rbdlsim/src/sconvcol.h

#ifndef SCONVCOL_H
#define SCONVCOL_H

#ifdef __cplusplus
extern "C" {
#endif

#include <assert.h>
#include <stdbool.h>
#include <float.h>

#include "vectorial/simd4x4f.h"

inline bool sch_simd4f_equal(simd4f a, simd4f b) {
  return (simd4f_get_x(simd4f_length4_squared(simd4f_sub(a, b))) == 0.f);
}

inline bool sch_simd4f_close(simd4f a, simd4f b, float tol) {
  return (simd4f_get_x(simd4f_length4_squared(simd4f_sub(a, b))) < tol * tol);
}

typedef struct sch_edge sch_edge;
typedef struct sch_vert sch_vert;
typedef struct sch_face sch_face;
typedef struct sch_hull sch_hull;
typedef struct sch_plane sch_plane;
typedef struct sch_hull_builder sch_hull_builder;
typedef struct sch_face_query sch_face_query;

struct sch_edge {
  sch_vert* vert;
  sch_edge* twin;
  sch_face* face;
  sch_edge* next;
};

struct sch_vert {
  simd4f p;
  sch_edge* edge;
};

struct sch_face {
  sch_edge* edge;
};

struct sch_hull {
  sch_face* faces;
  sch_edge* edges;
  sch_vert* vertices;
  simd4f center;
  int num_faces;
  int num_edges;
  int num_vertices;
};

struct sch_plane {
  simd4f p;
  simd4f n;
};

struct sch_face_query {
  float dist;
  int face_idx;
  sch_plane plane;
  simd4f vert;
};

//
// Hull Builder
//

#define SCH_BUILDER_MAX_NUM_VERTICES 1024
#define SCH_BUILDER_MAX_NUM_FACES 256
#define SCH_BUILDER_MAX_NUM_FACE_VERTICES 32

enum SchHullResult {
  SchHullResultOK = 0,
  SchHullResultConcaveVertex = -1,
  SchHullResultWrongWinding = -2,
  SchHullResultInvalidTwinEdges = -3,
  SchHullResultOpenHull = -4
};

typedef enum SchHullResult SchHullResult;

struct sch_hull_builder {
  int num_vertices;
  int num_faces;
  simd4f vertices[SCH_BUILDER_MAX_NUM_VERTICES];
  int face_vert_idx[SCH_BUILDER_MAX_NUM_FACES * SCH_BUILDER_MAX_NUM_VERTICES];
  int face_vert_idx_start[SCH_BUILDER_MAX_NUM_FACES];
  int face_vert_idx_end[SCH_BUILDER_MAX_NUM_FACES];
};

void sch_builder_reset(sch_hull_builder* builder);

void sch_builder_face_begin(sch_hull_builder* builder);

void sch_builder_face_vertex(sch_hull_builder* builder, simd4f vertex);

void sch_builder_face_end(sch_hull_builder* builder);

SchHullResult sch_builder_create_hull(sch_hull_builder* builder, sch_hull* out_hull);

//
// Calculations
//

float sch_plane_distance(const sch_plane* plane, const simd4f* v);

void sch_edge_get_dir(const sch_edge* edge, simd4f* out_dir);

void sch_hull_free_memory (sch_hull* hull);

void sch_hull_translate (sch_hull* hull, float x, float y, float z);

void sch_hull_rotate (sch_hull* hull, const float radians, const simd4f axis);

void sch_hull_transform (sch_hull* hull, simd4x4f mat);

void sch_hull_get_plane(const sch_hull* hull, const int index, sch_plane* out_plane);

sch_edge* sch_hull_find_edge (const sch_hull* hull, const simd4f v0, const simd4f v1);

void sch_hull_get_support(const sch_hull* hull, simd4f n, simd4f* out_vert);

float sch_query_face_directions (const sch_hull* hull_A, const sch_hull* hull_B, sch_face_query* result);

bool sch_hull_sat (const sch_hull* hullA, const sch_hull* hullB);

int sch_hull_is_vertex_concave(const sch_hull* hull, const simd4f p);

int sch_hull_is_closed (const sch_hull* hull);

int sch_hull_connect_face_edges(const sch_hull* hull, int face_index);

void sch_create_face(int num_vert, simd4f* vertices, sch_face* out_face);

void sch_create_unitbox(sch_hull* out_hull);

