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+// This code is in the public domain -- castanyo@yahoo.es
+
+#pragma once
+#ifndef NV_MATH_MATRIX_INL
+#define NV_MATH_MATRIX_INL
+
+#include "Matrix.h"
+
+namespace nv
+{
+ inline Matrix3::Matrix3() {}
+
+ inline Matrix3::Matrix3(float f)
+ {
+ for(int i = 0; i < 9; i++) {
+ m_data[i] = f;
+ }
+ }
+
+ inline Matrix3::Matrix3(identity_t)
+ {
+ for(int i = 0; i < 3; i++) {
+ for(int j = 0; j < 3; j++) {
+ m_data[3*j+i] = (i == j) ? 1.0f : 0.0f;
+ }
+ }
+ }
+
+ inline Matrix3::Matrix3(const Matrix3 & m)
+ {
+ for(int i = 0; i < 9; i++) {
+ m_data[i] = m.m_data[i];
+ }
+ }
+
+ inline Matrix3::Matrix3(Vector3::Arg v0, Vector3::Arg v1, Vector3::Arg v2)
+ {
+ m_data[0] = v0.x; m_data[1] = v0.y; m_data[2] = v0.z;
+ m_data[3] = v1.x; m_data[4] = v1.y; m_data[5] = v1.z;
+ m_data[6] = v2.x; m_data[7] = v2.y; m_data[8] = v2.z;
+ }
+
+ inline float Matrix3::data(uint idx) const
+ {
+ nvDebugCheck(idx < 9);
+ return m_data[idx];
+ }
+ inline float & Matrix3::data(uint idx)
+ {
+ nvDebugCheck(idx < 9);
+ return m_data[idx];
+ }
+ inline float Matrix3::get(uint row, uint col) const
+ {
+ nvDebugCheck(row < 3 && col < 3);
+ return m_data[col * 3 + row];
+ }
+ inline float Matrix3::operator()(uint row, uint col) const
+ {
+ nvDebugCheck(row < 3 && col < 3);
+ return m_data[col * 3 + row];
+ }
+ inline float & Matrix3::operator()(uint row, uint col)
+ {
+ nvDebugCheck(row < 3 && col < 3);
+ return m_data[col * 3 + row];
+ }
+
+ inline Vector3 Matrix3::row(uint i) const
+ {
+ nvDebugCheck(i < 3);
+ return Vector3(get(i, 0), get(i, 1), get(i, 2));
+ }
+ inline Vector3 Matrix3::column(uint i) const
+ {
+ nvDebugCheck(i < 3);
+ return Vector3(get(0, i), get(1, i), get(2, i));
+ }
+
+ inline void Matrix3::operator*=(float s)
+ {
+ for(int i = 0; i < 9; i++) {
+ m_data[i] *= s;
+ }
+ }
+
+ inline void Matrix3::operator/=(float s)
+ {
+ float is = 1.0f /s;
+ for(int i = 0; i < 9; i++) {
+ m_data[i] *= is;
+ }
+ }
+
+ inline void Matrix3::operator+=(const Matrix3 & m)
+ {
+ for(int i = 0; i < 9; i++) {
+ m_data[i] += m.m_data[i];
+ }
+ }
+
+ inline void Matrix3::operator-=(const Matrix3 & m)
+ {
+ for(int i = 0; i < 9; i++) {
+ m_data[i] -= m.m_data[i];
+ }
+ }
+
+ inline Matrix3 operator+(const Matrix3 & a, const Matrix3 & b)
+ {
+ Matrix3 m = a;
+ m += b;
+ return m;
+ }
+
+ inline Matrix3 operator-(const Matrix3 & a, const Matrix3 & b)
+ {
+ Matrix3 m = a;
+ m -= b;
+ return m;
+ }
+
+ inline Matrix3 operator*(const Matrix3 & a, float s)
+ {
+ Matrix3 m = a;
+ m *= s;
+ return m;
+ }
+
+ inline Matrix3 operator*(float s, const Matrix3 & a)
+ {
+ Matrix3 m = a;
+ m *= s;
+ return m;
+ }
+
+ inline Matrix3 operator/(const Matrix3 & a, float s)
+ {
+ Matrix3 m = a;
+ m /= s;
+ return m;
+ }
+
+ inline Matrix3 mul(const Matrix3 & a, const Matrix3 & b)
+ {
+ Matrix3 m;
+
+ for(int i = 0; i < 3; i++) {
+ const float ai0 = a(i,0), ai1 = a(i,1), ai2 = a(i,2);
+ m(i, 0) = ai0 * b(0,0) + ai1 * b(1,0) + ai2 * b(2,0);
+ m(i, 1) = ai0 * b(0,1) + ai1 * b(1,1) + ai2 * b(2,1);
+ m(i, 2) = ai0 * b(0,2) + ai1 * b(1,2) + ai2 * b(2,2);
+ }
+
+ return m;
+ }
+
+ inline Matrix3 operator*(const Matrix3 & a, const Matrix3 & b)
+ {
+ return mul(a, b);
+ }
+
+ // Transform the given 3d vector with the given matrix.
+ inline Vector3 transform(const Matrix3 & m, const Vector3 & p)
+ {
+ return Vector3(
+ p.x * m(0,0) + p.y * m(0,1) + p.z * m(0,2),
+ p.x * m(1,0) + p.y * m(1,1) + p.z * m(1,2),
+ p.x * m(2,0) + p.y * m(2,1) + p.z * m(2,2));
+ }
+
+ inline void Matrix3::scale(float s)
+ {
+ for (int i = 0; i < 9; i++) {
+ m_data[i] *= s;
+ }
+ }
+
+ inline void Matrix3::scale(Vector3::Arg s)
+ {
+ m_data[0] *= s.x; m_data[1] *= s.x; m_data[2] *= s.x;
+ m_data[3] *= s.y; m_data[4] *= s.y; m_data[5] *= s.y;
+ m_data[6] *= s.z; m_data[7] *= s.z; m_data[8] *= s.z;
+ }
+
+ inline float Matrix3::determinant() const
+ {
+ return
+ get(0,0) * get(1,1) * get(2,2) +
+ get(0,1) * get(1,2) * get(2,0) +
+ get(0,2) * get(1,0) * get(2,1) -
+ get(0,2) * get(1,1) * get(2,0) -
+ get(0,1) * get(1,0) * get(2,2) -
+ get(0,0) * get(1,2) * get(2,1);
+ }
+
+ // Inverse using Cramer's rule.
