Matrix/Vector multiplication and changes

Change Mat3 values to column-major (I think?) order.

Add Matrix/Matrix multiplication and tweak Matrix/Vector multiplication.

Fix Matrix rotation values since Mat3 representation changed.

Added more UnitTest tests.

src/sc_sacd.cpp

@@ -27,6 +27,30 @@ 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_Mat3 operator*(const SC_SACD_Mat3 &a, const SC_SACD_Mat3 &b) {
+  SC_SACD_Mat3 mat;
+
+  mat.x0 = b.x0 * a.x0 + b.y0 * a.x1 + b.z0 * a.x2;
+  mat.y0 = b.x0 * a.y0 + b.y0 * a.y1 + b.z0 * a.y2;
+  mat.z0 = b.x0 * a.z0 + b.y0 * a.z1 + b.z0 * a.z2;
+
+  mat.x1 = b.x1 * a.x0 + b.y1 * a.x1 + b.z1 * a.x2;
+  mat.y1 = b.x1 * a.y0 + b.y1 * a.y1 + b.z1 * a.y2;
+  mat.z1 = b.x1 * a.z0 + b.y1 * a.z1 + b.z1 * a.z2;
+
+  mat.x2 = b.x2 * a.x0 + b.y2 * a.x1 + b.z2 * a.x2;
+  mat.y2 = b.x2 * a.y0 + b.y2 * a.y1 + b.z2 * a.y2;
+  mat.z2 = b.x2 * a.z0 + b.y2 * a.z1 + b.z2 * a.z2;
+
+  return mat;
+}
+
+SC_SACD_Vec3 operator*(const SC_SACD_Mat3 &mat, const SC_SACD_Vec3 &vec) {
+  return SC_SACD_Vec3{vec.x * mat.x0 + vec.y * mat.x1 + vec.z * mat.x2,
+                      vec.x * mat.y0 + vec.y * mat.y1 + vec.z * mat.y2,
+                      vec.x * mat.z0 + vec.y * mat.z1 + vec.z * mat.z2};
+}
+
 std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Normals(
     const SC_SACD_Generic_Box *box) {
   std::vector<SC_SACD_Vec3> normals;
@@ -294,13 +318,17 @@ 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_Mat3 SC_SACD_Mat3_Identity(void) {
+  return SC_SACD_Mat3{1.0F, 0.0F, 0.0F, 0.0F, 1.0F, 0.0F, 0.0F, 0.0F, 1.0F};
+}
+
+SC_SACD_Mat3 SC_SACD_Mat3_Mult(const SC_SACD_Mat3 *a, const SC_SACD_Mat3 *b) {
+  return (*a) * (*b);
+}
+
 SC_SACD_Vec3 SC_SACD_Mat3_Vec3_Mult(const SC_SACD_Mat3 *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,
@@ -326,45 +354,69 @@ SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec, float x_axis,
   SC_SACD_Vec3 result;
 
   // About x_axis.
-  mat.x0 = 1.0F;
+  mat = SC_SACD_Rotation_Mat3_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);
 
   // About y_axis.
-  mat.x0 = std::cos(y_axis);
+  mat = SC_SACD_Rotation_Mat3_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);
 
   // About z_axis.
-  mat.x0 = std::cos(z_axis);
+  mat = SC_SACD_Rotation_Mat3_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);
 }
 
+SC_SACD_Mat3 SC_SACD_Rotation_Mat3_XAxis(float x_radians) {
+  SC_SACD_Mat3 mat;
+
+  mat.x0 = 1.0F;
+  mat.x1 = 0.0F;
+  mat.x2 = 0.0F;
+  mat.y0 = 0.0F;
+  mat.y1 = std::cos(x_radians);
+  mat.y2 = -std::sin(x_radians);
+  mat.z0 = 0.0F;
+  mat.z1 = -mat.y2;
+  mat.z2 = mat.y1;
+
+  return mat;
+}
+
+SC_SACD_Mat3 SC_SACD_Rotation_Mat3_YAxis(float y_radians) {
+  SC_SACD_Mat3 mat;
+
+  mat.x0 = std::cos(y_radians);
+  mat.x1 = 0.0F;
+  mat.x2 = std::sin(y_radians);
+  mat.y0 = 0.0F;
+  mat.y1 = 1.0F;
+  mat.y2 = 0.0F;
+  mat.z0 = -mat.x2;
+  mat.z1 = 0.0F;
+  mat.z2 = mat.x0;
+
+  return mat;
+}
+
+SC_SACD_Mat3 SC_SACD_Rotation_Mat3_ZAxis(float z_radians) {
+  SC_SACD_Mat3 mat;
+
+  mat.x0 = std::cos(z_radians);
+  mat.x1 = -std::sin(z_radians);
+  mat.x2 = 0.0F;
+  mat.y0 = -mat.x1;
+  mat.y1 = mat.x0;
+  mat.y2 = 0.0F;
+  mat.z0 = 0.0F;
+  mat.z1 = 0.0F;
+  mat.z2 = 1.0F;
+
+  return mat;
+}
+
 SC_SACD_Vec3 SC_SACD_Closest_Point_Dir_Normalized(const SC_SACD_Vec3 *pos,
                                                   const SC_SACD_Vec3 *dir,
                                                   const SC_SACD_Vec3 *point) {