//
// sconvcol Implementation
//

#ifdef SCONVCOL_IMPLEMENTATION

float sch_plane_distance(const sch_plane* plane, const simd4f* v) {
  return simd4f_dot3_scalar(simd4f_sub(*v, plane->p), plane->n);
}

void sch_create_face(int num_vert, simd4f* vertices, sch_face* out_face) {
  assert(out_face != NULL);
  assert(out_face->edge == NULL);

  int i = 0;
  sch_edge* f_edges = malloc(sizeof(sch_edge) * num_vert);
  sch_vert* f_verts = malloc(sizeof(sch_vert) * num_vert);

  while (i < num_vert) {
    sch_vert* vert = &f_verts[i];
    sch_edge* edge = &f_edges[i];

    edge->twin = NULL;
    edge->vert = vert;
    edge->face = out_face;
    edge->next = &f_edges[(i + 1) % num_vert];

    vert->edge = edge;
    vert->p = vertices[i];

    i++;
  }

  out_face->edge = &f_edges[0];
}

void sch_edge_get_dir(const sch_edge* edge, simd4f* out_dir) {
  *out_dir = simd4f_sub(edge->next->vert->p, edge->vert->p);
  float recip_len = 1.f / sqrtf(simd4f_dot3_scalar(*out_dir, *out_dir));
  *out_dir = simd4f_mul(*out_dir, simd4f_splat(recip_len));
}

void sch_builder_reset(sch_hull_builder* builder) {
  builder->num_vertices = 0;
  builder->num_faces = 0;
}

void sch_builder_face_begin(sch_hull_builder* builder) {
  int face_index = builder->num_faces;
  if (builder->num_faces == 0) {
    builder->face_vert_idx_start[face_index] = 0;
  } else {
    builder->face_vert_idx_start[face_index] = builder->face_vert_idx_end[face_index - 1] + 1;
  }

  builder->face_vert_idx_end[face_index] = -1;
}

void sch_builder_face_end(sch_hull_builder* builder) { builder->num_faces++; }

void sch_builder_allocate_memory (sch_hull_builder* builder, sch_hull* out_hull) {
  out_hull->faces = (sch_face*)malloc(sizeof(sch_face) * builder->num_faces);

  out_hull->num_vertices = builder->num_vertices;
  out_hull->vertices =
      (sch_vert*)malloc(sizeof(sch_vert) * builder->num_vertices);

  int num_edges = 0;
  for (int face_index = 0; face_index < builder->num_faces; face_index++) {
    int start_idx = builder->face_vert_idx_start[face_index];
    int end_idx = builder->face_vert_idx_end[face_index];
    int edge_count = end_idx - start_idx;

    num_edges += edge_count + 1;
  }

  out_hull->num_edges = num_edges;
  out_hull->edges = (sch_edge*)malloc(sizeof(sch_edge) * num_edges);
}

void sch_hull_translate (sch_hull* hull, float x, float y, float z) {
  simd4f r = simd4f_create (x, y, z, 0.f);
  hull->center = simd4f_add (hull->center, r);

  for (int vi = 0; vi < hull->num_vertices; vi++) {
    hull->vertices[vi].p = simd4f_add (hull->vertices[vi].p, r);
  }
}

void sch_hull_rotate (sch_hull* hull, const float radians, const simd4f axis) {
  simd4x4f rot_mat;
  simd4x4f_axis_rotation(&rot_mat, radians, axis);
  simd4x4f_matrix_vector_mul(&rot_mat, &hull->center, &hull->center);

  for (int vi = 0; vi < hull->num_vertices; vi++) {
    simd4x4f_matrix_vector_mul(&rot_mat, &hull->vertices[vi].p, &hull->vertices[vi].p);
  }
}

void sch_hull_transform (sch_hull* hull, simd4x4f mat) {
  simd4f v_temp = hull->center;
  simd4x4f_matrix_vector_mul(&mat, &v_temp, &hull->center);

  for (int vi = 0; vi < hull->num_vertices; vi++) {
    v_temp = hull->vertices[vi].p;
    simd4x4f_matrix_vector_mul(&mat, &v_temp, &hull->vertices[vi].p);
  }
}

void sch_hull_free_memory (sch_hull* hull) {
  free (hull->faces);
  hull->faces = NULL;
  hull->num_faces = 0;
  free (hull->vertices);
  hull->vertices = NULL;
  hull->num_vertices = 0;
  free (hull->edges);
  hull->edges = NULL;
  hull->num_edges = 0;
}