+ inline Matrix3 inverseCramer(const Matrix3 & m)
+ {
+ const float det = m.determinant();
+ if (equal(det, 0.0f, 0.0f)) {
+ return Matrix3(0);
+ }
+
+ Matrix3 r;
+
+ r.data(0) = - m.data(5) * m.data(7) + m.data(4) * m.data(8);
+ r.data(1) = + m.data(5) * m.data(6) - m.data(3) * m.data(8);
+ r.data(2) = - m.data(4) * m.data(6) + m.data(3) * m.data(7);
+
+ r.data(3) = + m.data(2) * m.data(7) - m.data(1) * m.data(8);
+ r.data(4) = - m.data(2) * m.data(6) + m.data(0) * m.data(8);
+ r.data(5) = + m.data(1) * m.data(6) - m.data(0) * m.data(7);
+
+ r.data(6) = - m.data(2) * m.data(4) + m.data(1) * m.data(5);
+ r.data(7) = + m.data(2) * m.data(3) - m.data(0) * m.data(5);
+ r.data(8) = - m.data(1) * m.data(3) + m.data(0) * m.data(4);
+
+ r.scale(1.0f / det);
+
+ return r;
+ }
+
+
+
+ inline Matrix::Matrix()
+ {
+ }
+
+ inline Matrix::Matrix(float f)
+ {
+ for(int i = 0; i < 16; i++) {
+ m_data[i] = 0.0f;
+ }
+ }
+
+ inline Matrix::Matrix(identity_t)
+ {
+ for(int i = 0; i < 4; i++) {
+ for(int j = 0; j < 4; j++) {
+ m_data[4*j+i] = (i == j) ? 1.0f : 0.0f;
+ }
+ }
+ }
+
+ inline Matrix::Matrix(const Matrix & m)
+ {
+ for(int i = 0; i < 16; i++) {
+ m_data[i] = m.m_data[i];
+ }
+ }
+
+ inline Matrix::Matrix(const Matrix3 & m)
+ {
+ for(int i = 0; i < 3; i++) {
+ for(int j = 0; j < 3; j++) {
+ operator()(i, j) = m.get(i, j);
+ }
+ }
+ for(int i = 0; i < 4; i++) {
+ operator()(3, i) = 0;
+ operator()(i, 3) = 0;
+ }
+ }
+
+ inline Matrix::Matrix(Vector4::Arg v0, Vector4::Arg v1, Vector4::Arg v2, Vector4::Arg v3)
+ {
+ m_data[ 0] = v0.x; m_data[ 1] = v0.y; m_data[ 2] = v0.z; m_data[ 3] = v0.w;
+ m_data[ 4] = v1.x; m_data[ 5] = v1.y; m_data[ 6] = v1.z; m_data[ 7] = v1.w;
+ m_data[ 8] = v2.x; m_data[ 9] = v2.y; m_data[10] = v2.z; m_data[11] = v2.w;
+ m_data[12] = v3.x; m_data[13] = v3.y; m_data[14] = v3.z; m_data[15] = v3.w;
+ }
+
+ /*inline Matrix::Matrix(const float m[])
+ {
+ for(int i = 0; i < 16; i++) {
+ m_data[i] = m[i];
+ }
+ }*/
+
+
+ // Accessors
+ inline float Matrix::data(uint idx) const
+ {
+ nvDebugCheck(idx < 16);
+ return m_data[idx];
+ }
+ inline float & Matrix::data(uint idx)
+ {
+ nvDebugCheck(idx < 16);
+ return m_data[idx];
+ }
+ inline float Matrix::get(uint row, uint col) const
+ {
+ nvDebugCheck(row < 4 && col < 4);
+ return m_data[col * 4 + row];
+ }
+ inline float Matrix::operator()(uint row, uint col) const
+ {
+ nvDebugCheck(row < 4 && col < 4);
+ return m_data[col * 4 + row];
+ }
+ inline float & Matrix::operator()(uint row, uint col)
+ {
+ nvDebugCheck(row < 4 && col < 4);
+ return m_data[col * 4 + row];
+ }
+
+ inline const float * Matrix::ptr() const
+ {
+ return m_data;
+ }
+
+ inline Vector4 Matrix::row(uint i) const
+ {
+ nvDebugCheck(i < 4);
+ return Vector4(get(i, 0), get(i, 1), get(i, 2), get(i, 3));
+ }
+
+ inline Vector4 Matrix::column(uint i) const
+ {
+ nvDebugCheck(i < 4);
+ return Vector4(get(0, i), get(1, i), get(2, i), get(3, i));
+ }
+
+ inline void Matrix::zero()
+ {
+ m_data[0] = 0; m_data[1] = 0; m_data[2] = 0; m_data[3] = 0;
+ m_data[4] = 0; m_data[5] = 0; m_data[6] = 0; m_data[7] = 0;
+ m_data[8] = 0; m_data[9] = 0; m_data[10] = 0; m_data[11] = 0;
+ m_data[12] = 0; m_data[13] = 0; m_data[14] = 0; m_data[15] = 0;
+ }
+
+ inline void Matrix::identity()
+ {
+ m_data[0] = 1; m_data[1] = 0; m_data[2] = 0; m_data[3] = 0;
+ m_data[4] = 0; m_data[5] = 1; m_data[6] = 0; m_data[7] = 0;
+ m_data[8] = 0; m_data[9] = 0; m_data[10] = 1; m_data[11] = 0;
+ m_data[12] = 0; m_data[13] = 0; m_data[14] = 0; m_data[15] = 1;
+ }
+
+ // Apply scale.
+ inline void Matrix::scale(float s)
+ {
+ m_data[0] *= s; m_data[1] *= s; m_data[2] *= s; m_data[3] *= s;
+ m_data[4] *= s; m_data[5] *= s; m_data[6] *= s; m_data[7] *= s;
+ m_data[8] *= s; m_data[9] *= s; m_data[10] *= s; m_data[11] *= s;
+ m_data[12] *= s; m_data[13] *= s; m_data[14] *= s; m_data[15] *= s;
+ }
+
+ // Apply scale.
+ inline void Matrix::scale(Vector3::Arg s)
+ {
+ m_data[0] *= s.x; m_data[1] *= s.x; m_data[2] *= s.x; m_data[3] *= s.x;
+ m_data[4] *= s.y; m_data[5] *= s.y; m_data[6] *= s.y; m_data[7] *= s.y;
+ m_data[8] *= s.z; m_data[9] *= s.z; m_data[10] *= s.z; m_data[11] *= s.z;
+ }
+
+ // Apply translation.
+ inline void Matrix::translate(Vector3::Arg t)
+ {
+ m_data[12] = m_data[0] * t.x + m_data[4] * t.y + m_data[8] * t.z + m_data[12];
+ m_data[13] = m_data[1] * t.x + m_data[5] * t.y + m_data[9] * t.z + m_data[13];
+ m_data[14] = m_data[2] * t.x + m_data[6] * t.y + m_data[10] * t.z + m_data[14];
+ m_data[15] = m_data[3] * t.x + m_data[7] * t.y + m_data[11] * t.z + m_data[15];
+ }
+
+ Matrix rotation(float theta, float v0, float v1, float v2);
+
+ // Apply rotation.
+ inline void Matrix::rotate(float theta, float v0, float v1, float v2)
+ {
+ Matrix R(rotation(theta, v0, v1, v2));
+ apply(R);
+ }
+
+ // Apply transform.
+ inline void Matrix::apply(Matrix::Arg m)
+ {
+ nvDebugCheck(this != &m);
+
+ for(int i = 0; i < 4; i++) {
+ const float ai0 = get(i,0), ai1 = get(i,1), ai2 = get(i,2), ai3 = get(i,3);
+ m_data[0 + i] = ai0 * m(0,0) + ai1 * m(1,0) + ai2 * m(2,0) + ai3 * m(3,0);
+ m_data[4 + i] = ai0 * m(0,1) + ai1 * m(1,1) + ai2 * m(2,1) + ai3 * m(3,1);
+ m_data[8 + i] = ai0 * m(0,2) + ai1 * m(1,2) + ai2 * m(2,2) + ai3 * m(3,2);
+ m_data[12+ i] = ai0 * m(0,3) + ai1 * m(1,3) + ai2 * m(2,3) + ai3 * m(3,3);
+ }
+ }
+
+ // Get scale matrix.
