3d_collision_helpers/src/sc_sacd.cpp

#include "sc_sacd.h"

// Standard library includes.
#include <array>
#include <cmath>
#include <span>
#include <stdfloat>
#include <vector>

// =============================================================================
// Private Helpers BEGIN
// =============================================================================

constexpr float INV_SQRT2 = 0.70710678118654752440F;

SC_SACD_Vec3 operator+(const SC_SACD_Vec3 &a, const SC_SACD_Vec3 &b) {
  return SC_SACD_Vec3{a.x + b.x, a.y + b.y, a.z + b.z};
}

SC_SACD_Vec3 operator-(const SC_SACD_Vec3 &a, const SC_SACD_Vec3 &b) {
  return SC_SACD_Vec3{a.x - b.x, a.y - b.y, a.z - b.z};
}

SC_SACD_Vec3 operator*(const SC_SACD_Vec3 &a, float scalar) {
  return SC_SACD_Vec3{a.x * scalar, a.y * scalar, a.z * scalar};
}

SC_SACD_Vec3 operator/(const SC_SACD_Vec3 &a, float scalar) {
  return SC_SACD_Vec3{a.x / scalar, a.y / scalar, a.z / scalar};
}

SC_SACD_Mat4 operator*(const SC_SACD_Mat4 &a, const SC_SACD_Mat4 &b) {
  SC_SACD_Mat4 mat;

  mat.x0 = b.x0 * a.x0 + b.y0 * a.x1 + b.z0 * a.x2 + b.w0 * a.x3;
  mat.y0 = b.x0 * a.y0 + b.y0 * a.y1 + b.z0 * a.y2 + b.w0 * a.y3;
  mat.z0 = b.x0 * a.z0 + b.y0 * a.z1 + b.z0 * a.z2 + b.w0 * a.z3;
  mat.w0 = b.x0 * a.w0 + b.y0 * a.w1 + b.z0 * a.w2 + b.w0 * a.w3;

  mat.x1 = b.x1 * a.x0 + b.y1 * a.x1 + b.z1 * a.x2 + b.w1 * a.x3;
  mat.y1 = b.x1 * a.y0 + b.y1 * a.y1 + b.z1 * a.y2 + b.w1 * a.y3;
  mat.z1 = b.x1 * a.z0 + b.y1 * a.z1 + b.z1 * a.z2 + b.w1 * a.z3;
  mat.w1 = b.x1 * a.w0 + b.y1 * a.w1 + b.z1 * a.w2 + b.w1 * a.w3;

  mat.x2 = b.x2 * a.x0 + b.y2 * a.x1 + b.z2 * a.x2 + b.w2 * a.x3;
  mat.y2 = b.x2 * a.y0 + b.y2 * a.y1 + b.z2 * a.y2 + b.w2 * a.y3;
  mat.z2 = b.x2 * a.z0 + b.y2 * a.z1 + b.z2 * a.z2 + b.w2 * a.z3;
  mat.w2 = b.x2 * a.w0 + b.y2 * a.w1 + b.z2 * a.w2 + b.w2 * a.w3;

  mat.x3 = b.x3 * a.x0 + b.y3 * a.x1 + b.z3 * a.x2 + b.w3 * a.x3;
  mat.y3 = b.x3 * a.y0 + b.y3 * a.y1 + b.z3 * a.y2 + b.w3 * a.y3;
  mat.z3 = b.x3 * a.z0 + b.y3 * a.z1 + b.z3 * a.z2 + b.w3 * a.z3;
  mat.w3 = b.x3 * a.w0 + b.y3 * a.w1 + b.z3 * a.w2 + b.w3 * a.w3;

  return mat;
}

SC_SACD_Vec3 operator*(const SC_SACD_Mat4 &mat, const SC_SACD_Vec3 &vec) {
  return SC_SACD_Vec3{
      vec.x * mat.x0 + vec.y * mat.x1 + vec.z * mat.x2 + mat.x3,
      vec.x * mat.y0 + vec.y * mat.y1 + vec.z * mat.y2 + mat.y3,
      vec.x * mat.z0 + vec.y * mat.z1 + vec.z * mat.z2 + mat.z3};
}

std::array<SC_SACD_Vec3, 3> SC_SACD_Get_Box_Normals(
    const SC_SACD_Generic_Box *box) {
  SC_SACD_Vec3 a, b, c;