SchHullResult sch_builder_create_hull(sch_hull_builder* builder, sch_hull* out_hull) {
  sch_builder_allocate_memory(builder, out_hull);
  out_hull->num_faces = 0;

  int hull_edge_idx = 0;

  for (int face_index = 0; face_index < builder->num_faces; face_index++) {
    sch_face* face = &out_hull->faces[face_index];

    int start_idx = builder->face_vert_idx_start[face_index];
    int end_idx = builder->face_vert_idx_end[face_index];

    sch_edge* prev_edge = NULL;

    for (int face_vert_idx = start_idx; face_vert_idx <= end_idx;
         face_vert_idx++) {
      sch_edge* edge = &out_hull->edges[hull_edge_idx];
      hull_edge_idx++;
      if (face_vert_idx == start_idx) {
        face->edge = edge;
      }

      int vert_idx = builder->face_vert_idx[face_vert_idx];
      sch_vert* vert = &out_hull->vertices[vert_idx];

      vert->p = builder->vertices[vert_idx];
      vert->edge = edge;
      edge->vert = vert;
      edge->twin = NULL;
      edge->face = face;

      if (sch_hull_is_vertex_concave(out_hull, vert->p)) {
        sch_hull_free_memory(out_hull);
        return SchHullResultConcaveVertex;
      }

      if (face_vert_idx == end_idx) {
        edge->next = face->edge;
      }
      if (prev_edge != NULL) {
        prev_edge->next = edge;
      }

      prev_edge = edge;
    }

    int edge_add_result = sch_hull_connect_face_edges (out_hull, face_index);
    if (edge_add_result != SchHullResultOK) {
      sch_hull_free_memory(out_hull);
      return edge_add_result;
    }

    out_hull->num_faces = face_index + 1;
  }

  assert (hull_edge_idx == out_hull->num_edges);

  return sch_hull_is_closed (out_hull);
}

void sch_builder_face_vertex(sch_hull_builder* builder, simd4f vertex) {
  int face_index = builder->num_faces;
  int vert_index = -1;
  for (int i = 0; i < builder->num_vertices; i++) {
    if (simd4f_get_x(
            simd4f_length4_squared(simd4f_sub(builder->vertices[i], vertex)))
        < 1.0e-4) {
      vert_index = i;
      break;
    }
  }

  if (vert_index == -1) {
    vert_index = builder->num_vertices;
    builder->vertices[vert_index] = vertex;
    builder->num_vertices++;
  }

  if (builder->face_vert_idx_end[face_index] == -1) {
    builder->face_vert_idx_end[face_index] =
        builder->face_vert_idx_start[face_index];
  } else {
    builder->face_vert_idx_end[face_index]++;
  }

  int face_end_idx = builder->face_vert_idx_end[face_index];
  builder->face_vert_idx[face_end_idx] = vert_index;
}

void sch_hull_get_plane(const sch_hull* hull, const int index, sch_plane* out_plane) {
  assert(hull != NULL);
  assert(index >= 0 && index < hull->num_faces);
  assert(out_plane != NULL);

  // TODO move plane calculation to create hull?
  sch_face* face = &hull->faces[index];
  sch_edge* edge0 = face->edge;
  sch_edge* edge1 = edge0->next;
  simd4f dir0;
  simd4f dir1;
  sch_edge_get_dir(edge0, &dir0);
  sch_edge_get_dir(edge1, &dir1);

  out_plane->p = edge0->vert->p;
  out_plane->n = simd4f_cross3(dir0, dir1);
}

sch_edge* sch_hull_find_edge (const sch_hull* hull, const simd4f v0, const simd4f v1) {
  for (int fi = 0; fi < hull->num_faces; fi++) {
    sch_face* face = &hull->faces[fi];
    sch_edge* edge0 = face->edge;
    sch_edge* edge = edge0;
    do {
      if (sch_simd4f_equal(edge->vert->p, v0)
          && sch_simd4f_equal(edge->next->vert->p, v1)) {
        return edge;
      }
      edge = edge->next;
    } while (edge != edge0);
  }

