|
|
// This code is in the public domain -- castanyo@yahoo.es
|
|
|
|
|
|
#pragma once
|
|
|
#ifndef NV_MATH_MATRIX_H
|
|
|
#define NV_MATH_MATRIX_H
|
|
|
|
|
|
#include <nvmath/nvmath.h>
|
|
|
#include <nvmath/Vector.h>
|
|
|
|
|
|
namespace nv
|
|
|
{
|
|
|
enum identity_t { identity };
|
|
|
|
|
|
class NVMATH_CLASS Matrix3
|
|
|
{
|
|
|
public:
|
|
|
Matrix3();
|
|
|
explicit Matrix3(float f);
|
|
|
explicit Matrix3(identity_t);
|
|
|
Matrix3(const Matrix3 & m);
|
|
|
Matrix3(Vector3::Arg v0, Vector3::Arg v1, Vector3::Arg v2);
|
|
|
|
|
|
scalar get(uint row, uint col) const;
|
|
|
scalar operator()(uint row, uint col) const;
|
|
|
scalar & operator()(uint row, uint col);
|
|
|
|
|
|
Vector3 row(uint i) const;
|
|
|
Vector3 column(uint i) const;
|
|
|
|
|
|
void operator*=(float s);
|
|
|
void operator/=(float s);
|
|
|
void operator+=(const Matrix3 & m);
|
|
|
void operator-=(const Matrix3 & m);
|
|
|
|
|
|
float determinant() const;
|
|
|
|
|
|
private:
|
|
|
scalar m_data[9];
|
|
|
};
|
|
|
|
|
|
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 scalar Matrix3::get(uint row, uint col) const
|
|
|
{
|
|
|
nvDebugCheck(row < 3 && col < 3);
|
|
|
return m_data[col * 3 + row];
|
|
|
}
|
|
|
inline scalar Matrix3::operator()(uint row, uint col) const
|
|
|
{
|
|
|
nvDebugCheck(row < 3 && col < 3);
|
|
|
return m_data[col * 3 + row];
|
|
|
}
|
|
|
inline scalar & 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 scalar 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);
|
|
|
}
|
|
|
|
|
|
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);
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/// 4x4 transformation matrix.
|
|
|
/// -# Matrices are stored in memory in column major order.
|
|
|
/// -# Points are to be though of as column vectors.
|
|
|
/// -# Transformation of a point p by a matrix M is: p' = M * p
|
|
|
class NVMATH_CLASS Matrix
|
|
|
{
|
|
|
public:
|
|
|
typedef Matrix const & Arg;
|
|
|
|
|
|
Matrix();
|
|
|
explicit Matrix(float f);
|
|
|
explicit Matrix(identity_t);
|
|
|
Matrix(const Matrix & m);
|
|
|
Matrix(Vector4::Arg v0, Vector4::Arg v1, Vector4::Arg v2, Vector4::Arg v3);
|
|
|
//explicit Matrix(const scalar m[]); // m is assumed to contain 16 elements
|
|
|
|
|
|
scalar data(uint idx) const;
|
|
|
scalar & data(uint idx);
|
|
|
scalar get(uint row, uint col) const;
|
|
|
scalar operator()(uint row, uint col) const;
|
|
|
scalar & operator()(uint row, uint col);
|
|
|
const scalar * ptr() const;
|
|
|
|
|
|
Vector4 row(uint i) const;
|
|
|
Vector4 column(uint i) const;
|
|
|
|
|
|
void scale(scalar s);
|
|
|
void scale(Vector3::Arg s);
|
|
|
void translate(Vector3::Arg t);
|
|
|
void rotate(scalar theta, scalar v0, scalar v1, scalar v2);
|
|
|
scalar determinant() const;
|
|
|
|
|
|
void apply(Matrix::Arg m);
|
|
|
|
|
|
private:
|
|
|
scalar m_data[16];
|
|
|
};
|
|
|
|
|
|
|
|
|
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(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 scalar m[])
|
|
|
{
|
|
|
for(int i = 0; i < 16; i++) {
|
|
|
m_data[i] = m[i];
|
|
|
}
|
|
|
}*/
|
|
|
|
|
|
|
|
|
// Accessors
|
|
|
inline scalar Matrix::data(uint idx) const
|
|
|
{
|
|
|
nvDebugCheck(idx < 16);
|
|
|
return m_data[idx];
|
|
|
}
|
|
|
inline scalar & Matrix::data(uint idx)
|
|
|
{
|
|
|
nvDebugCheck(idx < 16);
|
|
|
return m_data[idx];
|
|
|
}
|
|
|
inline scalar Matrix::get(uint row, uint col) const
|
|
|
{
|
|
|
nvDebugCheck(row < 4 && col < 4);
|
|
|
return m_data[col * 4 + row];
|
|
|
}
|
|
|
inline scalar Matrix::operator()(uint row, uint col) const
|
|
|
{
|
|
|
nvDebugCheck(row < 4 && col < 4);
|
|
|
return m_data[col * 4 + row];
|
|
|
}
|
|
|
inline scalar & Matrix::operator()(uint row, uint col)
|
|
|
{
|
|
|
nvDebugCheck(row < 4 && col < 4);
|
|
|
return m_data[col * 4 + row];
|
|
|
}
|
|
|
|
|
|
inline const scalar * 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));
|
|
|
}
|
|
|
|
|
|
/// Apply scale.
