#include #include "Math.h" int NextPow2(int x) { if (x <= 0) return 0; int i = 1; while (i < x) { i <<= 1; } return i; } Matrix44 Matrix44::Identity() { return Matrix44 { 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 }; } Matrix44 Matrix44::Scale(float x, float y, float z, float w) { return Matrix44 { x,0,0,0, 0,y,0,0, 0,0,z,0, 0,0,0,w }; } Matrix44 Matrix44::Translate(float x, float y, float z) { return Matrix44 { 1,0,0,0, 0,1,0,0, 0,0,1,0, x,y,z,1 }; } Matrix44 Matrix44::Transpose() { return Matrix44 { m[0],m[4],m[8],m[12], m[1],m[5],m[9],m[13], m[2],m[6],m[10],m[14], m[3],m[7],m[11],m[15] }; } Vector4 Matrix44::multiply(const Matrix44 &m, const Vector4 &v) { Vector4 r = { v.x * m.m[0] + v.y * m.m[4] + v.z * m.m[8] + v.w * m.m[12], v.x * m.m[1] + v.y * m.m[5] + v.z * m.m[9] + v.w * m.m[13], v.x * m.m[2] + v.y * m.m[6] + v.z * m.m[10] + v.w * m.m[14], v.x * m.m[3] + v.y * m.m[7] + v.z * m.m[11] + v.w * m.m[15] }; return r; } Matrix44 Matrix44::multiply(const Matrix44 &a, const Matrix44 &b) { Matrix44 o; o.m[0] = a.m[0] * b.m[0] + a.m[1] * b.m[4] + a.m[2] * b.m[8] + a.m[3] * b.m[12]; o.m[1] = a.m[0] * b.m[1] + a.m[1] * b.m[5] + a.m[2] * b.m[9] + a.m[3] * b.m[13]; o.m[2] = a.m[0] * b.m[2] + a.m[1] * b.m[6] + a.m[2] * b.m[10] + a.m[3] * b.m[14]; o.m[3] = a.m[0] * b.m[3] + a.m[1] * b.m[7] + a.m[2] * b.m[11] + a.m[3] * b.m[15]; o.m[4] = a.m[4] * b.m[0] + a.m[5] * b.m[4] + a.m[6] * b.m[8] + a.m[7] * b.m[12]; o.m[5] = a.m[4] * b.m[1] + a.m[5] * b.m[5] + a.m[6] * b.m[9] + a.m[7] * b.m[13]; o.m[6] = a.m[4] * b.m[2] + a.m[5] * b.m[6] + a.m[6] * b.m[10] + a.m[7] * b.m[14]; o.m[7] = a.m[4] * b.m[3] + a.m[5] * b.m[7] + a.m[6] * b.m[11] + a.m[7] * b.m[15]; o.m[8] = a.m[8] * b.m[0] + a.m[9] * b.m[4] + a.m[10] * b.m[8] + a.m[11] * b.m[12]; o.m[9] = a.m[8] * b.m[1] + a.m[9] * b.m[5] + a.m[10] * b.m[9] + a.m[11] * b.m[13]; o.m[10] = a.m[8] * b.m[2] + a.m[9] * b.m[6] + a.m[10] * b.m[10] + a.m[11] * b.m[14]; o.m[11] = a.m[8] * b.m[3] + a.m[9] * b.m[7] + a.m[10] * b.m[11] + a.m[11] * b.m[15]; o.m[12] = a.m[12] * b.m[0] + a.m[13] * b.m[4] + a.m[14] * b.m[8] + a.m[15] * b.m[12]; o.m[13] = a.m[12] * b.m[1] + a.m[13] * b.m[5] + a.m[14] * b.m[9] + a.m[15] * b.m[13]; o.m[14] = a.m[12] * b.m[2] + a.m[13] * b.m[6] + a.m[14] * b.m[10] + a.m[15] * b.m[14]; o.m[15] = a.m[12] * b.m[3] + a.m[13] * b.m[7] + a.m[14] * b.m[11] + a.m[15] * b.m[15]; return o; } Vector4 Matrix44::Multiply(const Vector4 &v) { return multiply(*this, v); } static bool InvertMatrix(const float m[16], float invOut[16]) { float inv[16], det; int i; inv[0] = m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15] + m[9] * m[7] * m[14] + m[13] * m[6] * m[11] - m[13] * m[7] * m[10]; inv[4] = -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15] - m[8] * m[7] * m[14] - m[12] * m[6] * m[11] + m[12] * m[7] * m[10]; inv[8] = m[4] * m[9] * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15] + m[8] * m[7] * m[13] + m[12] * m[5] * m[11] - m[12] * m[7] * m[9]; inv[12] = -m[4] * m[9] * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14] - m[8] * m[6] * m[13] - m[12] * m[5] * m[10] + m[12] * m[6] * m[9]; inv[1] = -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15] - m[9] * m[3] * m[14] - m[13] * m[2] * m[11] + m[13] * m[3] * m[10]; inv[5] = m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15] + m[8] * m[3] * m[14] + m[12] * m[2] * m[11] - m[12] * m[3] * m[10]; inv[9] = -m[0] * m[9] * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15] - m[8] * m[