  return NULL;
}

void sch_hull_get_support(const sch_hull* hull, simd4f normal, simd4f* out_vert) {
  sch_edge* edge = hull->faces[0].edge;
  sch_edge* last_edge = edge;
  float normal_dot_edge = -1.;

  do {
    simd4f dir = simd4f_normalize3(simd4f_sub (edge->next->vert->p, edge->vert->p));
    normal_dot_edge = simd4f_dot3_scalar(dir, normal);

    if (normal_dot_edge <= 0.) {
      edge = edge->twin->next;
    } else {
      edge = edge->next;
      last_edge = edge;
    }
  } while (last_edge != edge || normal_dot_edge > 0);

  *out_vert = edge->vert->p;
}

float sch_query_face_directions (const sch_hull* hull_A, const sch_hull* hull_B, sch_face_query* result) {
  result->dist = -FLT_MAX;
  for (int fi = 0; fi < hull_A->num_faces; fi++) {
    sch_plane plane;
    sch_hull_get_plane(hull_A, fi, &plane);
    simd4f vert;
    sch_hull_get_support(hull_B, simd4f_sub(simd4f_zero(), plane.n), &vert);
    float distance = sch_plane_distance(&plane, &vert);
    if (distance > result->dist) {
      result->dist = distance;
      result->face_idx = fi;
      result->plane = plane;
      result->vert = vert;
    }
  }

  return result->dist;
}

float sch_query_edge_directions (const sch_hull* hull_A, const sch_hull* hull_B, sch_face_query* result) {
  result->dist = -FLT_MAX;
  for (int iAe = 0; iAe < hull_A->num_edges; iAe++) {
    for (int iBe = 0; iBe < hull_B->num_edges; iBe++) {
      sch_edge* edge_A = &hull_A->edges[iAe];
      sch_edge* edge_B = &hull_B->edges[iBe];
      simd4f dir_A;
      sch_edge_get_dir(edge_A, &dir_A);

      simd4f dir_B;
      sch_edge_get_dir(edge_B, &dir_B);

      simd4f axis = simd4f_cross3 (dir_A, dir_B);
      if (simd4f_dot3_scalar(dir_A, simd4f_sub(edge_A->vert->p, hull_A->center) ) < 0.f) {
        axis = simd4f_sub(simd4f_zero(), axis);
      }

      if (simd4f_get_x(simd4f_length3_squared(axis)) < 0.001) {
        continue;
      }

      axis = simd4f_normalize3(axis);

      sch_plane plane_A;
      plane_A.n = axis;
      // Note: in Gregorius talk he uses the origin of edge_A. This is wrong as
      // there are likely points in hull_A that are further out along the plane
      // normal. We therefore use the support point of hull_A along the axis.
      sch_hull_get_support(hull_A, plane_A.n, &plane_A.p);

      simd4f vert_B;
      sch_hull_get_support(hull_B, simd4f_sub(simd4f_zero(), plane_A.n), &vert_B);

      float distance = sch_plane_distance(&plane_A, &vert_B);
      if (distance > result->dist) {
        result->dist = distance;
        result->plane = plane_A;
        result->vert = vert_B;
      }
    }
  }

  return result->dist;
}

bool sch_hull_sat (const sch_hull* hull_A, const sch_hull* hull_B) {
  sch_face_query query_A_B;
  sch_query_face_directions(hull_A, hull_B, &query_A_B);
  if (query_A_B.dist > 0.f) {
    return true;
  }

  sch_face_query query_B_A;
  sch_query_face_directions(hull_B, hull_A, &query_B_A);
  if (query_B_A.dist > 0.f) {
    return true;
  }

  sch_face_query query_edge;
  sch_query_edge_directions (hull_A, hull_B, &query_edge);
  if (query_edge.dist > 0.f) {
    return true;
  }

  bool is_face_contact_A = query_A_B.dist > query_edge.dist;
  bool is_face_contact_B = query_B_A.dist > query_edge.dist;
  if (is_face_contact_A && is_face_contact_B) {
    // sch_create_face_contact (manifold, &query_A_B, &hull_A, &query_B_A, &hull_B);
  } else {
    // sch_create_edge_contact (manifold, &query_edge, &hull_A, &hull_B);
  }

