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matrix4x4.h
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matrix4x4.h
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#ifndef _MATRIX4X4_H
#define _MATRIX4X4_H
#include <math.h>
#include <stdio.h>
#include "vector3.h"
template <typename T>
class matrix4x4 {
private:
T cell[16];
public:
matrix4x4 () {}
matrix4x4 (T val) {
cell[0] = cell[1] = cell[2] = cell[3] = cell[4] = cell[5] = cell[6] =
cell[7] = cell[8] = cell[9] = cell[10] = cell[11] = cell[12] = cell[13] =
cell[14] = cell[15] = val;
}
matrix4x4 (const T *vals) {
memcpy(cell, vals, sizeof(T)*16);
}
void SetTranslate(const vector3<T> v) { cell[12] = v.x; cell[13] = v.y; cell[14] = v.z; }
vector3<T> GetTranslate() const { return vector3<T>(cell[12], cell[13], cell[14]); }
void SetRotationOnly(const matrix4x4& m) {
for (int i=0; i<12; i++) cell[i] = m.cell[i];
}
// row-major 3x3 matrix
void LoadFrom3x3Matrix(const T *r) {
cell[0] = r[0]; cell[4] = r[1]; cell[8] = r[2]; cell[12] = 0;
cell[1] = r[3]; cell[5] = r[4]; cell[9] = r[5]; cell[13] = 0;
cell[2] = r[6]; cell[6] = r[7]; cell[10] = r[8]; cell[14] = 0;
cell[3] = 0; cell[7] = 0; cell[11] = 0; cell[15] = 1;
}
// row-major
void SaveTo3x3Matrix(T *r) const {
r[0] = cell[0]; r[1] = cell[4]; r[2] = cell[8];
r[3] = cell[1]; r[4] = cell[5]; r[5] = cell[9];
r[6] = cell[2]; r[7] = cell[6]; r[8] = cell[10];
}
static matrix4x4 Identity () {
matrix4x4 m = matrix4x4(0.0);
m.cell[0] = m.cell[5] = m.cell[10] = m.cell[15] = 1.0f;
return m;
}
//glscale equivalent
void Scale(T x, T y, T z) {
*this = (*this) * ScaleMatrix (x, y, z);
}
void Scale(T s) {
*this = (*this) * ScaleMatrix (s, s, s);
}
static matrix4x4 ScaleMatrix(T x, T y, T z) {
matrix4x4 m;
m[0] = x; m[1] = m[2] = m[3] = 0;
m[5] = y; m[4] = m[6] = m[7] = 0;
m[10] = z; m[8] = m[9] = m[11] = 0;
m[12] = m[13] = m[14] = 0; m[15] = 1;
return m;
}
static matrix4x4 ScaleMatrix(T scale) {
matrix4x4 m;
m[0] = scale; m[1] = m[2] = m[3] = 0;
m[5] = scale; m[4] = m[6] = m[7] = 0;
m[10] = scale; m[8] = m[9] = m[11] = 0;
m[12] = m[13] = m[14] = 0; m[15] = 1;
return m;
}
static matrix4x4 MakeRotMatrix(const vector3<T> &rx, const vector3<T> &ry, const vector3<T> &rz) {
matrix4x4 m;
m[0] = rx.x; m[4] = rx.y; m[8] = rx.z; m[12] = 0;
m[1] = ry.x; m[5] = ry.y; m[9] = ry.z; m[13] = 0;
m[2] = rz.x; m[6] = rz.y; m[10] = rz.z; m[14] = 0;
m[3] = 0; m[7] = 0; m[11] = 0; m[15] = 1;
return m;
}
static matrix4x4 MakeInvRotMatrix(const vector3<T> &rx, const vector3<T> &ry, const vector3<T> &rz) {
matrix4x4 m;
m[0] = rx.x; m[4] = ry.x; m[8] = rz.x; m[12] = 0;
m[1] = rx.y; m[5] = ry.y; m[9] = rz.y; m[13] = 0;
m[2] = rx.z; m[6] = ry.z; m[10] = rz.z; m[14] = 0;
m[3] = 0; m[7] = 0; m[11] = 0; m[15] = 1;
return m;
}
static matrix4x4 FrustumMatrix (T left, T right, T bottom, T top, T znear, T zfar) {
assert((znear > T(0)) && (zfar > T(0)));
// these expressions come from the documentation for glFrustum
const T sx = (T(2) * znear) / (right - left);
const T sy = (T(2) * znear) / (top - bottom);
const T A = (right + left) / (right - left);
const T B = (top + bottom) / (top - bottom);
const T C = -(zfar + znear) / (zfar - znear);
const T D = -(T(2) * zfar * znear) / (zfar - znear);
matrix4x4 m;
m[ 0] = sx; m[ 4] = 0; m[ 8] = A; m[12] = 0;
m[ 1] = 0; m[ 5] = sy; m[ 9] = B; m[13] = 0;
m[ 2] = 0; m[ 6] = 0; m[10] = C; m[14] = D;