+ inline Matrix scale(Vector3::Arg s)
+ {
+ Matrix m(identity);
+ m(0,0) = s.x;
+ m(1,1) = s.y;
+ m(2,2) = s.z;
+ return m;
+ }
+
+ // Get scale matrix.
+ inline Matrix scale(float s)
+ {
+ Matrix m(identity);
+ m(0,0) = m(1,1) = m(2,2) = s;
+ return m;
+ }
+
+ // Get translation matrix.
+ inline Matrix translation(Vector3::Arg t)
+ {
+ Matrix m(identity);
+ m(0,3) = t.x;
+ m(1,3) = t.y;
+ m(2,3) = t.z;
+ return m;
+ }
+
+ // Get rotation matrix.
+ inline Matrix rotation(float theta, float v0, float v1, float v2)
+ {
+ float cost = cosf(theta);
+ float sint = sinf(theta);
+
+ Matrix m(identity);
+
+ if( 1 == v0 && 0 == v1 && 0 == v2 ) {
+ m(1,1) = cost; m(2,1) = -sint;
+ m(1,2) = sint; m(2,2) = cost;
+ }
+ else if( 0 == v0 && 1 == v1 && 0 == v2 ) {
+ m(0,0) = cost; m(2,0) = sint;
+ m(1,2) = -sint; m(2,2) = cost;
+ }
+ else if( 0 == v0 && 0 == v1 && 1 == v2 ) {
+ m(0,0) = cost; m(1,0) = -sint;
+ m(0,1) = sint; m(1,1) = cost;
+ }
+ else {
+ float a2, b2, c2;
+ a2 = v0 * v0;
+ b2 = v1 * v1;
+ c2 = v2 * v2;
+
+ float iscale = 1.0f / sqrtf(a2 + b2 + c2);
+ v0 *= iscale;
+ v1 *= iscale;
+ v2 *= iscale;
+
+ float abm, acm, bcm;
+ float mcos, asin, bsin, csin;
+ mcos = 1.0f - cost;
+ abm = v0 * v1 * mcos;
+ acm = v0 * v2 * mcos;
+ bcm = v1 * v2 * mcos;
+ asin = v0 * sint;
+ bsin = v1 * sint;
+ csin = v2 * sint;
+ m(0,0) = a2 * mcos + cost;
+ m(1,0) = abm - csin;
+ m(2,0) = acm + bsin;
+ m(3,0) = abm + csin;
+ m(1,1) = b2 * mcos + cost;
+ m(2,1) = bcm - asin;
+ m(3,1) = acm - bsin;
+ m(1,2) = bcm + asin;
+ m(2,2) = c2 * mcos + cost;
+ }
+ return m;
+ }
+
+ //Matrix rotation(float yaw, float pitch, float roll);
+ //Matrix skew(float angle, Vector3::Arg v1, Vector3::Arg v2);
+
+ // Get frustum matrix.
+ inline Matrix frustum(float xmin, float xmax, float ymin, float ymax, float zNear, float zFar)
+ {
+ Matrix m(0.0f);
+
+ float doubleznear = 2.0f * zNear;
+ float one_deltax = 1.0f / (xmax - xmin);
+ float one_deltay = 1.0f / (ymax - ymin);
+ float one_deltaz = 1.0f / (zFar - zNear);
+
+ m(0,0) = doubleznear * one_deltax;
+ m(1,1) = doubleznear * one_deltay;
+ m(0,2) = (xmax + xmin) * one_deltax;
+ m(1,2) = (ymax + ymin) * one_deltay;
+ m(2,2) = -(zFar + zNear) * one_deltaz;
+ m(3,2) = -1.0f;
+ m(2,3) = -(zFar * doubleznear) * one_deltaz;
+
+ return m;
+ }
+
+ // Get inverse frustum matrix.
+ inline Matrix frustumInverse(float xmin, float xmax, float ymin, float ymax, float zNear, float zFar)
+ {
+ Matrix m(0.0f);
+
+ float one_doubleznear = 1.0f / (2.0f * zNear);
+ float one_doubleznearzfar = 1.0f / (2.0f * zNear * zFar);
+
+ m(0,0) = (xmax - xmin) * one_doubleznear;
+ m(0,3) = (xmax + xmin) * one_doubleznear;
+ m(1,1) = (ymax - ymin) * one_doubleznear;
+ m(1,3) = (ymax + ymin) * one_doubleznear;
+ m(2,3) = -1;
+ m(3,2) = -(zFar - zNear) * one_doubleznearzfar;
+ m(3,3) = (zFar + zNear) * one_doubleznearzfar;
+
+ return m;
+ }
+
+ // Get infinite frustum matrix.
+ inline Matrix frustum(float xmin, float xmax, float ymin, float ymax, float zNear)
+ {
+ Matrix m(0.0f);
+
+ float doubleznear = 2.0f * zNear;
+ float one_deltax = 1.0f / (xmax - xmin);
+ float one_deltay = 1.0f / (ymax - ymin);
+ float nudge = 1.0; // 0.999;
+
+ m(0,0) = doubleznear * one_deltax;
+ m(1,1) = doubleznear * one_deltay;
+ m(0,2) = (xmax + xmin) * one_deltax;
+ m(1,2) = (ymax + ymin) * one_deltay;
+ m(2,2) = -1.0f * nudge;
+ m(3,2) = -1.0f;
+ m(2,3) = -doubleznear * nudge;
+
+ return m;
+ }
+
+ // Get perspective matrix.
+ inline Matrix perspective(float fovy, float aspect, float zNear, float zFar)
+ {
+ float xmax = zNear * tan(fovy / 2);
+ float xmin = -xmax;
+
+ float ymax = xmax / aspect;
+ float ymin = -ymax;
+
+ return frustum(xmin, xmax, ymin, ymax, zNear, zFar);
+ }
+
+ // Get inverse perspective matrix.
+ inline Matrix perspectiveInverse(float fovy, float aspect, float zNear, float zFar)
+ {
+ float xmax = zNear * tan(fovy / 2);
+ float xmin = -xmax;
+
+ float ymax = xmax / aspect;
+ float ymin = -ymax;
+
+ return frustumInverse(xmin, xmax, ymin, ymax, zNear, zFar);
+ }
+
+ // Get infinite perspective matrix.
+ inline Matrix perspective(float fovy, float aspect, float zNear)
+ {
+ float x = zNear * tan(fovy / 2);
+ float y = x / aspect;
+ return frustum( -x, x, -y, y, zNear );
+ }
+
+ // Get matrix determinant.