3] * m[13] - m[12] * m[1] * m[11] + m[12] * m[3] * m[9]; inv[13] = m[0] * m[9] * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14] + m[8] * m[2] * m[13] + m[12] * m[1] * m[10] - m[12] * m[2] * m[9]; inv[2] = m[1] * m[6] * m[15] - m[1] * m[7] * m[14] - m[5] * m[2] * m[15] + m[5] * m[3] * m[14] + m[13] * m[2] * m[7] - m[13] * m[3] * m[6]; inv[6] = -m[0] * m[6] * m[15] + m[0] * m[7] * m[14] + m[4] * m[2] * m[15] - m[4] * m[3] * m[14] - m[12] * m[2] * m[7] + m[12] * m[3] * m[6]; inv[10] = m[0] * m[5] * m[15] - m[0] * m[7] * m[13] - m[4] * m[1] * m[15] + m[4] * m[3] * m[13] + m[12] * m[1] * m[7] - m[12] * m[3] * m[5]; inv[14] = -m[0] * m[5] * m[14] + m[0] * m[6] * m[13] + m[4] * m[1] * m[14] - m[4] * m[2] * m[13] - m[12] * m[1] * m[6] + m[12] * m[2] * m[5]; inv[3] = -m[1] * m[6] * m[11] + m[1] * m[7] * m[10] + m[5] * m[2] * m[11] - m[5] * m[3] * m[10] - m[9] * m[2] * m[7] + m[9] * m[3] * m[6]; inv[7] = m[0] * m[6] * m[11] - m[0] * m[7] * m[10] - m[4] * m[2] * m[11] + m[4] * m[3] * m[10] + m[8] * m[2] * m[7] - m[8] * m[3] * m[6]; inv[11] = -m[0] * m[5] * m[11] + m[0] * m[7] * m[9] + m[4] * m[1] * m[11] - m[4] * m[3] * m[9] - m[8] * m[1] * m[7] + m[8] * m[3] * m[5]; inv[15] = m[0] * m[5] * m[10] - m[0] * m[6] * m[9] - m[4] * m[1] * m[10] + m[4] * m[2] * m[9] + m[8] * m[1] * m[6] - m[8] * m[2] * m[5]; det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12]; if (det == 0) return false; det = 1.0 / det; for (i = 0; i < 16; i++) invOut[i] = inv[i] * det; return true; } Matrix44 Matrix44::Invert() { Matrix44 result; InvertMatrix(this->m, result.m); return result; } Matrix44 Matrix44::Ortho(float left, float right, float bottom, float top, float nearZ, float farZ) { float deltaX = right - left; float deltaY = top - bottom; float deltaZ = farZ - nearZ; Matrix44 ortho = { 2.0f / deltaX,0,0,0, 0,2.0f / deltaY,0,0, 0,0,-2.0f / deltaZ,0, -(right + left) / deltaX,-(top + bottom) / deltaY,-(nearZ + farZ) / deltaZ,1 }; return ortho; } Matrix44 Matrix44::OrthoLH(float l, float r, float b, float t, float zn, float zf) { return Matrix44 { 2.0f / (r - l), 0.0f, 0.0f, 0.0f, 0.0f, 2.0f / (t - b), 0.0f, 0.0f, 0.0f, 0.0f, // 2.0f / (zf - zn), // -1,1 depth range 1.0f / (zf - zn), // 0,1 depth range 0.0f, (l+r)/(l-r), (t+b)/(b-t) , // (zn + zf) / (zn - zf) , // -1,1 depth range (zn) / (zn - zf) , // 0,1 depth range 1.0f }; } Matrix44 Matrix44::PerspectiveFovAspectLH(float fovY, float aspect, float nearZ, float farZ) { float yscale = 1.0f / tanf(fovY * 0.5f); // 1 / tan == cot float xscale = yscale / aspect; float q = farZ / (farZ - nearZ); Matrix44 m = { xscale, 0.0f, 0.0f, 0.0f , 0.0f, yscale, 0.0f, 0.0f , 0.0f, 0.0f, q, 1.0f , 0.0f, 0.0f, q * -nearZ, 0.0f }; return m; } Matrix44 Matrix44::PerspectiveOffCenterRH(float l, float r, float b, float t, float zn, float zf) { #if 0 Matrix44 m = { 2*zn/(r-l), 0, 0, 0, 0, 2*zn*(t-b), 0, 0, (l+r)/(r-l), (t+b)/(t-b), zf/(zn-zf), -1, 0, 0, zn*zf/(zn-zf), 0 }; #else Matrix44 m = { 2*zn/(r-l), 0, 0, 0, 0, 2*zn*(t-b), 0, 0, (l+r)/(r-l), (t+b)/(t-b), 1.0f/(zn-zf), -1, 0, 0, zn/(zn-zf), 0 }; #endif return m; } Matrix44 Matrix44::PerspectiveOffCenterLH(float l, float r, float b, float t, float zn, float zf) { #if 0 Matrix44 m = { 2*zn/(r-l), 0 , 0 , 0, 0 , 2*zn/(t-b), 0 , 0, (l+r)/(l-r), (t+b)/(b-t), zf/(zf-zn) , 1, 0 , 0 , zn*zf/(zn-zf), 0 }; #else Matrix44 m = { 2*zn/(r-l), 0 , 0 , 0, 0 , 2*zn/(t-b), 0 , 0, (l+r)/(l-r), (t+b)/(b-t), 1.0f/(zf-zn) , 1, 0 , 0 , zn/(zn-zf), 0 }; #endif return m; }