|
|
|
inline void Matrix::scale(scalar 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(scalar theta, scalar v0, scalar v1, scalar v2);
|
|
|
|
|
|
/// Apply rotation.
|
|
|
inline void Matrix::rotate(scalar theta, scalar v0, scalar v1, scalar 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 scalar 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(scalar 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(scalar theta, scalar v0, scalar v1, scalar v2)
|
|
|
{
|
|
|
scalar cost = cosf(theta);
|
|
|
scalar 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 {
|
|
|
scalar a2, b2, c2;
|
|
|
a2 = v0 * v0;
|
|
|
b2 = v1 * v1;
|
|
|
c2 = v2 * v2;
|
|
|
|
|
|
scalar iscale = 1.0f / sqrtf(a2 + b2 + c2);
|
|
|
v0 *= iscale;
|
|
|
v1 *= iscale;
|
|
|
v2 *= iscale;
|
|
|
|
|
|
scalar abm, acm, bcm;
|
|
|
scalar 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(scalar yaw, scalar pitch, scalar roll);
|
|
|
//Matrix skew(scalar angle, Vector3::Arg v1, Vector3::Arg v2);
|
|
|
|
|
|
/// Get frustum matrix.
|
|
|
inline Matrix frustum(scalar xmin, scalar xmax, scalar ymin, scalar ymax, scalar zNear, scalar zFar)
|
|
|
{
|
|
|
Matrix m(0.0f);
|
|
|
|
|
|
scalar doubleznear = 2.0f * zNear;
|
|
|
scalar one_deltax = 1.0f / (xmax - xmin);
|
|
|
scalar one_deltay = 1.0f / (ymax - ymin);
|
|
|
scalar 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 infinite frustum matrix.
|
|
|
inline Matrix frustum(scalar xmin, scalar xmax, scalar ymin, scalar ymax, scalar zNear)
|
|
|
{
|
|
|
Matrix m(0.0f);
|
|
|
|
|
|
scalar doubleznear = 2.0f * zNear;
|
|
|
scalar one_deltax = 1.0f / (xmax - xmin);
|
|
|
scalar one_deltay = 1.0f / (ymax - ymin);
|
|
|
scalar 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(scalar fovy, scalar aspect, scalar zNear, scalar zFar)
|
|
|
{
|
|
|
scalar xmax = zNear * tan(fovy / 2);
|
|
|
scalar xmin = -xmax;
|
|
|
|
|
|
scalar ymax = xmax / aspect;
|
|
|
scalar ymin = -ymax;
|
|
|
|
|
|
return frustum(xmin, xmax, ymin, ymax, zNear, zFar);
|
|
|
}
|
|
|
|
|
|
/// Get infinite perspective matrix.
|
|
|
inline Matrix perspective(scalar fovy, scalar aspect, scalar zNear)
|
|
|
{
|
|
|
scalar x = zNear * tan(fovy / 2);
|
|
|
scalar y = x / aspect;
|
|
|
return frustum( -x, x, -y, y, zNear );
|
|
|
}
|
|
|
|
|
|
/// Get matrix determinant.
|
|
|
inline scalar 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;
|
|
|
}
|
|
|
|
|
|
inline Matrix inverse(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;
|
|
|
}
|
|
|
|
|
|
//Matrix affineInverse(Matrix::Arg m);
|
|
|
|
|
|
/// 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;
|
|
|
}
|
|
|
|
|
|
} // nv namespace
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
/** @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( scalar theta, scalar v0, scalar v1, scalar v2 ) {
|
|
|
scalar cost = cos(theta);
|
|
|
scalar 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.