+ inline float Matrix::determinant() const
+ {
+ return
+ m_data[3] * m_data[6] * m_data[ 9] * m_data[12] - m_data[2] * m_data[7] * m_data[ 9] * m_data[12] - m_data[3] * m_data[5] * m_data[10] * m_data[12] + m_data[1] * m_data[7] * m_data[10] * m_data[12] +
+ m_data[2] * m_data[5] * m_data[11] * m_data[12] - m_data[1] * m_data[6] * m_data[11] * m_data[12] - m_data[3] * m_data[6] * m_data[ 8] * m_data[13] + m_data[2] * m_data[7] * m_data[ 8] * m_data[13] +
+ m_data[3] * m_data[4] * m_data[10] * m_data[13] - m_data[0] * m_data[7] * m_data[10] * m_data[13] - m_data[2] * m_data[4] * m_data[11] * m_data[13] + m_data[0] * m_data[6] * m_data[11] * m_data[13] +
+ m_data[3] * m_data[5] * m_data[ 8] * m_data[14] - m_data[1] * m_data[7] * m_data[ 8] * m_data[14] - m_data[3] * m_data[4] * m_data[ 9] * m_data[14] + m_data[0] * m_data[7] * m_data[ 9] * m_data[14] +
+ m_data[1] * m_data[4] * m_data[11] * m_data[14] - m_data[0] * m_data[5] * m_data[11] * m_data[14] - m_data[2] * m_data[5] * m_data[ 8] * m_data[15] + m_data[1] * m_data[6] * m_data[ 8] * m_data[15] +
+ m_data[2] * m_data[4] * m_data[ 9] * m_data[15] - m_data[0] * m_data[6] * m_data[ 9] * m_data[15] - m_data[1] * m_data[4] * m_data[10] * m_data[15] + m_data[0] * m_data[5] * m_data[10] * m_data[15];
+ }
+
+ inline Matrix transpose(Matrix::Arg m)
+ {
+ Matrix r;
+ for (int i = 0; i < 4; i++)
+ {
+ for (int j = 0; j < 4; j++)
+ {
+ r(i, j) = m(j, i);
+ }
+ }
+ return r;
+ }
+
+ // Inverse using Cramer's rule.
+ inline Matrix inverseCramer(Matrix::Arg m)
+ {
+ Matrix r;
+ r.data( 0) = m.data(6)*m.data(11)*m.data(13) - m.data(7)*m.data(10)*m.data(13) + m.data(7)*m.data(9)*m.data(14) - m.data(5)*m.data(11)*m.data(14) - m.data(6)*m.data(9)*m.data(15) + m.data(5)*m.data(10)*m.data(15);
+ r.data( 1) = m.data(3)*m.data(10)*m.data(13) - m.data(2)*m.data(11)*m.data(13) - m.data(3)*m.data(9)*m.data(14) + m.data(1)*m.data(11)*m.data(14) + m.data(2)*m.data(9)*m.data(15) - m.data(1)*m.data(10)*m.data(15);
+ r.data( 2) = m.data(2)*m.data( 7)*m.data(13) - m.data(3)*m.data( 6)*m.data(13) + m.data(3)*m.data(5)*m.data(14) - m.data(1)*m.data( 7)*m.data(14) - m.data(2)*m.data(5)*m.data(15) + m.data(1)*m.data( 6)*m.data(15);
+ r.data( 3) = m.data(3)*m.data( 6)*m.data( 9) - m.data(2)*m.data( 7)*m.data( 9) - m.data(3)*m.data(5)*m.data(10) + m.data(1)*m.data( 7)*m.data(10) + m.data(2)*m.data(5)*m.data(11) - m.data(1)*m.data( 6)*m.data(11);
+ r.data( 4) = m.data(7)*m.data(10)*m.data(12) - m.data(6)*m.data(11)*m.data(12) - m.data(7)*m.data(8)*m.data(14) + m.data(4)*m.data(11)*m.data(14) + m.data(6)*m.data(8)*m.data(15) - m.data(4)*m.data(10)*m.data(15);
+ r.data( 5) = m.data(2)*m.data(11)*m.data(12) - m.data(3)*m.data(10)*m.data(12) + m.data(3)*m.data(8)*m.data(14) - m.data(0)*m.data(11)*m.data(14) - m.data(2)*m.data(8)*m.data(15) + m.data(0)*m.data(10)*m.data(15);
+ r.data( 6) = m.data(3)*m.data( 6)*m.data(12) - m.data(2)*m.data( 7)*m.data(12) - m.data(3)*m.data(4)*m.data(14) + m.data(0)*m.data( 7)*m.data(14) + m.data(2)*m.data(4)*m.data(15) - m.data(0)*m.data( 6)*m.data(15);
+ r.data( 7) = m.data(2)*m.data( 7)*m.data( 8) - m.data(3)*m.data( 6)*m.data( 8) + m.data(3)*m.data(4)*m.data(10) - m.data(0)*m.data( 7)*m.data(10) - m.data(2)*m.data(4)*m.data(11) + m.data(0)*m.data( 6)*m.data(11);
+ r.data( 8) = m.data(5)*m.data(11)*m.data(12) - m.data(7)*m.data( 9)*m.data(12) + m.data(7)*m.data(8)*m.data(13) - m.data(4)*m.data(11)*m.data(13) - m.data(5)*m.data(8)*m.data(15) + m.data(4)*m.data( 9)*m.data(15);
+ r.data( 9) = m.data(3)*m.data( 9)*m.data(12) - m.data(1)*m.data(11)*m.data(12) - m.data(3)*m.data(8)*m.data(13) + m.data(0)*m.data(11)*m.data(13) + m.data(1)*m.data(8)*m.data(15) - m.data(0)*m.data( 9)*m.data(15);
+ r.data(10) = m.data(1)*m.data( 7)*m.data(12) - m.data(3)*m.data( 5)*m.data(12) + m.data(3)*m.data(4)*m.data(13) - m.data(0)*m.data( 7)*m.data(13) - m.data(1)*m.data(4)*m.data(15) + m.data(0)*m.data( 5)*m.data(15);
+ r.data(11) = m.data(3)*m.data( 5)*m.data( 8) - m.data(1)*m.data( 7)*m.data( 8) - m.data(3)*m.data(4)*m.data( 9) + m.data(0)*m.data( 7)*m.data( 9) + m.data(1)*m.data(4)*m.data(11) - m.data(0)*m.data( 5)*m.data(11);
+ r.data(12) = m.data(6)*m.data( 9)*m.data(12) - m.data(5)*m.data(10)*m.data(12) - m.data(6)*m.data(8)*m.data(13) + m.data(4)*m.data(10)*m.data(13) + m.data(5)*m.data(8)*m.data(14) - m.data(4)*m.data( 9)*m.data(14);
+ r.data(13) = m.data(1)*m.data(10)*m.data(12) - m.data(2)*m.data( 9)*m.data(12) + m.data(2)*m.data(8)*m.data(13) - m.data(0)*m.data(10)*m.data(13) - m.data(1)*m.data(8)*m.data(14) + m.data(0)*m.data( 9)*m.data(14);
+ r.data(14) = m.data(2)*m.data( 5)*m.data(12) - m.data(1)*m.data( 6)*m.data(12) - m.data(2)*m.data(4)*m.data(13) + m.data(0)*m.data( 6)*m.data(13) + m.data(1)*m.data(4)*m.data(14) - m.data(0)*m.data( 5)*m.data(14);
+ r.data(15) = m.data(1)*m.data( 6)*m.data( 8) - m.data(2)*m.data( 5)*m.data( 8) + m.data(2)*m.data(4)*m.data( 9) - m.data(0)*m.data( 6)*m.data( 9) - m.data(1)*m.data(4)*m.data(10) + m.data(0)*m.data( 5)*m.data(10);
+ r.scale(1.0f / m.determinant());
+ return r;
+ }
+
+ inline Matrix isometryInverse(Matrix::Arg m)
+ {
+ Matrix r(identity);
+
+ // transposed 3x3 upper left matrix
+ for (int i = 0; i < 3; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ r(i, j) = m(j, i);
+ }
+ }
+
+ // translate by the negative offsets
+ r.translate(-Vector3(m.data(12), m.data(13), m.data(14)));
+
+ return r;
+ }
+
+ // Transform the given 3d point with the given matrix.