  // Facing positive x-axis.
  a.x = 0.0F;
  a.y = 0.0F;
  a.z = 0.0F;

  b.x = 0.0F;
  b.y = 1.0F;
  b.z = 0.0F;

  c.x = 0.0F;
  c.y = 0.0F;
  c.z = 1.0F;

  a = box->transform * a;
  b = box->transform * b;
  c = box->transform * c;

  b = b - a;
  c = c - a;

  auto normal_x = SC_SACD_Cross_Product(b, c);

  // Facing positive y-axis.
  a.x = 0.0F;
  a.y = 0.0F;
  a.z = 0.0F;

  b.x = 1.0F;
  b.y = 0.0F;
  b.z = 0.0F;

  c.x = 0.0F;
  c.y = 0.0F;
  c.z = -1.0F;

  a = box->transform * a;
  b = box->transform * b;
  c = box->transform * c;

  b = b - a;
  c = c - a;

  auto normal_y = SC_SACD_Cross_Product(b, c);

  // Facing positive z-axis.
  a.x = 0.0F;
  a.y = 0.0F;
  a.z = 0.0F;

  b.x = 0.0F;
  b.y = 1.0F;
  b.z = 0.0F;

  c.x = -1.0F;
  c.y = 0.0F;
  c.z = 0.0F;

  a = box->transform * a;
  b = box->transform * b;
  c = box->transform * c;

  b = b - a;
  c = c - a;

  auto normal_z = SC_SACD_Cross_Product(b, c);

  return {normal_x, normal_y, normal_z};
}

std::array<SC_SACD_Vec3, 3> SC_SACD_Get_Box_Normals_Normalized(
    const SC_SACD_Generic_Box *box) {
  auto normals = SC_SACD_Get_Box_Normals(box);

  for (auto &normal : normals) {
    normal = normal / std::sqrt(SC_SACD_Dot_Product(normal, normal));
  }

  return normals;
}

std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Corners(
    const SC_SACD_Generic_Box *box) {
  std::vector<SC_SACD_Vec3> corners;

  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
                                                  -box->height / 2.0F,
                                                  -box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
                                                  -box->height / 2.0F,
                                                  -box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
                                                  box->height / 2.0F,
                                                  -box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
                                                  box->height / 2.0F,
                                                  -box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
                                                  -box->height / 2.0F,
                                                  box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
                                                  -box->height / 2.0F,
                                                  box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
                                                  box->height / 2.0F,
                                                  box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
                                                  box->height / 2.0F,
                                                  box->depth / 2.0F});
  corners.back().x += box->x;
  corners.back().y += box->y;
  corners.back().z += box->z;

  return corners;
}

struct SC_SACD_MinMax {
  float min, max;
};

std::vector<SC_SACD_MinMax> SC_SACD_Get_Box_MinMax(
    const SC_SACD_Generic_Box *box, const std::span<SC_SACD_Vec3> normals) {
  std::vector<SC_SACD_MinMax> minmaxes;

  std::vector<SC_SACD_Vec3> corners = SC_SACD_Get_Box_Corners(box);

  // Assuming normals are not normalized, and will not normalize anyway.
  // MinMax count should be same as normals count.
  for (const auto &normal : normals) {
    SC_SACD_MinMax minmax{INFINITY, -INFINITY};
    for (const auto &corner : corners) {
      float projected = SC_SACD_Dot_Product(corner, normal);
      if (projected > minmax.max) {
        minmax.max = projected;
      }
      if (projected < minmax.min) {
        minmax.min = projected;
      }
    }
    minmaxes.push_back(minmax);
  }

  return minmaxes;
}

// =============================================================================
// Private Helpers END
// =============================================================================