|
|
|
scalar a2, b2, c2;
|
|
|
a2 = v0 * v0;
|
|
|
b2 = v1 * v1;
|
|
|
c2 = v2 * v2;
|
|
|
|
|
|
scalar iscale = 1.0f / sqrtf(a2 + b2 + c2);
|
|
|
v0 *= iscale;
|
|
|
v1 *= iscale;
|
|
|
v2 *= iscale;
|
|
|
|
|
|
scalar abm, acm, bcm;
|
|
|
scalar 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(scalar angle, const Vec3 & v1, const Vec3 & v2) {
|
|
|
v1.Normalize();
|
|
|
v2.Normalize();
|
|
|
|
|
|
Vec3 v3;
|
|
|
v3.Cross(v1, v2);
|
|
|
v3.Normalize();
|
|
|
|
|
|
// Get skew factor.
|
|
|
scalar costheta = Vec3DotProduct(v1, v2);
|
|
|
scalar sintheta = Real.Sqrt(1 - costheta * costheta);
|
|
|
scalar 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;<3B>// 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( scalar yaw, scalar pitch, scalar roll ) {
|
|
|
scalar sy = sin(yaw+ToRadian(90));
|
|
|
scalar cy = cos(yaw+ToRadian(90));
|
|
|
scalar sp = sin(pitch-ToRadian(90));
|
|
|
scalar cp = cos(pitch-ToRadian(90));
|
|
|
scalar sr = sin(roll);
|
|
|
scalar 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( scalar xmin, scalar xmax, scalar ymin, scalar ymax, scalar zNear, scalar zFar ) {
|
|
|
scalar 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] = (scalar)(doubleznear * one_deltax);
|
|
|
data[1] = 0.0f;
|
|
|
data[2] = 0.0f;
|
|
|
data[3] = 0.0f;
|
|
|
data[4] = 0.0f;
|
|
|
data[5] = (scalar)(doubleznear * one_deltay);
|
|
|
data[6] = 0.f;
|
|
|
data[7] = 0.f;
|
|
|
data[8] = (scalar)((xmax + xmin) * one_deltax);
|
|
|
data[9] = (scalar)((ymax + ymin) * one_deltay);
|
|
|
data[10] = (scalar)(-(zFar + zNear) * one_deltaz);
|
|
|
data[11] = -1.f;
|
|
|
data[12] = 0.f;
|
|
|
data[13] = 0.f;
|
|
|
data[14] = (scalar)(-(zFar * doubleznear) * one_deltaz);
|
|
|
data[15] = 0.f;
|
|
|
}
|
|
|
|
|
|
/** Create a frustum matrix with the far plane at the infinity. */
|
|
|
void FrustumInf( scalar xmin, scalar xmax, scalar ymin, scalar ymax, scalar zNear ) {
|
|
|
scalar 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( scalar left, scalar right, scalar bottom, scalar top, scalar zNear ) {
|
|
|
// this matrix is wrong (not tested scalarly) 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( scalar fov, scalar aspect, scalar zNear, scalar zFar ) {
|
|
|
scalar 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( scalar fov, scalar aspect, scalar zNear ) {
|
|
|
scalar x = zNear * tan( fov/2 );
|
|
|
scalar y = x / aspect;
|
|
|
FrustumInf( -x, x, -y, y, zNear );
|
|
|
}
|
|
|
|
|
|
/** Create an inverse projection matrix with far plane at the infinity. */
|
|
|
void PerspectiveInfInv( scalar fov, scalar aspect, scalar zNear ) {
|
|
|
scalar x = zNear * tan( fov/2 );
|
|
|
scalar y = x / aspect;
|
|
|
FrustumInfInv( -x, x, -y, y, zNear );
|
|
|
}
|
|
|
|
|
|
/** Build bone matrix from quatertion and offset. */
|
|
|
void BoneMatrix(const Quat & q, const Vec3 & offset) {
|
|
|
scalar 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( scalar x, scalar y, scalar 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( scalar 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( scalar theta, scalar v0, scalar v1, scalar 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( scalar x, scalar y, scalar 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. */
|
|
|
scalar 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 scalar 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 scalar 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. */
|
|
|
scalar TransformPointAndNormalize(const Vec3 & restrict orig, Vec3 * restrict dest) const {
|
|
|
piDebugCheck(&orig != dest);
|
|
|
scalar 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. */
|
|
|
scalar 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(scalar * s, scalar * t, scalar * 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:
|
|
|
|
|
|
scalar data[16];
|
|
|
|
|
|
};
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#endif // NV_MATH_MATRIX_H
|