Merge branch 'dev', Version 2.0.0

CMakeLists.txt

@@ -6,7 +6,7 @@ set(SC_3D_CollisionDetectionHelpers_HEADERS "${CMAKE_CURRENT_SOURCE_DIR}/src/sc_
 
 add_library(SC_3D_CollisionDetectionHelpers ${SC_3D_CollisionDetectionHelpers_SOURCES})
 
-set_target_properties(SC_3D_CollisionDetectionHelpers PROPERTIES VERSION 1.0.0 SOVERSION 1)
+set_target_properties(SC_3D_CollisionDetectionHelpers PROPERTIES VERSION 2.0.0 SOVERSION 2)
 
 if(NOT DEFINED CMAKE_BUILD_TYPE OR "${CMAKE_BUILD_TYPE}" STREQUAL "")
     message("Defaulting to \"Debug\" build type.")

Changelog.md

@@ -1,5 +1,15 @@
 # Changelog
 
+## Version 2.0.0
+
+Add collision detection with Spheres.
+
+Add some more vector/matrix math stuff.
+
+Replace Mat3 with Mat4.
+
+Replace xyz-axis rotation floats in GenericBox with Mat4.
+
 ## Version 1.0.0
 
 First version of this library.

src/sc_sacd.cpp

@@ -9,27 +9,89 @@
 // 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::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Normals(
     const SC_SACD_Generic_Box *box) {
   std::vector<SC_SACD_Vec3> normals;
 
   normals.emplace_back(SC_SACD_Vec3{1.0F, 0.0F, 0.0F});
-  normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
+  normals.back() = box->transform * normals.back();
-                                       box->y_radians, box->z_radians);
 
   normals.emplace_back(SC_SACD_Vec3{0.0F, 1.0F, 0.0F});
-  normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
+  normals.back() = box->transform * normals.back();
-                                       box->y_radians, box->z_radians);
 
   normals.emplace_back(SC_SACD_Vec3{0.0F, 0.0F, 1.0F});
-  normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
+  normals.back() = box->transform * normals.back();
-                                       box->y_radians, box->z_radians);
+
+  return normals;
+}
+
+std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Normals_Normalized(
+    const SC_SACD_Generic_Box *box) {
+  std::vector<SC_SACD_Vec3> normals;
+
+  normals.emplace_back(SC_SACD_Vec3{1.0F, 0.0F, 0.0F});
+  normals.back() = box->transform * normals.back();
+  normals.back() = normals.back() / SC_SACD_Vec3_Length(normals.back());
+
+  normals.emplace_back(SC_SACD_Vec3{0.0F, 1.0F, 0.0F});
+  normals.back() = box->transform * normals.back();
+  normals.back() = normals.back() / SC_SACD_Vec3_Length(normals.back());
+
+  normals.emplace_back(SC_SACD_Vec3{0.0F, 0.0F, 1.0F});
+  normals.back() = box->transform * normals.back();
+  normals.back() = normals.back() / SC_SACD_Vec3_Length(normals.back());
 
-  // Not normalizing the normals on purpose for optimization. (No unit vectors.)
   return normals;
 }
 
@@ -37,55 +99,61 @@ std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Corners(
     const SC_SACD_Generic_Box *box) {
   std::vector<SC_SACD_Vec3> corners;
 
-  SC_SACD_Vec3 pos{box->x, box->y, 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(
+  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, -box->height / 2.0F,
+                                                  -box->height / 2.0F,
-                                       -box->depth / 2.0F},
+                                                  -box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, -box->height / 2.0F,
+                                                  box->height / 2.0F,
-                                       -box->depth / 2.0F},
+                                                  -box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, box->height / 2.0F,
+                                                  box->height / 2.0F,
-                                       -box->depth / 2.0F},
+                                                  -box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, box->height / 2.0F,
+                                                  -box->height / 2.0F,
-                                       -box->depth / 2.0F},
+                                                  box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, -box->height / 2.0F,
+                                                  -box->height / 2.0F,
-                                       box->depth / 2.0F},
+                                                  box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{-box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, -box->height / 2.0F,
+                                                  box->height / 2.0F,
-                                       box->depth / 2.0F},
+                                                  box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
+  corners.back().z += box->z;
 