+ inline Vector3 transformPoint(Matrix::Arg m, Vector3::Arg p)
+ {
+ return Vector3(
+ p.x * m(0,0) + p.y * m(0,1) + p.z * m(0,2) + m(0,3),
+ p.x * m(1,0) + p.y * m(1,1) + p.z * m(1,2) + m(1,3),
+ p.x * m(2,0) + p.y * m(2,1) + p.z * m(2,2) + m(2,3));
+ }
+
+ // Transform the given 3d vector with the given matrix.
+ inline Vector3 transformVector(Matrix::Arg m, Vector3::Arg p)
+ {
+ return Vector3(
+ p.x * m(0,0) + p.y * m(0,1) + p.z * m(0,2),
+ p.x * m(1,0) + p.y * m(1,1) + p.z * m(1,2),
+ p.x * m(2,0) + p.y * m(2,1) + p.z * m(2,2));
+ }
+
+ // Transform the given 4d vector with the given matrix.
+ inline Vector4 transform(Matrix::Arg m, Vector4::Arg p)
+ {
+ return Vector4(
+ p.x * m(0,0) + p.y * m(0,1) + p.z * m(0,2) + p.w * m(0,3),
+ p.x * m(1,0) + p.y * m(1,1) + p.z * m(1,2) + p.w * m(1,3),
+ p.x * m(2,0) + p.y * m(2,1) + p.z * m(2,2) + p.w * m(2,3),
+ p.x * m(3,0) + p.y * m(3,1) + p.z * m(3,2) + p.w * m(3,3));
+ }
+
+ inline Matrix mul(Matrix::Arg a, Matrix::Arg b)
+ {
+ // @@ Is this the right order? mul(a, b) = b * a
+ Matrix m = a;
+ m.apply(b);
+ return m;
+ }
+
+ inline void Matrix::operator+=(const Matrix & m)
+ {
+ for(int i = 0; i < 16; i++) {
+ m_data[i] += m.m_data[i];
+ }
+ }
+
+ inline void Matrix::operator-=(const Matrix & m)
+ {
+ for(int i = 0; i < 16; i++) {
+ m_data[i] -= m.m_data[i];
+ }
+ }
+
+ inline Matrix operator+(const Matrix & a, const Matrix & b)
+ {
+ Matrix m = a;
+ m += b;
+ return m;
+ }
+
+ inline Matrix operator-(const Matrix & a, const Matrix & b)
+ {
+ Matrix m = a;
+ m -= b;
+ return m;
+ }
+
+
+} // nv namespace
+
+
+#if 0 // old code.
+/** @name Special matrices. */
+//@{
+/** Generate a translation matrix. */
+void TranslationMatrix(const Vec3 & v) {
+ data[0] = 1; data[1] = 0; data[2] = 0; data[3] = 0;
+ data[4] = 0; data[5] = 1; data[6] = 0; data[7] = 0;
+ data[8] = 0; data[9] = 0; data[10] = 1; data[11] = 0;
+ data[12] = v.x; data[13] = v.y; data[14] = v.z; data[15] = 1;
+}
+
+/** Rotate theta degrees around v. */
+void RotationMatrix( float theta, float v0, float v1, float v2 ) {
+ float cost = cos(theta);
+ float sint = sin(theta);
+
+ if( 1 == v0 && 0 == v1 && 0 == v2 ) {
+ data[0] = 1.0f; data[1] = 0.0f; data[2] = 0.0f; data[3] = 0.0f;
+ data[4] = 0.0f; data[5] = cost; data[6] = -sint;data[7] = 0.0f;
+ data[8] = 0.0f; data[9] = sint; data[10] = cost;data[11] = 0.0f;
+ data[12] = 0.0f;data[13] = 0.0f;data[14] = 0.0f;data[15] = 1.0f;
+ }
+ else if( 0 == v0 && 1 == v1 && 0 == v2 ) {
+ data[0] = cost; data[1] = 0.0f; data[2] = sint; data[3] = 0.0f;
+ data[4] = 0.0f; data[5] = 1.0f; data[6] = 0.0f; data[7] = 0.0f;
+ data[8] = -sint;data[9] = 0.0f;data[10] = cost; data[11] = 0.0f;
+ data[12] = 0.0f;data[13] = 0.0f;data[14] = 0.0f;data[15] = 1.0f;
+ }
+ else if( 0 == v0 && 0 == v1 && 1 == v2 ) {
+ data[0] = cost; data[1] = -sint;data[2] = 0.0f; data[3] = 0.0f;
+ data[4] = sint; data[5] = cost; data[6] = 0.0f; data[7] = 0.0f;
+ data[8] = 0.0f; data[9] = 0.0f; data[10] = 1.0f;data[11] = 0.0f;
+ data[12] = 0.0f;data[13] = 0.0f;data[14] = 0.0f;data[15] = 1.0f;
+ }
+ else {
+ //we need scale a,b,c to unit length.
+ float a2, b2, c2;
+ a2 = v0 * v0;
+ b2 = v1 * v1;
+ c2 = v2 * v2;
+
+ float iscale = 1.0f / sqrtf(a2 + b2 + c2);
+ v0 *= iscale;
+ v1 *= iscale;
+ v2 *= iscale;
+
+ float abm, acm, bcm;
+ float mcos, asin, bsin, csin;
+ mcos = 1.0f - cost;
+ abm = v0 * v1 * mcos;
+ acm = v0 * v2 * mcos;
+ bcm = v1 * v2 * mcos;
+ asin = v0 * sint;
+ bsin = v1 * sint;
+ csin = v2 * sint;
+ data[0] = a2 * mcos + cost;
+ data[1] = abm - csin;
+ data[2] = acm + bsin;
+ data[3] = abm + csin;
+ data[4] = 0.0f;
+ data[5] = b2 * mcos + cost;
+ data[6] = bcm - asin;
+ data[7] = acm - bsin;
+ data[8] = 0.0f;
+ data[9] = bcm + asin;
+ data[10] = c2 * mcos + cost;
+ data[11] = 0.0f;
+ data[12] = 0.0f;
+ data[13] = 0.0f;
+ data[14] = 0.0f;
+ data[15] = 1.0f;
+ }
+}
+
+/*
+void SkewMatrix(float angle, const Vec3 & v1, const Vec3 & v2) {
+v1.Normalize();
+v2.Normalize();
+
+Vec3 v3;
+v3.Cross(v1, v2);
+v3.Normalize();
+
+// Get skew factor.
+float costheta = Vec3DotProduct(v1, v2);
+float sintheta = Real.Sqrt(1 - costheta * costheta);
+float skew = tan(Trig.DegreesToRadians(angle) + acos(sintheta)) * sintheta - costheta;
+
+// Build orthonormal matrix.
+v1 = FXVector3.Cross(v3, v2);
+v1.Normalize();
+
+Matrix R = Matrix::Identity;
+R[0, 0] = v3.X; // Not sure this is in the correct order...
+R[1, 0] = v3.Y;
+R[2, 0] = v3.Z;
+R[0, 1] = v1.X;
+R[1, 1] = v1.Y;
+R[2, 1] = v1.Z;
+R[0, 2] = v2.X;
+R[1, 2] = v2.Y;
+R[2, 2] = v2.Z;
+
+// Build skew matrix.
