Simplify projection matrix calculation and add more explanatory comments

src/Graphics.h

@@ -200,10 +200,13 @@ CC_API void Gfx_LoadMatrix(MatrixType type, const struct Matrix* matrix);
 CC_API void Gfx_LoadIdentityMatrix(MatrixType type);
 CC_API void Gfx_EnableTextureOffset(float x, float y);
 CC_API void Gfx_DisableTextureOffset(void);
-/* Calculates an orthographic matrix suitable with this backend. (usually for 2D) */
+
+/* Calculates an orthographic projection matrix suitable with this backend. (usually for 2D) */
 void Gfx_CalcOrthoMatrix(float width, float height, struct Matrix* matrix);
-/* Calculates a projection matrix suitable with this backend. (usually for 3D) */
+/* Calculates a perspective projection matrix suitable with this backend. (usually for 3D) */
 void Gfx_CalcPerspectiveMatrix(float fov, float aspect, float zFar, struct Matrix* matrix);
+/* NOTE: Projection matrix calculation is here because it can depend the graphics backend */
+/* (e.g. OpenGL uses a Z clip range of [-1, 1], whereas Direct3D9 uses a range of [0, 1]) */
 
 /* Outputs a .png screenshot of the backbuffer. */
 cc_result Gfx_TakeScreenshot(struct Stream* output);

src/Graphics_D3D9.c

@@ -717,9 +717,18 @@ void Gfx_DisableTextureOffset(void) {
 }
 
 void Gfx_CalcOrthoMatrix(float width, float height, struct Matrix* matrix) {
-	Matrix_Orthographic(matrix, 0.0f, width, 0.0f, height, ORTHO_NEAR, ORTHO_FAR);
-	matrix->row3.Z = 1.0f       / (ORTHO_NEAR - ORTHO_FAR);
-	matrix->row4.Z = ORTHO_NEAR / (ORTHO_NEAR - ORTHO_FAR);
+	/* Source https://learn.microsoft.com/en-us/windows/win32/direct3d9/d3dxmatrixorthooffcenterrh */
+	/* The simplified calculation below uses: L = 0, R = width, T = 0, B = height */
+	float zNear = ORTHO_NEAR, zFar = ORTHO_FAR;
+	*matrix = Matrix_Identity;
+
+	matrix->row1.X =  2.0f / width;
+	matrix->row2.Y = -2.0f / height;
+	matrix->row3.Z =  1.0f / (zNear - zFar);
+
+	matrix->row4.X = -1.0f;
+	matrix->row4.Y =  1.0f;
+	matrix->row4.Z = zNear / (zNear - zFar);
 }
 
 static float CalcZNear(float fov) {
@@ -732,11 +741,24 @@ static float CalcZNear(float fov) {
 	return 0.00390625f;
 }
 
+static double Cotangent(double x) { return Math_Cos(x) / Math_Sin(x); }
 void Gfx_CalcPerspectiveMatrix(float fov, float aspect, float zFar, struct Matrix* matrix) {
-	Matrix_PerspectiveFieldOfView(matrix, fov, aspect, CalcZNear(fov), zFar);
-	/* Adjust the projection matrix to produce reversed Z values */
-	matrix->row3.Z = -matrix->row3.Z - 1.0f;
-	matrix->row4.Z = -matrix->row4.Z;
+	/* Deliberately swap zNear/zFar in projection matrix calculation to produce */
+	/*  a projection matrix that results in a reversed depth buffer */
+	/* https://developer.nvidia.com/content/depth-precision-visualized */
+	float zNear_ = zFar;
+	float zFar_  = CalcZNear(fov);
+
+	/* Source https://learn.microsoft.com/en-us/windows/win32/direct3d9/d3dxmatrixperspectivefovrh */
+	float c = (float)Cotangent(0.5f * fov);
+	*matrix = Matrix_Identity;
+
+	matrix->row1.X =  c / aspect;
+	matrix->row2.Y =  c;
+	matrix->row3.Z = zFar_ / (zNear_ - zFar_);
+	matrix->row3.W = -1.0f;
+	matrix->row4.Z = (zNear_ * zFar_) / (zNear_ - zFar_);
+	matrix->row4.W =  0.0f;
 }
 
 

src/Vectors.c

@@ -167,7 +167,7 @@ void Matrix_Mul(struct Matrix* result, const struct Matrix* left, const struct M
 }
 
 void Matrix_Orthographic(struct Matrix* result, float left, float right, float top, float bottom, float zNear, float zFar) {
-	/* Transposed, source https://msdn.microsoft.com/en-us/library/dd373965(v=vs.85).aspx */
+	/* Transposed, source https://learn.microsoft.com/en-us/windows/win32/opengl/glortho */
 	*result = Matrix_Identity;
 
 	result->row1.X =  2.0f / (right - left);
@@ -181,20 +181,20 @@ void Matrix_Orthographic(struct Matrix* result, float left, float right, float t
 
 static double Tan_Simple(double x) { return Math_Sin(x) / Math_Cos(x); }
 void Matrix_PerspectiveFieldOfView(struct Matrix* result, float fovy, float aspect, float zNear, float zFar) {
-	float c = zNear * (float)Tan_Simple(0.5f * fovy);
+	float c = (float)Tan_Simple(0.5f * fovy);
 
-	/* Transposed, source https://msdn.microsoft.com/en-us/library/dd373537(v=vs.85).aspx */
+	/* Transposed, source https://learn.microsoft.com/en-us/windows/win32/opengl/glfrustum */
 	/* For a FOV based perspective matrix, left/right/top/bottom are calculated as: */
 	/*   left = -c * aspect, right = c * aspect, bottom = -c, top = c */
 	/* Calculations are simplified because of left/right and top/bottom symmetry */
 	*result = Matrix_Identity;
-	result->row4.W = 0.0f;
 
-	result->row1.X =  zNear / (c * aspect);
-	result->row2.Y =  zNear / c;
-	result->row4.Z = -(2.0f * zFar * zNear) / (zFar - zNear);
+	result->row1.X =  1.0f / (c * aspect);
+	result->row2.Y =  1.0f / c;
 	result->row3.Z = -(zFar + zNear) / (zFar - zNear);
+	result->row4.Z = -(2.0f * zFar * zNear) / (zFar - zNear);
 	result->row3.W = -1.0f;
+	result->row4.W =  0.0f;
 }
 
 void Matrix_LookRot(struct Matrix* result, Vec3 pos, Vec2 rot) {

src/_GraphicsBase.h

@@ -236,6 +236,9 @@ void Gfx_RestoreAlphaState(cc_uint8 draw) {
 }
 
 
+/*########################################################################################################################*
+*---------------------------------------------------------Textures--------------------------------------------------------*
+*#########################################################################################################################*/
 static void CopyTextureData(void* dst, int dstStride, const struct Bitmap* src, int srcStride) {
 	/* We need to copy scanline by scanline, as generally srcStride != dstStride */
 	cc_uint8* src_ = (cc_uint8*)src->scan0;