src/sc_sacd.h

@@ -25,9 +25,9 @@ typedef struct SC_SACD_EXPORT SC_SACD_Vec3 {
 } SC_SACD_Vec3;
 
 typedef struct SC_SACD_EXPORT SC_SACD_Mat3 {
-  float x0, y0, z0;
+  float x0, x1, x2;
-  float x1, y1, z1;
+  float y0, y1, y2;
-  float x2, y2, z2;
+  float z0, z1, z2;
 } SC_SACD_Mat3;
 
 typedef struct SC_SACD_EXPORT SC_SACD_AABB_Box {
@@ -94,6 +94,11 @@ SC_SACD_EXPORT float SC_SACD_Dot_Product(const SC_SACD_Vec3 a,
 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_Mat3 SC_SACD_Mat3_Identity(void);
+
+SC_SACD_EXPORT SC_SACD_Mat3 SC_SACD_Mat3_Mult(const SC_SACD_Mat3 *a,
+                                              const SC_SACD_Mat3 *b);
+
 SC_SACD_EXPORT SC_SACD_Vec3 SC_SACD_Mat3_Vec3_Mult(const SC_SACD_Mat3 *mat,
                                                    const SC_SACD_Vec3 vec);
 
@@ -101,6 +106,10 @@ 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_Mat3 SC_SACD_Rotation_Mat3_XAxis(float x_radians);
+SC_SACD_EXPORT SC_SACD_Mat3 SC_SACD_Rotation_Mat3_YAxis(float y_radians);
+SC_SACD_EXPORT SC_SACD_Mat3 SC_SACD_Rotation_Mat3_ZAxis(float z_radians);
+
 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);

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() {
@@ -358,6 +369,165 @@ int main() {
     CHECK_TRUE(SC_SACD_Sphere_Box_Collision(&sphere, &box));
   }
 
+  // Test matrix/vector multiplication.
+  {
+    SC_SACD_Mat3 mat_a{1.0F, 2.0F, 3.0F, 4.0F, 5.0F, 6.0F, 7.0F, 8.0F, 9.0F};
+
+    SC_SACD_Mat3 mat_b{1.0F, 0.0F, 0.0F, 0.0F, 1.0F, 0.0F, 0.0F, 0.0F, 1.0F};
+
+    {
+      auto result = SC_SACD_Mat3_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.y0 == result.y0);
+      CHECK_TRUE(mat_a.y1 == result.y1);
+      CHECK_TRUE(mat_a.y2 == result.y2);
+      CHECK_TRUE(mat_a.z0 == result.z0);
+      CHECK_TRUE(mat_a.z1 == result.z1);
+      CHECK_TRUE(mat_a.z2 == result.z2);
+    }
+
+    mat_b.x0 = 2.0F;
+    mat_b.y1 = 0.0F;
+    mat_b.z2 = 0.0F;
+    {
+      auto result = SC_SACD_Mat3_Mult(&mat_a, &mat_b);
+      CHECK_FLOAT(result.x0, 2.0F);
+      CHECK_FLOAT(result.y0, 8.0F);
+      CHECK_FLOAT(result.z0, 14.0F);
+      CHECK_FLOAT(result.x1, 0.0F);
+      CHECK_FLOAT(result.y1, 0.0F);
+      CHECK_FLOAT(result.z1, 0.0F);
+      CHECK_FLOAT(result.x2, 0.0F);
+      CHECK_FLOAT(result.y2, 0.0F);
+      CHECK_FLOAT(result.z2, 0.0F);
+    }
+
+    mat_b = SC_SACD_Mat3_Identity();
+    SC_SACD_Vec3 vec_a{1.0F, 0.0F, 0.0F};
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_ZAxis(std::numbers::pi_v<float> / 2.0F);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_ZAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_ZAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_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_Mat3_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_Mat3_XAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_XAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_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_Mat3_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_Mat3_YAxis(std::numbers::pi_v<float>);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_YAxis(std::numbers::pi_v<float> * 3.0F / 2.0F);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_YAxis(std::numbers::pi_v<float> / 4.0F);
+    mat_b = SC_SACD_Rotation_Mat3_ZAxis(std::numbers::pi_v<float> / 4.0F);
+    // Apply mat_a, then mat_b.
+    mat_a = SC_SACD_Mat3_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_ZAxis(std::numbers::pi_v<float> / 4.0F);
+    mat_a = SC_SACD_Mat3_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat3_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_Mat3_XAxis(std::numbers::pi_v<float> / 2.0F);
+    mat_a = SC_SACD_Mat3_Mult(&mat_b, &mat_a);
+    {
+      auto result = SC_SACD_Mat3_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);
+    }
+  }
   std::cout << "Checks checked: " << checks_checked << '\n'
             << "Checks passed:  " << checks_passed << '\n';