+Matrix S = Matrix::Identity;
+S[2, 1] = -skew;
+
+// Return skew transform.
+return R * S * R.Transpose; // Not sure this is in the correct order...
+}
+*/
+
+/**
+* Generate rotation matrix for the euler angles. This is the same as computing
+* 3 rotation matrices and multiplying them together in our custom order.
+*
+* @todo Have to recompute this code for our new convention.
+**/
+void RotationMatrix( float yaw, float pitch, float roll ) {
+ float sy = sin(yaw+ToRadian(90));
+ float cy = cos(yaw+ToRadian(90));
+ float sp = sin(pitch-ToRadian(90));
+ float cp = cos(pitch-ToRadian(90));
+ float sr = sin(roll);
+ float cr = cos(roll);
+
+ data[0] = cr*cy + sr*sp*sy;
+ data[1] = cp*sy;
+ data[2] = -sr*cy + cr*sp*sy;
+ data[3] = 0;
+
+ data[4] = -cr*sy + sr*sp*cy;
+ data[5] = cp*cy;
+ data[6] = sr*sy + cr*sp*cy;
+ data[7] = 0;
+
+ data[8] = sr*cp;
+ data[9] = -sp;
+ data[10] = cr*cp;
+ data[11] = 0;
+
+ data[12] = 0;
+ data[13] = 0;
+ data[14] = 0;
+ data[15] = 1;
+}
+
+/** Create a frustum matrix with the far plane at the infinity. */
+void Frustum( float xmin, float xmax, float ymin, float ymax, float zNear, float zFar ) {
+ float one_deltax, one_deltay, one_deltaz, doubleznear;
+
+ doubleznear = 2.0f * zNear;
+ one_deltax = 1.0f / (xmax - xmin);
+ one_deltay = 1.0f / (ymax - ymin);
+ one_deltaz = 1.0f / (zFar - zNear);
+
+ data[0] = (float)(doubleznear * one_deltax);
+ data[1] = 0.0f;
+ data[2] = 0.0f;
+ data[3] = 0.0f;
+ data[4] = 0.0f;
+ data[5] = (float)(doubleznear * one_deltay);
+ data[6] = 0.f;
+ data[7] = 0.f;
+ data[8] = (float)((xmax + xmin) * one_deltax);
+ data[9] = (float)((ymax + ymin) * one_deltay);
+ data[10] = (float)(-(zFar + zNear) * one_deltaz);
+ data[11] = -1.f;
+ data[12] = 0.f;
+ data[13] = 0.f;
+ data[14] = (float)(-(zFar * doubleznear) * one_deltaz);
+ data[15] = 0.f;
+}
+
+/** Create a frustum matrix with the far plane at the infinity. */
+void FrustumInf( float xmin, float xmax, float ymin, float ymax, float zNear ) {
+ float one_deltax, one_deltay, doubleznear, nudge;
+
+ doubleznear = 2.0f * zNear;
+ one_deltax = 1.0f / (xmax - xmin);
+ one_deltay = 1.0f / (ymax - ymin);
+ nudge = 1.0; // 0.999;
+
+ data[0] = doubleznear * one_deltax;
+ data[1] = 0.0f;
+ data[2] = 0.0f;
+ data[3] = 0.0f;
+
+ data[4] = 0.0f;
+ data[5] = doubleznear * one_deltay;
+ data[6] = 0.f;
+ data[7] = 0.f;
+
+ data[8] = (xmax + xmin) * one_deltax;
+ data[9] = (ymax + ymin) * one_deltay;
+ data[10] = -1.0f * nudge;
+ data[11] = -1.0f;
+
+ data[12] = 0.f;
+ data[13] = 0.f;
+ data[14] = -doubleznear * nudge;
+ data[15] = 0.f;
+}
+
+/** Create an inverse frustum matrix with the far plane at the infinity. */
+void FrustumInfInv( float left, float right, float bottom, float top, float zNear ) {
+ // this matrix is wrong (not tested floatly) I think it should be transposed.
+ data[0] = (right - left) / (2 * zNear);
+ data[1] = 0;
+ data[2] = 0;
+ data[3] = (right + left) / (2 * zNear);
+ data[4] = 0;
+ data[5] = (top - bottom) / (2 * zNear);
+ data[6] = 0;
+ data[7] = (top + bottom) / (2 * zNear);
+ data[8] = 0;
+ data[9] = 0;
+ data[10] = 0;
+ data[11] = -1;
+ data[12] = 0;
+ data[13] = 0;
+ data[14] = -1 / (2 * zNear);
+ data[15] = 1 / (2 * zNear);
+}
+
+/** Create an homogeneous projection matrix. */
+void Perspective( float fov, float aspect, float zNear, float zFar ) {
+ float xmin, xmax, ymin, ymax;
+
+ xmax = zNear * tan( fov/2 );
+ xmin = -xmax;
+
+ ymax = xmax / aspect;
+ ymin = -ymax;
+
+ Frustum(xmin, xmax, ymin, ymax, zNear, zFar);
+}
+
+/** Create a projection matrix with the far plane at the infinity. */
+void PerspectiveInf( float fov, float aspect, float zNear ) {
+ float x = zNear * tan( fov/2 );
+ float y = x / aspect;
+ FrustumInf( -x, x, -y, y, zNear );
+}
+
+/** Create an inverse projection matrix with far plane at the infinity. */
+void PerspectiveInfInv( float fov, float aspect, float zNear ) {
+ float x = zNear * tan( fov/2 );
+ float y = x / aspect;
+ FrustumInfInv( -x, x, -y, y, zNear );
+}
+
+/** Build bone matrix from quatertion and offset. */
+void BoneMatrix(const Quat & q, const Vec3 & offset) {
+ float x2, y2, z2, xx, xy, xz, yy, yz, zz, wx, wy, wz;
+
+ // calculate coefficients
+ x2 = q.x + q.x;
+ y2 = q.y + q.y;
+ z2 = q.z + q.z;
+
+ xx = q.x * x2; xy = q.x * y2; xz = q.x * z2;
+ yy = q.y * y2; yz = q.y * z2; zz = q.z * z2;
+ wx = q.w * x2; wy = q.w * y2; wz = q.w * z2;
+
+ data[0] = 1.0f - (yy + zz);
+ data[1] = xy - wz;
+ data[2] = xz + wy;
+ data[3] = 0.0f;
+
+ data[4] = xy + wz;
+ data[5] = 1.0f - (xx + zz);
+ data[6] = yz - wx;
+ data[7] = 0.0f;
+
+ data[8] = xz - wy;
+ data[9] = yz + wx;
+ data[10] = 1.0f - (xx + yy);
+ data[11] = 0.0f;
+
+ data[12] = offset.x;
+ data[13] = offset.y;
+ data[14] = offset.z;
+ data[15] = 1.0f;
+}
+
+//@}
+
+
+/** @name Transformations: */
+//@{
+
+/** Apply a general scale. */
+void Scale( float x, float y, float z ) {
+ data[0] *= x; data[4] *= y; data[8] *= z;
+ data[1] *= x; data[5] *= y; data[9] *= z;
+ data[2] *= x; data[6] *= y; data[10] *= z;
+ data[3] *= x; data[7] *= y; data[11] *= z;
+}
+
+/** Apply a rotation of theta degrees around the axis v*/
+void Rotate( float theta, const Vec3 & v ) {
+ Matrix b;
+ b.RotationMatrix( theta, v[0], v[1], v[2] );
+ Multiply4x3( b );
+}
+
+/** Apply a rotation of theta degrees around the axis v*/
+void Rotate( float theta, float v0, float v1, float v2 ) {
+ Matrix b;
+ b.RotationMatrix( theta, v0, v1, v2 );
+ Multiply4x3( b );
+}
+
+/**
+* Translate the matrix by t. This is the same as multiplying by a
+* translation matrix with the given offset.