SC_SACD_Generic_Box SC_SACD_Generic_Box_Default() {
  return {
      0.0F, 0.0F, 0.0F, 2.0F, 2.0F, 2.0F, SC_SACD_Mat4_Identity(),
  };
}

int SC_SACD_AABB_Box_Collision(const SC_SACD_AABB_Box *a,
                               const SC_SACD_AABB_Box *b) {
  float ax_min = a->x - a->width / 2.0F;
  float ax_max = a->x + a->width / 2.0F;
  float ay_min = a->y - a->height / 2.0F;
  float ay_max = a->y + a->height / 2.0F;
  float az_min = a->z - a->depth / 2.0F;
  float az_max = a->z + a->depth / 2.0F;

  float bx_min = b->x - b->width / 2.0F;
  float bx_max = b->x + b->width / 2.0F;
  float by_min = b->y - b->height / 2.0F;
  float by_max = b->y + b->height / 2.0F;
  float bz_min = b->z - b->depth / 2.0F;
  float bz_max = b->z + b->depth / 2.0F;

  return (ax_min < bx_max && ax_max > bx_min && ay_min < by_max &&
          ay_max > by_min && az_min < bz_max && az_max > bz_min)
             ? 1
             : 0;
}

int SC_SACD_Generic_Box_Collision(const SC_SACD_Generic_Box *a,
                                  const SC_SACD_Generic_Box *b) {
  // Get all normals.
  std::vector<SC_SACD_Vec3> normals;
  {
    for (const auto &normal : SC_SACD_Get_Box_Normals(a)) {
      normals.push_back(normal);
    }
    for (const auto &normal : SC_SACD_Get_Box_Normals(b)) {
      normals.push_back(normal);
    }
  }

  // Get all minmaxes.
  std::vector<SC_SACD_MinMax> minmaxes_a = SC_SACD_Get_Box_MinMax(a, normals);
  std::vector<SC_SACD_MinMax> minmaxes_b = SC_SACD_Get_Box_MinMax(b, normals);

  // Check minmaxes.
  for (unsigned int i = 0; i < normals.size(); ++i) {
    if (minmaxes_a[i].max < minmaxes_b[i].min ||
        minmaxes_b[i].max < minmaxes_a[i].min) {
      return 0;
    }
  }

  return 1;
}

int SC_SACD_AABB_Generic_Box_Collision(const SC_SACD_AABB_Box *a,
                                       const SC_SACD_Generic_Box *b) {
  SC_SACD_Generic_Box a_conv;

  a_conv.x = a->x;
  a_conv.y = a->y;
  a_conv.z = a->z;
  a_conv.width = a->width;
  a_conv.height = a->height;
  a_conv.depth = a->depth;
  a_conv.transform = SC_SACD_Mat4_Identity();
  return SC_SACD_Generic_Box_Collision(&a_conv, b);
}

int SC_SACD_Sphere_Collision(const SC_SACD_Sphere *a, const SC_SACD_Sphere *b) {
  SC_SACD_Vec3 vec{a->x - b->x, a->y - b->y, a->z - b->z};

  return (a->radius + b->radius) > std::sqrt(SC_SACD_Dot_Product(vec, vec)) ? 1
                                                                            : 0;
}

int SC_SACD_Sphere_AABB_Box_Collision(const SC_SACD_Sphere *sphere,
                                      const SC_SACD_AABB_Box *box) {
  SC_SACD_Vec3 box_min{
      box->x - box->width / 2.0F,
      box->y - box->height / 2.0F,
      box->z - box->depth / 2.0F,
  };
  SC_SACD_Vec3 box_max{
      box->x + box->width / 2.0F,
      box->y + box->height / 2.0F,
      box->z + box->depth / 2.0F,
  };

  SC_SACD_Vec3 clamped{std::max(box_min.x, std::min(sphere->x, box_max.x)),
                       std::max(box_min.y, std::min(sphere->y, box_max.y)),
                       std::max(box_min.z, std::min(sphere->z, box_max.z))};

  SC_SACD_Vec3 diff = clamped - SC_SACD_Vec3{sphere->x, sphere->y, sphere->z};

  float dist = std::sqrt(SC_SACD_Dot_Product(diff, diff));

  return dist < sphere->radius;
}

int SC_SACD_Sphere_Box_Collision(const SC_SACD_Sphere *sphere,
                                 const SC_SACD_Generic_Box *box) {
  // Adapted from Generic_Box/Generic_Box collision.

  // First check plane where normal = box_pos - sphere_pos.

