; i < m->npoints; i++, n += 3) {
             n[0] *= x;
             n[1] *= y;
             n[2] *= z;
             par_shapes__normalize3(n);
         }
     }
 }
 
 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() / (float) 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;
 }
 
 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,
         sizeof(PAR_SHAPES_T) * 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;
             assert(nindex < mesh->npoints);
             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) {
             assert(a < mesh->npoints);
             assert(b < mesh->npoints);
             assert(c < mesh->npoints);
             *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
 
 // par_shapes is distributed under the MIT license:
 //
 // Copyright (c) 2019 Philip Rideout
 //
 // Permission is hereby granted, free of charge, to any person obtaining a copy
 // of this software and associated documentation files (the "Software"), to deal
 // in the Software without restriction, including without limitation the rights
 // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 // copies of the Software, and to permit persons to whom the Software is
 // furnished to do so, subject to the following conditions:
 //
 // The above copyright notice and this permission notice shall be included in
 // all copies or substantial portions of the Software.
 //
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.