-  corners.push_back(
+  corners.push_back(box->transform * SC_SACD_Vec3{box->width / 2.0F,
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, box->height / 2.0F,
+                                                  box->height / 2.0F,
-                                       box->depth / 2.0F},
+                                                  box->depth / 2.0F});
-                          box->x_radians, box->y_radians, box->z_radians) +
+  corners.back().x += box->x;
-      pos);
+  corners.back().y += box->y;
-
+  corners.back().z += box->z;
-  corners.push_back(
-      SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, box->height / 2.0F,
-                                       box->depth / 2.0F},
-                          box->x_radians, box->y_radians, box->z_radians) +
-      pos);
 
   return corners;
 }
@@ -123,6 +191,12 @@ std::vector<SC_SACD_MinMax> SC_SACD_Get_Box_MinMax(
 // 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;
@@ -178,12 +252,96 @@ int SC_SACD_AABB_Generic_Box_Collision(const SC_SACD_AABB_Box *a,
   a_conv.width = a->width;
   a_conv.height = a->height;
   a_conv.depth = a->depth;
-  a_conv.x_radians = 0.0F;
+  a_conv.transform = SC_SACD_Mat4_Identity();
-  a_conv.y_radians = 0.0F;
-  a_conv.z_radians = 0.0F;
   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};
+  SC_SACD_Vec3 sphere_box_normal =
+      SC_SACD_Vec3{box->x, box->y, box->z} - sphere_pos;
+  sphere_box_normal =
+      sphere_box_normal /
+      std::sqrt(SC_SACD_Dot_Product(sphere_box_normal, sphere_box_normal));
+
+  std::vector<SC_SACD_Vec3> normals{sphere_box_normal};
+
+  std::vector<SC_SACD_MinMax> box_minmaxes =
+      SC_SACD_Get_Box_MinMax(box, normals);
+
+  float projected_0 = SC_SACD_Dot_Product(
+      sphere_box_normal, sphere_pos + sphere_box_normal * sphere->radius);
+  float projected_1 = SC_SACD_Dot_Product(
+      sphere_box_normal, sphere_pos - sphere_box_normal * 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.
+
+  normals = SC_SACD_Get_Box_Normals(box);
+  box_minmaxes = SC_SACD_Get_Box_MinMax(box, normals);
+  for (unsigned int i = 0; i < normals.size(); ++i) {
+    projected_0 = SC_SACD_Dot_Product(normals[i],
+                                      sphere_pos + normals[i] * sphere->radius);
+    projected_1 = SC_SACD_Dot_Product(normals[i],
+                                      sphere_pos - 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;
 }
@@ -193,13 +351,18 @@ SC_SACD_Vec3 SC_SACD_Cross_Product(const SC_SACD_Vec3 a, const SC_SACD_Vec3 b) {
                       a.x * b.y - a.y * b.x};
 }
 
-SC_SACD_Vec3 SC_SACD_Mat3_Vec3_Mult(const SC_SACD_Mat3 *mat,
+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 SC_SACD_Vec3{
+  return (*mat) * vec;
-      vec.x * mat->x0 + vec.y * mat->y0 + vec.z * mat->z0,
-      vec.x * mat->x1 + vec.y * mat->y1 + vec.z * mat->z1,
-      vec.x * mat->x2 + vec.y * mat->y2 + vec.z * mat->z2,
-  };
 }
 
 SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec, float x_axis,
@@ -221,45 +384,125 @@ SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec, float x_axis,
    * [ -sin, 0, cos ]
    */
 
-  SC_SACD_Mat3 mat;
+  SC_SACD_Mat4 mat;
   SC_SACD_Vec3 result;
 
   // About x_axis.
-  mat.x0 = 1.0F;
+  mat = SC_SACD_Rotation_Mat4_XAxis(x_axis);
-  mat.y0 = 0.0F;
-  mat.z0 = 0.0F;
-  mat.x1 = 0.0F;
-  mat.y1 = std::cos(x_axis);
-  mat.z1 = -std::sin(x_axis);
-  mat.x2 = 0.0F;
-  mat.y2 = -mat.z1;
-  mat.z2 = mat.y1;
 
-  result = SC_SACD_Mat3_Vec3_Mult(&mat, vec);
+  result = SC_SACD_Mat4_Vec3_Mult(&mat, vec);
 
   // About y_axis.
-  mat.x0 = std::cos(y_axis);
+  mat = SC_SACD_Rotation_Mat4_YAxis(y_axis);
-  mat.y0 = 0.0F;
-  mat.z0 = std::sin(y_axis);
-  mat.x1 = 0.0F;
-  mat.y1 = 1.0F;
-  mat.z1 = 0.0F;
-  mat.x2 = -mat.z0;
-  mat.y2 = 0.0F;
-  mat.z2 = mat.x0;
 