+* this = T * this
+*/
+void Translate( const Vec3 &t ) {
+ data[12] = data[0] * t.x + data[4] * t.y + data[8] * t.z + data[12];
+ data[13] = data[1] * t.x + data[5] * t.y + data[9] * t.z + data[13];
+ data[14] = data[2] * t.x + data[6] * t.y + data[10] * t.z + data[14];
+ data[15] = data[3] * t.x + data[7] * t.y + data[11] * t.z + data[15];
+}
+
+/**
+* Translate the matrix by x, y, z. This is the same as multiplying by a
+* translation matrix with the given offsets.
+*/
+void Translate( float x, float y, float z ) {
+ data[12] = data[0] * x + data[4] * y + data[8] * z + data[12];
+ data[13] = data[1] * x + data[5] * y + data[9] * z + data[13];
+ data[14] = data[2] * x + data[6] * y + data[10] * z + data[14];
+ data[15] = data[3] * x + data[7] * y + data[11] * z + data[15];
+}
+
+/** Compute the transposed matrix. */
+void Transpose() {
+ piSwap(data[1], data[4]);
+ piSwap(data[2], data[8]);
+ piSwap(data[6], data[9]);
+ piSwap(data[3], data[12]);
+ piSwap(data[7], data[13]);
+ piSwap(data[11], data[14]);
+}
+
+/** Compute the inverse of a rigid-body/isometry/orthonormal matrix. */
+void IsometryInverse() {
+ // transposed 3x3 upper left matrix
+ piSwap(data[1], data[4]);
+ piSwap(data[2], data[8]);
+ piSwap(data[6], data[9]);
+
+ // translate by the negative offsets
+ Vec3 v(-data[12], -data[13], -data[14]);
+ data[12] = data[13] = data[14] = 0;
+ Translate(v);
+}
+
+/** Compute the inverse of the affine portion of this matrix. */
+void AffineInverse() {
+ data[12] = data[13] = data[14] = 0;
+ Transpose();
+}
+//@}
+
+/** @name Matrix operations: */
+//@{
+
+/** Return the determinant of this matrix. */
+float Determinant() const {
+ return data[0] * data[5] * data[10] * data[15] +
+ data[1] * data[6] * data[11] * data[12] +
+ data[2] * data[7] * data[ 8] * data[13] +
+ data[3] * data[4] * data[ 9] * data[14] -
+ data[3] * data[6] * data[ 9] * data[12] -
+ data[2] * data[5] * data[ 8] * data[15] -
+ data[1] * data[4] * data[11] * data[14] -
+ data[0] * data[7] * data[10] * data[12];
+}
+
+
+/** Standard matrix product: this *= B. */
+void Multiply4x4( const Matrix & restrict B ) {
+ Multiply4x4(*this, B);
+}
+
+/** Standard matrix product: this = A * B. this != B*/
+void Multiply4x4( const Matrix & A, const Matrix & restrict B ) {
+ piDebugCheck(this != &B);
+
+ for(int i = 0; i < 4; i++) {
+ const float ai0 = A(i,0), ai1 = A(i,1), ai2 = A(i,2), ai3 = A(i,3);
+ GetElem(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
+ GetElem(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
+ GetElem(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
+ GetElem(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
+ }
+
+ /* Unrolled but does not allow this == A
+ data[0] = A.data[0] * B.data[0] + A.data[4] * B.data[1] + A.data[8] * B.data[2] + A.data[12] * B.data[3];
+ data[1] = A.data[1] * B.data[0] + A.data[5] * B.data[1] + A.data[9] * B.data[2] + A.data[13] * B.data[3];
+ data[2] = A.data[2] * B.data[0] + A.data[6] * B.data[1] + A.data[10] * B.data[2] + A.data[14] * B.data[3];
+ data[3] = A.data[3] * B.data[0] + A.data[7] * B.data[1] + A.data[11] * B.data[2] + A.data[15] * B.data[3];
+ data[4] = A.data[0] * B.data[4] + A.data[4] * B.data[5] + A.data[8] * B.data[6] + A.data[12] * B.data[7];
+ data[5] = A.data[1] * B.data[4] + A.data[5] * B.data[5] + A.data[9] * B.data[6] + A.data[13] * B.data[7];
+ data[6] = A.data[2] * B.data[4] + A.data[6] * B.data[5] + A.data[10] * B.data[6] + A.data[14] * B.data[7];
+ data[7] = A.data[3] * B.data[4] + A.data[7] * B.data[5] + A.data[11] * B.data[6] + A.data[15] * B.data[7];
+ data[8] = A.data[0] * B.data[8] + A.data[4] * B.data[9] + A.data[8] * B.data[10] + A.data[12] * B.data[11];
+ data[9] = A.data[1] * B.data[8] + A.data[5] * B.data[9] + A.data[9] * B.data[10] + A.data[13] * B.data[11];
+ data[10]= A.data[2] * B.data[8] + A.data[6] * B.data[9] + A.data[10] * B.data[10] + A.data[14] * B.data[11];
+ data[11]= A.data[3] * B.data[8] + A.data[7] * B.data[9] + A.data[11] * B.data[10] + A.data[15] * B.data[11];
+ data[12]= A.data[0] * B.data[12] + A.data[4] * B.data[13] + A.data[8] * B.data[14] + A.data[12] * B.data[15];
+ data[13]= A.data[1] * B.data[12] + A.data[5] * B.data[13] + A.data[9] * B.data[14] + A.data[13] * B.data[15];
+ data[14]= A.data[2] * B.data[12] + A.data[6] * B.data[13] + A.data[10] * B.data[14] + A.data[14] * B.data[15];
+ data[15]= A.data[3] * B.data[12] + A.data[7] * B.data[13] + A.data[11] * B.data[14] + A.data[15] * B.data[15];
+ */
+}
+
+/** Standard matrix product: this *= B. */
+void Multiply4x3( const Matrix & restrict B ) {
+ Multiply4x3(*this, B);
+}
+
+/** Standard product of matrices, where the last row is [0 0 0 1]. */
+void Multiply4x3( const Matrix & A, const Matrix & restrict B ) {
+ piDebugCheck(this != &B);
+
+ for(int i = 0; i < 3; i++) {
+ const float ai0 = A(i,0), ai1 = A(i,1), ai2 = A(i,2), ai3 = A(i,3);
+ GetElem(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
+ GetElem(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
+ GetElem(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
+ GetElem(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
+ }
+ data[3] = 0.0f; data[7] = 0.0f; data[11] = 0.0f; data[15] = 1.0f;
+
+ /* Unrolled but does not allow this == A
+ data[0] = a.data[0] * b.data[0] + a.data[4] * b.data[1] + a.data[8] * b.data[2] + a.data[12] * b.data[3];