  SC_SACD_Vec3 sphere_pos{sphere->x, sphere->y, sphere->z};
  std::array<SC_SACD_Vec3, 1> sphere_box_normal = {
      SC_SACD_Vec3{box->x, box->y, box->z} - sphere_pos};
  if (sphere_box_normal[0].x < 0.0001F && sphere_box_normal[0].x > -0.0001F &&
      sphere_box_normal[0].y < 0.0001F && sphere_box_normal[0].y > -0.0001F &&
      sphere_box_normal[0].z < 0.0001F && sphere_box_normal[0].z > -0.0001F) {
    // Sphere center is box center.
    return 1;
  }
  sphere_box_normal[0] =
      sphere_box_normal[0] / std::sqrt(SC_SACD_Dot_Product(
                                 sphere_box_normal[0], sphere_box_normal[0]));

  std::vector<SC_SACD_MinMax> box_minmaxes =
      SC_SACD_Get_Box_MinMax(box, sphere_box_normal);

  float projected_0 = SC_SACD_Dot_Product(
      sphere_box_normal[0], sphere_pos + sphere_box_normal[0] * sphere->radius);
  float projected_1 = SC_SACD_Dot_Product(
      sphere_box_normal[0], sphere_pos - sphere_box_normal[0] * sphere->radius);
  if (projected_0 < projected_1) {
    if (box_minmaxes[0].max < projected_0 ||
        box_minmaxes[0].min > projected_1) {
      return 0;
    }
  } else if (box_minmaxes[0].max < projected_1 ||
             box_minmaxes[0].min > projected_0) {
    return 0;
  }

  // Next check the planes for the 3 normals of the box.

  auto box_normals = SC_SACD_Get_Box_Normals(box);
  box_minmaxes = SC_SACD_Get_Box_MinMax(box, box_normals);
  for (unsigned int i = 0; i < box_normals.size(); ++i) {
    projected_0 = SC_SACD_Dot_Product(
        box_normals[i], sphere_pos + box_normals[i] * sphere->radius);
    projected_1 = SC_SACD_Dot_Product(
        box_normals[i], sphere_pos - box_normals[i] * sphere->radius);
    if (projected_0 < projected_1) {
      if (box_minmaxes[i].max < projected_0 ||
          box_minmaxes[i].min > projected_1) {
        return 0;
      }
    } else if (box_minmaxes[i].max < projected_1 ||
               box_minmaxes[i].min > projected_0) {
      return 0;
    }
  }

  return 1;
}

float SC_SACD_Dot_Product(const SC_SACD_Vec3 a, const SC_SACD_Vec3 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}

SC_SACD_Vec3 SC_SACD_Cross_Product(const SC_SACD_Vec3 a, const SC_SACD_Vec3 b) {
  return SC_SACD_Vec3{a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z,
                      a.x * b.y - a.y * b.x};
}

SC_SACD_Mat4 SC_SACD_Mat4_Identity(void) {
  return SC_SACD_Mat4{1.0F, 0.0F, 0.0F, 0.0F, 0.0F, 1.0F, 0.0F, 0.0F,
                      0.0F, 0.0F, 1.0F, 0.0F, 0.0F, 0.0F, 0.0F, 1.0F};
}

SC_SACD_Mat4 SC_SACD_Mat4_Mult(const SC_SACD_Mat4 *a, const SC_SACD_Mat4 *b) {
  return (*a) * (*b);
}

SC_SACD_Vec3 SC_SACD_Mat4_Vec3_Mult(const SC_SACD_Mat4 *mat,
                                    const SC_SACD_Vec3 vec) {
  return (*mat) * vec;
}

SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec, float x_axis,
                                 float y_axis, float z_axis) {
  /*
   * z_axis counter-clockwise affects x and y.
   * [  cos, -sin, 0 ]
   * [  sin,  cos, 0 ]
   * [  0,    0,   1 ]
   *
   * x_axis counter-clockwise affects y and z.
   * [ 1,    0,    0 ]
   * [ 0,  cos, -sin ]
   * [ 0,  sin,  cos ]
   *
   * y_axis counter-clockwise affects x and z.
   * [  cos, 0, sin ]
   * [    0, 1,   0 ]
   * [ -sin, 0, cos ]
   */

  SC_SACD_Mat4 mat;
  SC_SACD_Vec3 result;

  // About x_axis.
  mat = SC_SACD_Rotation_Mat4_XAxis(x_axis);

  result = SC_SACD_Mat4_Vec3_Mult(&mat, vec);