m[ 3] = 0; m[ 7] = 0; m[11] = -1; m[15] = 0;
return m;
}
//glRotate equivalent (except radians instead of degrees)
void Rotate (T ang, T x, T y, T z) {
*this = (*this) * RotateMatrix (ang, x, y, z);
}
// (x,y,z) must be normalized
static matrix4x4 RotateMatrix (T ang, T x, T y, T z) {
matrix4x4 m;
T c = cos(ang);
T s = sin(ang);
m[0] = x*x*(1-c)+c;
m[1] = y*x*(1-c)+z*s;
m[2] = x*z*(1-c)-y*s;
m[3] = 0;
m[4] = x*y*(1-c)-z*s;
m[5] = y*y*(1-c)+c;
m[6] = y*z*(1-c)+x*s;
m[7] = 0;
m[8] = x*z*(1-c)+y*s;
m[9] = y*z*(1-c)-x*s;
m[10] = z*z*(1-c)+c;
m[11] = 0;
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1;
return m;
}
void RotateZ (T radians) { *this = (*this) * RotateZMatrix (radians); }
void RotateY (T radians) { *this = (*this) * RotateYMatrix (radians); }
void RotateX (T radians) { *this = (*this) * RotateXMatrix (radians); }
static matrix4x4 RotateXMatrix (T radians) {
matrix4x4 m;
T cos_r = cosf (float(radians));
T sin_r = sinf (float(radians));
m[0] = 1.0f;
m[1] = 0;
m[2] = 0;
m[3] = 0;
m[4] = 0;
m[5] = cos_r;
m[6] = -sin_r;
m[7] = 0;
m[8] = 0;
m[9] = sin_r;
m[10] = cos_r;
m[11] = 0;
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1.0f;
return m;
}
static matrix4x4 RotateYMatrix (T radians) {
matrix4x4 m;
T cos_r = cosf (float(radians));
T sin_r = sinf (float(radians));
m[0] = cos_r;
m[1] = 0;
m[2] = sin_r;
m[3] = 0;
m[4] = 0;
m[5] = 1;
m[6] = 0;
m[7] = 0;
m[8] = -sin_r;
m[9] = 0;
m[10] = cos_r;
m[11] = 0;
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1.0f;
return m;
}
static matrix4x4 RotateZMatrix (T radians) {
matrix4x4 m;
T cos_r = cosf(float(radians));
T sin_r = sinf(float(radians));
m[0] = cos_r;
m[1] = -sin_r;
m[2] = 0;
m[3] = 0;
m[4] = sin_r;
m[5] = cos_r;
m[6] = 0;
m[7] = 0;
m[8] = 0;
m[9] = 0;
m[10] = 1.0f;
m[11] = 0;
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1.0f;
return m;
}
void Renormalize() {
vector3<T> x(cell[0], cell[4], cell[8]);
vector3<T> y(cell[1], cell[5], cell[9]);
vector3<T> z(cell[2], cell[6], cell[10]);
x = x.Normalized();
z = x.Cross(y).Normalized();
y = z.Cross(x).Normalized();
cell[0] = x.x; cell[4] = x.y; cell[8] = x.z;
cell[1] = y.x; cell[5] = y.y; cell[9] = y.z;
cell[2] = z.x; cell[6] = z.y; cell[10] = z.z;
}
void ClearToRotOnly() {
cell[12] = 0;
cell[13] = 0;
cell[14] = 0;
}
T& operator [] (const size_t i) { return cell[i]; }
const T& operator[] (const size_t i) const { return cell[i]; }
const T* Data() const { return cell; }
T* Data() { return cell; }
friend matrix4x4 operator+ (const matrix4x4 &a, const matrix4x4 &b) {
matrix4x4 m;
for (int i=0; i<16; i++) m.cell[i] = a.cell[i] + b.cell[i];
return m;
}
friend matrix4x4 operator- (const matrix4x4 &a, const matrix4x4 &b) {
matrix4x4 m;
for (int i=0; i<16; i++) m.cell[i] = a.cell[i] - b.cell[i];
return m;
}
friend matrix4x4 operator* (const matrix4x4 &a, const matrix4x4 &b) {
matrix4x4 m;
m.cell[0] = a.cell[0]*b.cell[0] + a.cell[4]*b.cell[1] + a.cell[8]*b.cell[2] + a.cell[12]*b.cell[3];
m.cell[1] = a.cell[1]*b.cell[0] + a.cell[5]*b.cell[1] + a.cell[9]*b.cell[2] + a.cell[13]*b.cell[3];
m.cell[2] = a.cell[2]*b.cell[0] + a.cell[6]*b.cell[1] + a.cell[10]*b.cell[2] + a.cell[14]*b.cell[3];
m.cell[3] = a.cell[3]*b.cell[0] + a.cell[7]*b.cell[1] + a.cell[11]*b.cell[2] + a.cell[15]*b.cell[3];
m.cell[4] = a.cell[0]*b.cell[4] + a.cell[4]*b.cell[5] + a.cell[8]*b.cell[6] + a.cell[12]*b.cell[7];