+ data[1] = a.data[1] * b.data[0] + a.data[5] * b.data[1] + a.data[9] * b.data[2] + a.data[13] * b.data[3];
+ data[2] = a.data[2] * b.data[0] + a.data[6] * b.data[1] + a.data[10] * b.data[2] + a.data[14] * b.data[3];
+ data[3] = 0.0f;
+ data[4] = a.data[0] * b.data[4] + a.data[4] * b.data[5] + a.data[8] * b.data[6] + a.data[12] * b.data[7];
+ data[5] = a.data[1] * b.data[4] + a.data[5] * b.data[5] + a.data[9] * b.data[6] + a.data[13] * b.data[7];
+ data[6] = a.data[2] * b.data[4] + a.data[6] * b.data[5] + a.data[10] * b.data[6] + a.data[14] * b.data[7];
+ data[7] = 0.0f;
+ data[8] = a.data[0] * b.data[8] + a.data[4] * b.data[9] + a.data[8] * b.data[10] + a.data[12] * b.data[11];
+ data[9] = a.data[1] * b.data[8] + a.data[5] * b.data[9] + a.data[9] * b.data[10] + a.data[13] * b.data[11];
+ data[10]= a.data[2] * b.data[8] + a.data[6] * b.data[9] + a.data[10] * b.data[10] + a.data[14] * b.data[11];
+ data[11]= 0.0f;
+ data[12]= a.data[0] * b.data[12] + a.data[4] * b.data[13] + a.data[8] * b.data[14] + a.data[12] * b.data[15];
+ data[13]= a.data[1] * b.data[12] + a.data[5] * b.data[13] + a.data[9] * b.data[14] + a.data[13] * b.data[15];
+ data[14]= a.data[2] * b.data[12] + a.data[6] * b.data[13] + a.data[10] * b.data[14] + a.data[14] * b.data[15];
+ data[15]= 1.0f;
+ */
+}
+//@}
+
+
+/** @name Vector operations: */
+//@{
+
+/** Transform 3d vector (w=0). */
+void TransformVec3(const Vec3 & restrict orig, Vec3 * restrict dest) const {
+ piDebugCheck(&orig != dest);
+ dest->x = orig.x * data[0] + orig.y * data[4] + orig.z * data[8];
+ dest->y = orig.x * data[1] + orig.y * data[5] + orig.z * data[9];
+ dest->z = orig.x * data[2] + orig.y * data[6] + orig.z * data[10];
+}
+/** Transform 3d vector by the transpose (w=0). */
+void TransformVec3T(const Vec3 & restrict orig, Vec3 * restrict dest) const {
+ piDebugCheck(&orig != dest);
+ dest->x = orig.x * data[0] + orig.y * data[1] + orig.z * data[2];
+ dest->y = orig.x * data[4] + orig.y * data[5] + orig.z * data[6];
+ dest->z = orig.x * data[8] + orig.y * data[9] + orig.z * data[10];
+}
+
+/** Transform a 3d homogeneous vector, where the fourth coordinate is assumed to be 1. */
+void TransformPoint(const Vec3 & restrict orig, Vec3 * restrict dest) const {
+ piDebugCheck(&orig != dest);
+ dest->x = orig.x * data[0] + orig.y * data[4] + orig.z * data[8] + data[12];
+ dest->y = orig.x * data[1] + orig.y * data[5] + orig.z * data[9] + data[13];
+ dest->z = orig.x * data[2] + orig.y * data[6] + orig.z * data[10] + data[14];
+}
+
+/** Transform a point, normalize it, and return w. */
+float TransformPointAndNormalize(const Vec3 & restrict orig, Vec3 * restrict dest) const {
+ piDebugCheck(&orig != dest);
+ float w;
+ dest->x = orig.x * data[0] + orig.y * data[4] + orig.z * data[8] + data[12];
+ dest->y = orig.x * data[1] + orig.y * data[5] + orig.z * data[9] + data[13];
+ dest->z = orig.x * data[2] + orig.y * data[6] + orig.z * data[10] + data[14];
+ w = 1 / (orig.x * data[3] + orig.y * data[7] + orig.z * data[11] + data[15]);
+ *dest *= w;
+ return w;
+}
+
+/** Transform a point and return w. */
+float TransformPointReturnW(const Vec3 & restrict orig, Vec3 * restrict dest) const {
+ piDebugCheck(&orig != dest);
+ dest->x = orig.x * data[0] + orig.y * data[4] + orig.z * data[8] + data[12];
+ dest->y = orig.x * data[1] + orig.y * data[5] + orig.z * data[9] + data[13];
+ dest->z = orig.x * data[2] + orig.y * data[6] + orig.z * data[10] + data[14];
+ return orig.x * data[3] + orig.y * data[7] + orig.z * data[11] + data[15];
+}
+
+/** Transform a normalized 3d point by a 4d matrix and return the resulting 4d vector. */
+void TransformVec4(const Vec3 & orig, Vec4 * dest) const {
+ dest->x = orig.x * data[0] + orig.y * data[4] + orig.z * data[8] + data[12];
+ dest->y = orig.x * data[1] + orig.y * data[5] + orig.z * data[9] + data[13];
+ dest->z = orig.x * data[2] + orig.y * data[6] + orig.z * data[10] + data[14];
+ dest->w = orig.x * data[3] + orig.y * data[7] + orig.z * data[11] + data[15];
+}
+//@}
+
+/** @name Matrix analysis. */
+//@{
+
+/** Get the ZYZ euler angles from the matrix. Assumes the matrix is orthonormal. */
+void GetEulerAnglesZYZ(float * s, float * t, float * r) const {
+ if( GetElem(2,2) < 1.0f ) {
+ if( GetElem(2,2) > -1.0f ) {
+ // cs*ct*cr-ss*sr -ss*ct*cr-cs*sr st*cr
+ // cs*ct*sr+ss*cr -ss*ct*sr+cs*cr st*sr
+ // -cs*st ss*st ct
+ *s = atan2(GetElem(1,2), -GetElem(0,2));
+ *t = acos(GetElem(2,2));
+ *r = atan2(GetElem(2,1), GetElem(2,0));
+ }
+ else {
+ // -c(s-r) s(s-r) 0
+ // s(s-r) c(s-r) 0
+ // 0 0 -1
+ *s = atan2(GetElem(0, 1), -GetElem(0, 0)); // = s-r
+ *t = PI;
+ *r = 0;
+ }
+ }
+ else {
+ // c(s+r) -s(s+r) 0
+ // s(s+r) c(s+r) 0
+ // 0 0 1
+ *s = atan2(GetElem(0, 1), GetElem(0, 0)); // = s+r
+ *t = 0;
+ *r = 0;
+ }
+}
+
+//@}
+
+MATHLIB_API friend PiStream & operator<< ( PiStream & s, Matrix & m );
+
+/** Print to debug output. */
+void Print() const {
+ piDebug( "[ %5.2f %5.2f %5.2f %5.2f ]\n", data[0], data[4], data[8], data[12] );
+ piDebug( "[ %5.2f %5.2f %5.2f %5.2f ]\n", data[1], data[5], data[9], data[13] );
+ piDebug( "[ %5.2f %5.2f %5.2f %5.2f ]\n", data[2], data[6], data[10], data[14] );
+ piDebug( "[ %5.2f %5.2f %5.2f %5.2f ]\n", data[3], data[7], data[11], data[15] );
+}
+
+
+public:
+
+ float data[16];
+
+};
+#endif
+
+
+#endif // NV_MATH_MATRIX_INL
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