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Torque3D/Engine/source/math/mMatrix.h
marauder2k7 9af22dc302 BUG: Probe baking look at matrix was wrong 
Multiple fixes in files sent by Az but matrix look at function was creating a view matrix that messed up the capture.
Look at function for matrix now returns the correct matrix and bakes looking better
2025-01-07 15:44:19 +00:00

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//-----------------------------------------------------------------------------
// Copyright (c) 2012 GarageGames, LLC
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
//-----------------------------------------------------------------------------
#ifndef _MMATRIX_H_
#define _MMATRIX_H_
#include <algorithm>
#ifndef _MPLANE_H_
#include "math/mPlane.h"
#endif
#ifndef _MBOX_H_
#include "math/mBox.h"
#endif
#ifndef _MPOINT4_H_
#include "math/mPoint4.h"
#endif
#ifndef _ENGINETYPEINFO_H_
#include "console/engineTypeInfo.h"
#endif
#ifndef _FRAMEALLOCATOR_H_
#include "core/frameAllocator.h"
#endif
#ifndef _STRINGFUNCTIONS_H_
#include "core/strings/stringFunctions.h"
#endif
#ifndef _CONSOLE_H_
#include "console/console.h"
#endif
#ifndef USE_TEMPLATE_MATRIX
/// 4x4 Matrix Class
///
/// This runs at F32 precision.
class MatrixF
{
friend class MatrixFEngineExport;
private:
F32 m[16]; ///< Note: Torque uses row-major matrices
public:
/// Create an uninitialized matrix.
///
/// @param identity If true, initialize to the identity matrix.
explicit MatrixF(bool identity=false);
/// Create a matrix to rotate about origin by e.
/// @see set
explicit MatrixF( const EulerF &e);
/// Create a matrix to rotate about p by e.
/// @see set
MatrixF( const EulerF &e, const Point3F& p);
/// Get the index in m to element in column i, row j
///
/// This is necessary as we have m as a one dimensional array.
///
/// @param i Column desired.
/// @param j Row desired.
static U32 idx(U32 i, U32 j) { return (i + j*4); }
/// Initialize matrix to rotate about origin by e.
MatrixF& set( const EulerF &e);
/// Initialize matrix to rotate about p by e.
MatrixF& set( const EulerF &e, const Point3F& p);
/// Initialize matrix with a cross product of p.
MatrixF& setCrossProduct( const Point3F &p);
/// Initialize matrix with a tensor product of p.
MatrixF& setTensorProduct( const Point3F &p, const Point3F& q);
operator F32*() { return (m); } ///< Allow people to get at m.
operator const F32*() const { return (F32*)(m); } ///< Allow people to get at m.
bool isAffine() const; ///< Check to see if this is an affine matrix.
bool isIdentity() const; ///< Checks for identity matrix.
/// Make this an identity matrix.
MatrixF& identity();
/// Invert m.
MatrixF& inverse();
/// Copy the inversion of this into out matrix.
void invertTo( MatrixF *out );
/// Take inverse of matrix assuming it is affine (rotation,
/// scale, sheer, translation only).
MatrixF& affineInverse();
/// Swap rows and columns.
MatrixF& transpose();
/// M * Matrix(p) -> M
MatrixF& scale( const Point3F &s );
MatrixF& scale( F32 s ) { return scale( Point3F( s, s, s ) ); }
/// Return scale assuming scale was applied via mat.scale(s).
Point3F getScale() const;
EulerF toEuler() const;
F32 determinant() const {
return m_matF_determinant(*this);
}
/// Compute the inverse of the matrix.
///
/// Computes inverse of full 4x4 matrix. Returns false and performs no inverse if
/// the determinant is 0.
///
/// Note: In most cases you want to use the normal inverse function. This method should
/// be used if the matrix has something other than (0,0,0,1) in the bottom row.
bool fullInverse();
/// Reverse depth for projection matrix
/// Simplifies reversal matrix mult to 4 subtractions
void reverseProjection();
/// Swaps rows and columns into matrix.
void transposeTo(F32 *matrix) const;
/// Normalize the matrix.
void normalize();
/// Copy the requested column into a Point4F.
void getColumn(S32 col, Point4F *cptr) const;
Point4F getColumn4F(S32 col) const { Point4F ret; getColumn(col,&ret); return ret; }
/// Copy the requested column into a Point3F.