-  result = SC_SACD_Mat3_Vec3_Mult(&mat, result);
+  result = SC_SACD_Mat4_Vec3_Mult(&mat, result);
 
   // About z_axis.
-  mat.x0 = std::cos(z_axis);
+  mat = SC_SACD_Rotation_Mat4_ZAxis(z_axis);
-  mat.y0 = -std::sin(z_axis);
-  mat.z0 = 0.0F;
-  mat.x1 = -mat.y0;
-  mat.y1 = mat.x0;
-  mat.z1 = 0.0F;
-  mat.x2 = 0.0F;
-  mat.y2 = 0.0F;
-  mat.z2 = 1.0F;
 
-  return SC_SACD_Mat3_Vec3_Mult(&mat, result);
+  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{0.0F, 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));
 }

src/sc_sacd.h

@@ -24,11 +24,12 @@ typedef struct SC_SACD_EXPORT SC_SACD_Vec3 {
   float x, y, z;
 } SC_SACD_Vec3;
 
-typedef struct SC_SACD_EXPORT SC_SACD_Mat3 {
+typedef struct SC_SACD_EXPORT SC_SACD_Mat4 {
-  float x0, y0, z0;
+  float x0, x1, x2, x3;
-  float x1, y1, z1;
+  float y0, y1, y2, y3;
-  float x2, y2, z2;
+  float z0, z1, z2, z3;
-} SC_SACD_Mat3;
+  float w0, w1, w2, w3;
+} SC_SACD_Mat4;
 
 typedef struct SC_SACD_EXPORT SC_SACD_AABB_Box {
   /// Coordinates are to center of box.
@@ -43,6 +44,7 @@ typedef struct SC_SACD_EXPORT SC_SACD_AABB_Box {
   float depth;
 } SC_SACD_AABB_Box;
 
+/// Must not be zero initialized. Use SC_SACD_Generix_Box_Default() instead.
 typedef struct SC_SACD_EXPORT SC_SACD_Generic_Box {
   /// Coordinates are to center of box.
   float x;
@@ -54,12 +56,20 @@ typedef struct SC_SACD_EXPORT SC_SACD_Generic_Box {
   float height;
   /// z-axis depth.
   float depth;
-  /// Rotation about center of box about axis.
+  /// Local transform; expects center of box as origin.
-  float x_radians;
+  SC_SACD_Mat4 transform;
-  float y_radians;
-  float z_radians;
 } SC_SACD_Generic_Box;
 
+typedef struct SC_SACD_EXPORT SC_SACD_Sphere {
+  float x;
+  float y;
+  float z;
+  float radius;
+} SC_SACD_Sphere;
+
+/// Returns a box at origin with width/height/depth of 2 each.
+SC_SACD_EXPORT SC_SACD_Generic_Box SC_SACD_Generic_Box_Default(void);
+
 /// Returns non-zero if there is collision.
 SC_SACD_EXPORT int SC_SACD_AABB_Box_Collision(const SC_SACD_AABB_Box *a,
                                               const SC_SACD_AABB_Box *b);
@@ -72,19 +82,55 @@ SC_SACD_EXPORT int SC_SACD_Generic_Box_Collision(const SC_SACD_Generic_Box *a,
 SC_SACD_EXPORT int SC_SACD_AABB_Generic_Box_Collision(
     const SC_SACD_AABB_Box *a, const SC_SACD_Generic_Box *b);
 
+/// Returns non-zero if there is collision.
+SC_SACD_EXPORT int SC_SACD_Sphere_Collision(const SC_SACD_Sphere *a,
+                                            const SC_SACD_Sphere *b);
+
+/// Returns non-zero if there is collision.
+SC_SACD_EXPORT int SC_SACD_Sphere_AABB_Box_Collision(
+    const SC_SACD_Sphere *sphere, const SC_SACD_AABB_Box *box);
+
+/// Returns non-zero if there is collision.
+SC_SACD_EXPORT int SC_SACD_Sphere_Box_Collision(const SC_SACD_Sphere *sphere,
+                                                const SC_SACD_Generic_Box *box);
+
 SC_SACD_EXPORT float SC_SACD_Dot_Product(const SC_SACD_Vec3 a,
                                          const SC_SACD_Vec3 b);
 
 SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Cross_Product(const SC_SACD_Vec3 a,
                                                   const SC_SACD_Vec3 b);
 
-SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Mat3_Vec3_Mult(const SC_SACD_Mat3 *mat,
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Mat4_Identity(void);
+
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Mat4_Mult(const SC_SACD_Mat4 *a,
+                                              const SC_SACD_Mat4 *b);
+
+SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Mat4_Vec3_Mult(const SC_SACD_Mat4 *mat,
                                                    const SC_SACD_Vec3 vec);
 
+/// Rotates by x-axis first, then y-axis, then finally z-axis.
 SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec,
                                                 float x_axis, float y_axis,
                                                 float z_axis);
 
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Rotation_Mat4_XAxis(float x_radians);
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Rotation_Mat4_YAxis(float y_radians);
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Rotation_Mat4_ZAxis(float z_radians);
+
+SC_SACD_EXPORT SC_SACD_Mat4 SC_SACD_Translate_Mat4(float x, float y, float z);
+
+/// This variant of Closest_Point expects "dir" to be a unit vector.
+SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Closest_Point_Dir_Normalized(
+    const SC_SACD_Vec3 *pos, const SC_SACD_Vec3 *dir,
+    const SC_SACD_Vec3 *point);
+
+/// This variant of Closest_Point expects "dir" to NOT be a unit vector.
+SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Closest_Point(const SC_SACD_Vec3 *pos,
+                                                  const SC_SACD_Vec3 *dir,
+                                                  const SC_SACD_Vec3 *point);
+
+SC_SACD_EXPORT float SC_SACD_Vec3_Length(const SC_SACD_Vec3 vec);
+
 #ifdef __cplusplus
 }
 #endif

src/test.cpp

@@ -1,3 +1,4 @@
+#include <cmath>
 #include <iostream>
 #include <numbers>
 
@@ -25,6 +26,16 @@ static int checks_passed = 0;
     }                                                                  \
   } while (false);
 
+#define CHECK_FLOAT(var, value)                                        \
+  do {                                                                 \
+    ++checks_checked;                                                  \
+    if ((var) > (value)-0.0001F && (var) < (value) + 0.0001F) {        \
+      ++checks_passed;                                                 \
+    } else {                                                           \
+      std::cout << "CHECK_FLOAT at line " << __LINE__ << " failed!\n"; \
+    }                                                                  \
+  } while (false);
+
 #include "sc_sacd.h"
 
 int main() {
@@ -85,8 +96,10 @@ int main() {
 
   // Test Separating_Axis_Collision check.
   {
-    SC_SACD_Generic_Box a{0.0F, 0.0F, 0.0F, 1.0F, 1.0F, 1.0F, 0.0F, 0.0F, 0.0F};
+    SC_SACD_Generic_Box a{
-    SC_SACD_Generic_Box b{0.0F, 0.0F, 0.0F, 1.0F, 1.0F, 1.0F, 0.0F, 0.0F, 0.0F};
+        0.0F, 0.0F, 0.0F, 1.0F, 1.0F, 1.0F, SC_SACD_Mat4_Identity()};
+    SC_SACD_Generic_Box b{
+        0.0F, 0.0F, 0.0F, 1.0F, 1.0F, 1.0F, SC_SACD_Mat4_Identity()};
 
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
 
@@ -95,44 +108,468 @@ int main() {
     b.x = -1.1F;
     CHECK_FALSE(SC_SACD_Generic_Box_Collision(&a, &b));
 
-    a.z_radians = std::numbers::pi_v<float> / 4.0F;
+    a.transform = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F);
-    b.z_radians = a.z_radians;
+    b.transform = a.transform;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
     b.x = 1.1F;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
 
     b.x = 0.0F;
     b.y = 1.1F;
-    a.z_radians = 0.0F;
+    a.transform = SC_SACD_Mat4_Identity();
-    b.z_radians = 0.0F;
+    b.transform = a.transform;
     CHECK_FALSE(SC_SACD_Generic_Box_Collision(&a, &b));
     b.y = -1.1F;
     CHECK_FALSE(SC_SACD_Generic_Box_Collision(&a, &b));
 