m.cell[5] = a.cell[1]*b.cell[4] + a.cell[5]*b.cell[5] + a.cell[9]*b.cell[6] + a.cell[13]*b.cell[7];
m.cell[6] = a.cell[2]*b.cell[4] + a.cell[6]*b.cell[5] + a.cell[10]*b.cell[6] + a.cell[14]*b.cell[7];
m.cell[7] = a.cell[3]*b.cell[4] + a.cell[7]*b.cell[5] + a.cell[11]*b.cell[6] + a.cell[15]*b.cell[7];
m.cell[8] = a.cell[0]*b.cell[8] + a.cell[4]*b.cell[9] + a.cell[8]*b.cell[10] + a.cell[12]*b.cell[11];
m.cell[9] = a.cell[1]*b.cell[8] + a.cell[5]*b.cell[9] + a.cell[9]*b.cell[10] + a.cell[13]*b.cell[11];
m.cell[10] = a.cell[2]*b.cell[8] + a.cell[6]*b.cell[9] + a.cell[10]*b.cell[10] + a.cell[14]*b.cell[11];
m.cell[11] = a.cell[3]*b.cell[8] + a.cell[7]*b.cell[9] + a.cell[11]*b.cell[10] + a.cell[15]*b.cell[11];
m.cell[12] = a.cell[0]*b.cell[12] + a.cell[4]*b.cell[13] + a.cell[8]*b.cell[14] + a.cell[12]*b.cell[15];
m.cell[13] = a.cell[1]*b.cell[12] + a.cell[5]*b.cell[13] + a.cell[9]*b.cell[14] + a.cell[13]*b.cell[15];
m.cell[14] = a.cell[2]*b.cell[12] + a.cell[6]*b.cell[13] + a.cell[10]*b.cell[14] + a.cell[14]*b.cell[15];
m.cell[15] = a.cell[3]*b.cell[12] + a.cell[7]*b.cell[13] + a.cell[11]*b.cell[14] + a.cell[15]*b.cell[15];
return m;
}
friend vector3<T> operator * (const matrix4x4 &a, const vector3<T> &v) {
vector3<T> out;
out.x = a.cell[0]*v.x + a.cell[4]*v.y + a.cell[8]*v.z + a.cell[12];
out.y = a.cell[1]*v.x + a.cell[5]*v.y + a.cell[9]*v.z + a.cell[13];
out.z = a.cell[2]*v.x + a.cell[6]*v.y + a.cell[10]*v.z + a.cell[14];
return out;
}
// scam for doing a transpose operation
friend vector3<T> operator * (const vector3<T> &v, const matrix4x4 &a) {
vector3<T> out;
out.x = a.cell[0]*v.x + a.cell[1]*v.y + a.cell[2]*v.z;
out.y = a.cell[4]*v.x + a.cell[5]*v.y + a.cell[6]*v.z;
out.z = a.cell[8]*v.x + a.cell[9]*v.y + a.cell[10]*v.z;
return out;
}
friend matrix4x4 operator* (const matrix4x4 &a, T v) {
matrix4x4 m;
for (int i=0; i<16; i++) m[i] = a.cell[i] * v;
return m;
}
friend matrix4x4 operator* (T v, const matrix4x4 &a) {
return (a*v);
}
vector3<T> ApplyRotationOnly (const vector3<T> &v) const {
vector3<T> out;
out.x = cell[0]*v.x + cell[4]*v.y + cell[8]*v.z;
out.y = cell[1]*v.x + cell[5]*v.y + cell[9]*v.z;
out.z = cell[2]*v.x + cell[6]*v.y + cell[10]*v.z;
return out;
}
//gltranslate equivalent
void Translate(const vector3<T> &t) {
Translate(t.x, t.y, t.z);
}
void Translate(T x, T y, T z) {
matrix4x4 m = Identity ();
m[12] = x;
m[13] = y;
m[14] = z;
*this = (*this) * m;
}
static matrix4x4 Translation(const vector3<T> &v) {
return Translation(v.x, v.y, v.z);
}
static matrix4x4 Translation(T x, T y, T z) {
matrix4x4 m = Identity ();
m[12] = x;
m[13] = y;
m[14] = z;
return m;
}
matrix4x4 InverseOf () const {
matrix4x4 m;
// this only works for matrices containing only rotation and transform
m[0] = cell[0]; m[1] = cell[4]; m[2] = cell[8];
m[4] = cell[1]; m[5] = cell[5]; m[6] = cell[9];
m[8] = cell[2]; m[9] = cell[6]; m[10] = cell[10];
m[12] = -(cell[0]*cell[12] + cell[1]*cell[13] + cell[2]*cell[14]);
m[13] = -(cell[4]*cell[12] + cell[5]*cell[13] + cell[6]*cell[14]);
m[14] = -(cell[8]*cell[12] + cell[9]*cell[13] + cell[10]*cell[14]);
m[3] = m[7] = m[11] = 0;
m[15] = 1.0f;
return m;
}
void Print () const {
for (int i=0; i<4; i++) {
printf ("%.2f %.2f %.2f %.2f\n", cell[i], cell[i+4], cell[i+8], cell[i+12]);
}
printf ("\n");
}
};
typedef matrix4x4<float> matrix4x4f;
typedef matrix4x4<double> matrix4x4d;
#endif /* _MATRIX4X4_H */