  return false;
}

int sch_hull_is_vertex_concave(const sch_hull* hull, const simd4f v) {
  sch_plane plane;
  for (int i = 0; i < hull->num_faces; i++) {
    sch_hull_get_plane(hull, i, &plane);
    float distance = sch_plane_distance(&plane, &v);
    return (distance > 0.);
  }

  return 0;
}

int sch_hull_connect_face_edges(const sch_hull* hull, int new_face_index) {
  sch_face* new_face = &hull->faces[new_face_index];

  sch_edge* new_face_edge0 = new_face->edge;
  sch_edge* new_face_edge = new_face_edge0;

  do {
    sch_vert* new_edge_v0 = new_face_edge->vert;
    sch_vert* new_edge_v1 = new_face_edge->next->vert;

    for (int fi = 0; fi < hull->num_faces; fi++) {
      if (fi == new_face_index) {
        continue;
      }

      sch_face* face = &hull->faces[fi];
      sch_edge* face_edge0 = face->edge;
      sch_edge* face_edge = face_edge0;

      do {
        sch_vert* edge_v0 = face_edge->vert;
        sch_vert* edge_v1 = face_edge->next->vert;

        if (sch_simd4f_equal(new_edge_v0->p, edge_v0->p)
            && sch_simd4f_equal(new_edge_v1->p, edge_v1->p)) {
          return SchHullResultWrongWinding;
        } else if (sch_simd4f_equal(new_edge_v0->p, edge_v1->p)
                              && sch_simd4f_equal(new_edge_v1->p, edge_v0->p)) {
          if (new_face_edge->twin == NULL && face_edge->twin == NULL) {
            new_face_edge->twin = face_edge;
            face_edge->twin = new_face_edge;
          } else if (new_face_edge->twin == face_edge->twin) {
            // nothing to do
          } else if ((new_face_edge->twin == NULL && face_edge->twin != NULL)
              || (new_face_edge->twin != NULL && face_edge->twin == NULL)) {
            return SchHullResultInvalidTwinEdges;
          }
        }

        face_edge = face_edge->next;
      } while (face_edge != face_edge0);
    }

    new_face_edge = new_face_edge->next;
  } while (new_face_edge != new_face_edge0);

  return SchHullResultOK;
}

int sch_hull_is_closed (const sch_hull* hull) {
  for (int ei = 0; ei < hull->num_edges; ei++) {
    if (hull->edges[ei].twin == NULL) {
      return SchHullResultOpenHull;
    }
  }

  return SchHullResultOK;
}

void sch_create_unitbox(sch_hull* out_hull) {
  sch_hull_builder builder;
  sch_builder_reset(&builder);

  // +x
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create (0.5f, -0.5f, 0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, 0.5f,  -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create (0.5f, 0.5f,  0.5f, 1.f));
  sch_builder_face_end(&builder);

  // -x
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( -0.5f, -0.5f, 0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( -0.5f, 0.5f,  0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, 0.5f,  -0.5f, 1.f));
  sch_builder_face_end(&builder);

  // +y
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create (0.5f, 0.5f, 0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, 0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( -0.5f, 0.5f,  -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, 0.5f,  0.5f, 1.f));
  sch_builder_face_end(&builder);

  // +y
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, -0.5f,  0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, -0.5f,  0.5f, 1.f));
  sch_builder_face_end(&builder);

  // +z
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, -0.5f, 0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, -0.5f, 0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create ( 0.5f, 0.5f,  0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create (-0.5f, 0.5f,  0.5f, 1.f));
  sch_builder_face_end(&builder);

  // -z
  sch_builder_face_begin(&builder);
  sch_builder_face_vertex(&builder, simd4f_create(0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create(-0.5f, -0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create(-0.5f, 0.5f, -0.5f, 1.f));
  sch_builder_face_vertex(&builder, simd4f_create(0.5f, 0.5f, -0.5f, 1.f));
  sch_builder_face_end(&builder);

  int hull_result = sch_builder_create_hull(&builder, out_hull);
  out_hull->center = simd4f_create(0.f, 0.f, 0.f, 1.f);
  assert (hull_result == SchHullResultOK);
}

#endif /* SCONVCOL_IMPLEMENTATION */

#ifdef __cplusplus
}
#endif

#endif /* SCONVCOL_H */