  // About y_axis.
  mat = SC_SACD_Rotation_Mat4_YAxis(y_axis);

  result = SC_SACD_Mat4_Vec3_Mult(&mat, result);

  // About z_axis.
  mat = SC_SACD_Rotation_Mat4_ZAxis(z_axis);

  return SC_SACD_Mat4_Vec3_Mult(&mat, result);
}

SC_SACD_Mat4 SC_SACD_Rotation_Mat4_XAxis(float x_radians) {
  SC_SACD_Mat4 mat;

  mat.x0 = 1.0F;
  mat.x1 = 0.0F;
  mat.x2 = 0.0F;
  mat.x3 = 0.0F;

  mat.y0 = 0.0F;
  mat.y1 = std::cos(x_radians);
  mat.y2 = -std::sin(x_radians);
  mat.y3 = 0.0F;

  mat.z0 = 0.0F;
  mat.z1 = -mat.y2;
  mat.z2 = mat.y1;
  mat.z3 = 0.0F;

  mat.w0 = 0.0F;
  mat.w1 = 0.0F;
  mat.w2 = 0.0F;
  mat.w3 = 1.0F;

  return mat;
}

SC_SACD_Mat4 SC_SACD_Rotation_Mat4_YAxis(float y_radians) {
  SC_SACD_Mat4 mat;

  mat.x0 = std::cos(y_radians);
  mat.x1 = 0.0F;
  mat.x2 = std::sin(y_radians);
  mat.x3 = 0.0F;

  mat.y0 = 0.0F;
  mat.y1 = 1.0F;
  mat.y2 = 0.0F;
  mat.y3 = 0.0F;

  mat.z0 = -mat.x2;
  mat.z1 = 0.0F;
  mat.z2 = mat.x0;
  mat.z3 = 0.0F;

  mat.w0 = 0.0F;
  mat.w1 = 0.0F;
  mat.w2 = 0.0F;
  mat.w3 = 1.0F;

  return mat;
}

SC_SACD_Mat4 SC_SACD_Rotation_Mat4_ZAxis(float z_radians) {
  SC_SACD_Mat4 mat;

  mat.x0 = std::cos(z_radians);
  mat.x1 = -std::sin(z_radians);
  mat.x2 = 0.0F;
  mat.x3 = 0.0F;

  mat.y0 = -mat.x1;
  mat.y1 = mat.x0;
  mat.y2 = 0.0F;
  mat.y3 = 0.0F;

  mat.z0 = 0.0F;
  mat.z1 = 0.0F;
  mat.z2 = 1.0F;
  mat.z3 = 0.0F;

  mat.w0 = 0.0F;
  mat.w1 = 0.0F;
  mat.w2 = 0.0F;
  mat.w3 = 1.0F;

  return mat;
}

SC_SACD_Mat4 SC_SACD_Translate_Mat4(float x, float y, float z) {
  return SC_SACD_Mat4{1.0F, 0.0F, 0.0F, x, 0.0F, 1.0F, 0.0F, y,
                      0.0F, 0.0F, 1.0F, z, 0.0F, 0.0F, 0.0F, 1.0F};
}

SC_SACD_Vec3 SC_SACD_Closest_Point_Dir_Normalized(const SC_SACD_Vec3 *pos,
                                                  const SC_SACD_Vec3 *dir,
                                                  const SC_SACD_Vec3 *point) {
  float alpha =
      SC_SACD_Dot_Product(*dir, *point) - SC_SACD_Dot_Product(*dir, *pos);
  return *pos + *dir * alpha;
}

SC_SACD_Vec3 SC_SACD_Closest_Point(const SC_SACD_Vec3 *pos,
                                   const SC_SACD_Vec3 *dir,
                                   const SC_SACD_Vec3 *point) {
  float alpha =
      (SC_SACD_Dot_Product(*dir, *point) - SC_SACD_Dot_Product(*dir, *pos)) /
      SC_SACD_Dot_Product(*dir, *dir);
  return *pos + *dir * alpha;
}

float SC_SACD_Vec3_Length(const SC_SACD_Vec3 vec) {
  return std::sqrt(SC_SACD_Dot_Product(vec, vec));
}