text: // 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>
  #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
  #include <locale.h>
  
  #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 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__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;
  }
  
  static void par_shapes__compute_welded_normals(par_shapes_mesh* m)
  {
      if (!m->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, 0.000001, weldmap); // LWJGL: smaller epsilon
      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_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, 0.0000001);
      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, 0.0000001);
      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_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 || x != z || y != z)) {
          x = 1.0f / x;
          y = 1.0f / y;
          z = 1.0f / z;
          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;
      float argf;
  } 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);
      scene->points = PAR_REALLOC(float, scene->points, npoints * 3);
      float* newpts = scene->points + scene->npoints * 3;
      memcpy(newpts, cylinder->points + (slices + 1) * 3,
          sizeof(float) * (slices + 1) * 3);
  
      // Create the new triangle list.
      int ntriangles = scene->ntriangles + 2 * slices * stacks;
      scene->triangles = PAR_REALLOC(PAR_SHAPES_T, scene->triangles, ntriangles * 3);
      int v = scene->npoints - (slices + 1);
      PAR_SHAPES_T* face = scene->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;
      }
  
      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;
  
      char decimal_point = localeconv()->decimal_point[0];
  
      // 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;
              if (strcmp(cmd, "shape") && strcmp(cmd, "call")) {
                  if (decimal_point != '.') {
                      char *s = arg;
                      while (*s != 0) {
                          if (*s == '.') {
                              *s = decimal_point;
                              break;
                          }
                          s++;
                      }
                  }
                  current_command->argf = atof(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
  
          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 {
              float value = cmd->argf;
              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_shapes_free_mesh(tube);
      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, 0.000001, 0); // LWJGL: smaller epsilon
      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) {
                          // LWJGL: With greater epsilons, the check below fails and the condensed_map loop below produces garbage
                          //if (p < nindex ) {
                          weldmap[nindex] = p;
                          //} else {
                              //weldmap[p] = weldmap[nindex];
                          //}
                          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
  
  // 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.
  