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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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