-    a.z_radians = std::numbers::pi_v<float> / 4.0F;
+    a.transform = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F);
-    b.z_radians = a.z_radians;
+    b.transform = a.transform;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
     b.y = 1.1F;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
 
     b.y = 0.0F;
-    a.z_radians = 0.0F;
+    a.transform = SC_SACD_Mat4_Identity();
-    b.z_radians = 0.0F;
+    b.transform = a.transform;
 
     b.z = 1.1F;
     CHECK_FALSE(SC_SACD_Generic_Box_Collision(&a, &b));
     b.z = -1.1F;
     CHECK_FALSE(SC_SACD_Generic_Box_Collision(&a, &b));
 
-    a.y_radians = std::numbers::pi_v<float> / 4.0F;
+    a.transform = SC_SACD_Rotation_Mat4_YAxis(std::numbers::pi_v<float> / 4.0F);
-    b.y_radians = a.y_radians;
+    b.transform = a.transform;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
     b.z = 1.1F;
     CHECK_TRUE(SC_SACD_Generic_Box_Collision(&a, &b));
   }
 
+  // Test Sphere/Sphere collision check.
+  {
+    SC_SACD_Sphere a{0.0F, 0.0F, 0.0F, 1.0F};
+    SC_SACD_Sphere b{0.0F, 0.0F, 0.0F, 1.0F};
+    CHECK_TRUE(SC_SACD_Sphere_Collision(&a, &b));
+
+    a.x = 10.0F;
+    a.y = 10.0F;
+    a.z = 10.0F;
+    b.x = 10.0F;
+    b.y = 10.5F;
+    b.z = 10.0F;
+    CHECK_TRUE(SC_SACD_Sphere_Collision(&a, &b));
+    b.y = 12.0F;
+    b.z = 12.0F;
+    CHECK_FALSE(SC_SACD_Sphere_Collision(&a, &b));
+    b.y = 11.0F;
+    b.z = 11.0F;
+    CHECK_TRUE(SC_SACD_Sphere_Collision(&a, &b));
+  }
+
+  // Test Sphere/AABB collision check.
+  {
+    SC_SACD_Sphere sphere{0.0F, 0.0F, 0.0F, 1.0F};
+    SC_SACD_AABB_Box box{0.0F, 0.0F, 0.0F, 2.0F, 2.0F, 2.0F};
+
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = -2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 0.0F;
+    sphere.y = 2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.y = -2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.y = 0.0F;
+    sphere.z = 2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.z = -2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.z = 0.0F;
+    sphere.x = 1.0F;
+    sphere.y = 1.0F;
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = -1.0F;
+    sphere.y = -1.0F;
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.0F;
+    sphere.y = 2.0F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = -2.0F;
+    sphere.y = -2.0F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 1.0F;
+    sphere.y = 0.0F;
+    sphere.z = 1.0F;
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = -1.0F;
+    sphere.z = -1.0F;
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.0F;
+    sphere.z = 2.0F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = -2.0F;
+    sphere.z = -2.0F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 1.0F;
+    sphere.z = 1.5F;
+    CHECK_TRUE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+
+    sphere.x = 1.0F;
+    sphere.z = 2.0F;
+    CHECK_FALSE(SC_SACD_Sphere_AABB_Box_Collision(&sphere, &box));
+  }
+
+  // Test Sphere/Generic_Box collision check.
+  {
+    SC_SACD_Sphere sphere{0.0F, 0.0F, 0.0F, 1.0F};
+    SC_SACD_Generic_Box box{
+        0.0F,
+        0.0F,
+        0.0F,
+        2.0F,
+        2.0F,
+        2.0F,
+        SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F)};
+
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = -2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = -2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 0.0F;
+    sphere.y = 2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = -2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = 2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = -2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.y = 0.0F;
+    sphere.z = 2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = -2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = 1.9F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = -1.9F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 1.5F;
+    sphere.y = 1.5F;
+    sphere.z = 0.0F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 1.4F;
+    sphere.y = 1.4F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.2F;
+    sphere.y = 0.7929F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 2.1F;
+    sphere.y = 0.6929F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = -1.5F;
+    sphere.y = -1.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = -1.4F;
+    sphere.y = -1.4F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = -2.2F;
+    sphere.y = -0.7929F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = -2.1F;
+    sphere.y = -0.6929F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    box.x = 10.0F;
+    box.y = -10.0F;
+    box.z = 13.0F;
+
+    sphere.y = -10.0F;
+    sphere.z = 13.0F;
+    sphere.x = 10.0F + 2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 10.0F + -2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 10.0F + 2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 10.0F + -2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + 0.0F;
+    sphere.y = -10.0F + 2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = -10.0F + -2.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = -10.0F + 2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.y = -10.0F + -2.3F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.y = -10.0F + 0.0F;
+    sphere.z = 13.0F + 2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = 13.0F + -2.1F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = 13.0F + 1.9F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.z = 13.0F + -1.9F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + 1.5F;
+    sphere.y = -10.0F + 1.5F;
+    sphere.z = 13.0F + 0.0F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 10.0F + 1.4F;
+    sphere.y = -10.0F + 1.4F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + 2.2F;
+    sphere.y = -10.0F + 0.7929F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + 2.1F;
+    sphere.y = -10.0F + 0.6929F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + -1.5F;
+    sphere.y = -10.0F + -1.5F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+    sphere.x = 10.0F + -1.4F;
+    sphere.y = -10.0F + -1.4F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + -2.2F;
+    sphere.y = -10.0F + -0.7929F;
+    CHECK_FALSE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+
+    sphere.x = 10.0F + -2.1F;
+    sphere.y = -10.0F + -0.6929F;
+    CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
+  }
+
+  // Test matrix/vector multiplication.
+  {
+    SC_SACD_Mat4 mat_a{1.0F, 2.0F,  3.0F,  4.0F,  5.0F,  6.0F,  7.0F,  8.0F,
+                       9.0F, 10.0F, 11.0F, 12.0F, 13.0F, 14.0F, 15.0F, 16.0F};
+
+    SC_SACD_Mat4 mat_b = SC_SACD_Mat4_Identity();
+
+    {
+      auto result = SC_SACD_Mat4_Mult(&mat_a, &mat_b);
+      CHECK_TRUE(mat_a.x0 == result.x0);
+      CHECK_TRUE(mat_a.x1 == result.x1);
+      CHECK_TRUE(mat_a.x2 == result.x2);
+      CHECK_TRUE(mat_a.x3 == result.x3);
+      CHECK_TRUE(mat_a.y0 == result.y0);
+      CHECK_TRUE(mat_a.y1 == result.y1);
+      CHECK_TRUE(mat_a.y2 == result.y2);
+      CHECK_TRUE(mat_a.y3 == result.y3);
+      CHECK_TRUE(mat_a.z0 == result.z0);
+      CHECK_TRUE(mat_a.z1 == result.z1);
+      CHECK_TRUE(mat_a.z2 == result.z2);
+      CHECK_TRUE(mat_a.z3 == result.z3);
+      CHECK_TRUE(mat_a.w0 == result.w0);
+      CHECK_TRUE(mat_a.w1 == result.w1);
+      CHECK_TRUE(mat_a.w2 == result.w2);
+      CHECK_TRUE(mat_a.w3 == result.w3);
+    }
+
+    mat_b.x0 = 2.0F;
+    mat_b.y1 = 0.0F;
+    mat_b.z2 = 0.0F;
+    {
+      auto result = SC_SACD_Mat4_Mult(&mat_a, &mat_b);
+      CHECK_FLOAT(result.x0, 2.0F);
+      CHECK_FLOAT(result.y0, 10.0F);
+      CHECK_FLOAT(result.z0, 18.0F);
+      CHECK_FLOAT(result.w0, 26.0F);
+      CHECK_FLOAT(result.x1, 0.0F);
+      CHECK_FLOAT(result.y1, 0.0F);
+      CHECK_FLOAT(result.z1, 0.0F);
+      CHECK_FLOAT(result.w1, 0.0F);
+      CHECK_FLOAT(result.x2, 0.0F);
+      CHECK_FLOAT(result.y2, 0.0F);
+      CHECK_FLOAT(result.z2, 0.0F);
+      CHECK_FLOAT(result.w2, 0.0F);
+      CHECK_FLOAT(result.x3, 4.0F);
+      CHECK_FLOAT(result.y3, 8.0F);
+      CHECK_FLOAT(result.z3, 12.0F);
+      CHECK_FLOAT(result.w3, 16.0F);
+    }
+
+    mat_b = SC_SACD_Mat4_Identity();
+    SC_SACD_Vec3 vec_a{1.0F, 0.0F, 0.0F};
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_b, vec_a);
+      CHECK_TRUE(result.x == vec_a.x);
+      CHECK_TRUE(result.y == vec_a.y);
+      CHECK_TRUE(result.z == vec_a.z);
+    }
+
+    // Rotations about each axis.
+    mat_a = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 2.0F);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < 1.0001F && result.y > 0.9999F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    mat_a = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < -0.9999F && result.x > -1.0001F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    mat_a =
+        SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < -0.9999F && result.y > -1.0001F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    mat_a = SC_SACD_Rotation_Mat4_XAxis(std::numbers::pi_v<float> / 2.0F);
+    vec_a.x = 0.0F;
+    vec_a.y = 1.0F;
+    vec_a.z = 0.0F;
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < 1.0001F && result.z > 0.9999F);
+    }
+
+    mat_a = SC_SACD_Rotation_Mat4_XAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < -0.9999F && result.y > -1.0001F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    mat_a =
+        SC_SACD_Rotation_Mat4_XAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < -0.9999F && result.z > -1.0001F);
+    }
+
+    mat_a = SC_SACD_Rotation_Mat4_YAxis(std::numbers::pi_v<float> / 2.0F);
+    vec_a.x = 0.0F;
+    vec_a.y = 0.0F;
+    vec_a.z = 1.0F;
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 1.0001F && result.x > 0.9999F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    mat_a = SC_SACD_Rotation_Mat4_YAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < 0.0001F && result.x > -0.0001F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < -0.9999F && result.z > -1.0001F);
+    }
+
+    mat_a =
+        SC_SACD_Rotation_Mat4_YAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_TRUE(result.x < -0.9999F && result.x > -1.0001F);
+      CHECK_TRUE(result.y < 0.0001F && result.y > -0.0001F);
+      CHECK_TRUE(result.z < 0.0001F && result.z > -0.0001F);
+    }
+
+    // Combined axis rotation.
+    vec_a.x = 1.0F;
+    vec_a.y = 0.0F;
+    vec_a.z = 0.0F;
+    mat_a = SC_SACD_Rotation_Mat4_YAxis(std::numbers::pi_v<float> / 4.0F);
+    mat_b = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F);
+    // Apply mat_a, then mat_b.
+    mat_a = SC_SACD_Mat4_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_FLOAT(result.x, 0.5F);
+      CHECK_FLOAT(result.y, 0.5F);
+      CHECK_FLOAT(result.z, -std::sqrt(2.0F) / 2.0F);
+    }
+    // Apply another rotation on combined mat_a.
+    mat_b = SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F);
+    mat_a = SC_SACD_Mat4_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_FLOAT(result.x, 0.0F);
+      CHECK_FLOAT(result.y, std::sqrt(2.0F) / 2.0F);
+      CHECK_FLOAT(result.z, -std::sqrt(2.0F) / 2.0F);
+    }
+    // Apply another rotation on combined mat_a.
+    mat_b = SC_SACD_Rotation_Mat4_XAxis(std::numbers::pi_v<float> / 2.0F);
+    mat_a = SC_SACD_Mat4_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat4_Vec3_Mult(&mat_a, vec_a);
+      CHECK_FLOAT(result.x, 0.0F);
+      CHECK_FLOAT(result.y, std::sqrt(2.0F) / 2.0F);
+      CHECK_FLOAT(result.z, std::sqrt(2.0F) / 2.0F);
+    }
+  }
+
+  // Mat4 rotation and translation.
+  {
+    SC_SACD_Mat4 mat_a = SC_SACD_Translate_Mat4(1.0F, 1.0F, 1.0F);
+    SC_SACD_Mat4 mat_b =
+        SC_SACD_Rotation_Mat4_ZAxis(std::numbers::pi_v<float> / 4.0F);
+    mat_a = SC_SACD_Mat4_Mult(&mat_b, &mat_a);
+    mat_b = SC_SACD_Translate_Mat4(0.0F, 0.0F, -1.0F);
+    mat_a = SC_SACD_Mat4_Mult(&mat_b, &mat_a);
+
+    {
+      auto result =
+          SC_SACD_Mat4_Vec3_Mult(&mat_a, SC_SACD_Vec3{0.0F, 0.0F, 0.0F});
+      CHECK_FLOAT(result.x, 0.0F);
+      CHECK_FLOAT(result.z, 0.0F);
+      CHECK_FLOAT(result.y, std::sqrt(2.0F));
+    }
+  }
   std::cout << "Checks checked: " << checks_checked << '\n'
             << "Checks passed:  " << checks_passed << '\n';
 
-  return 0;
+  return checks_checked == checks_passed ? 0 : 1;
 }