///
/// This drops the bottom-most row.
void getColumn(S32 col, Point3F *cptr) const;
Point3F getColumn3F(S32 col) const { Point3F ret; getColumn(col,&ret); return ret; }
/// Set the specified column from a Point4F.
void setColumn(S32 col, const Point4F& cptr);
/// Set the specified column from a Point3F.
///
/// The bottom-most row is not set.
void setColumn(S32 col, const Point3F& cptr);
/// Copy the specified row into a Point4F.
void getRow(S32 row, Point4F *cptr) const;
Point4F getRow4F(S32 row) const { Point4F ret; getRow(row,&ret); return ret; }
/// Copy the specified row into a Point3F.
///
/// Right-most item is dropped.
void getRow(S32 row, Point3F *cptr) const;
Point3F getRow3F(S32 row) const { Point3F ret; getRow(row,&ret); return ret; }
/// Set the specified row from a Point4F.
void setRow(S32 row, const Point4F& cptr);
/// Set the specified row from a Point3F.
///
/// The right-most item is not set.
void setRow(S32 row, const Point3F& cptr);
/// Get the position of the matrix.
///
/// This is the 4th column of the matrix.
Point3F getPosition() const;
/// Set the position of the matrix.
///
/// This is the 4th column of the matrix.
void setPosition( const Point3F &pos ) { setColumn( 3, pos ); }
/// Add the passed delta to the matrix position.
void displace( const Point3F &delta );
/// Get the x axis of the matrix.
///
/// This is the 1st column of the matrix and is
/// normally considered the right vector.
VectorF getRightVector() const;
/// Get the y axis of the matrix.
///
/// This is the 2nd column of the matrix and is
/// normally considered the forward vector.
VectorF getForwardVector() const;
/// Get the z axis of the matrix.
///
/// This is the 3rd column of the matrix and is
/// normally considered the up vector.
VectorF getUpVector() const;
MatrixF& mul(const MatrixF &a); ///< M * a -> M
MatrixF& mulL(const MatrixF &a); ///< a * M -> M
MatrixF& mul(const MatrixF &a, const MatrixF &b); ///< a * b -> M
// Scalar multiplies
MatrixF& mul(const F32 a); ///< M * a -> M
MatrixF& mul(const MatrixF &a, const F32 b); ///< a * b -> M
void mul( Point4F& p ) const; ///< M * p -> p (full [4x4] * [1x4])
void mulP( Point3F& p ) const; ///< M * p -> p (assume w = 1.0f)
void mulP( const Point3F &p, Point3F *d) const; ///< M * p -> d (assume w = 1.0f)
void mulV( VectorF& p ) const; ///< M * v -> v (assume w = 0.0f)
void mulV( const VectorF &p, Point3F *d) const; ///< M * v -> d (assume w = 0.0f)
void mul(Box3F& b) const; ///< Axial box -> Axial Box
MatrixF& add( const MatrixF& m );
/// <summary>
/// Turns this matrix into a view matrix that looks at target.
/// </summary>
/// <param name="eye">The eye position.</param>
/// <param name="target">The target position/direction.</param>
/// <param name="up">The up direction.</param>
void LookAt(const VectorF& eye, const VectorF& target, const VectorF& up);
/// Convenience function to allow people to treat this like an array.
F32& operator ()(S32 row, S32 col) { return m[idx(col,row)]; }
F32 operator ()(S32 row, S32 col) const { return m[idx(col,row)]; }
void dumpMatrix(const char *caption=NULL) const;
// Math operator overloads
//------------------------------------
friend MatrixF operator * ( const MatrixF &m1, const MatrixF &m2 );
MatrixF& operator *= ( const MatrixF &m );
MatrixF &operator = (const MatrixF &m);
bool isNaN();
// Static identity matrix
const static MatrixF Identity;
};
class MatrixFEngineExport
{
public:
static EngineFieldTable::Field getMatrixField();
};
//--------------------------------------
// Inline Functions
inline MatrixF::MatrixF(bool _identity)
{
if (_identity)
identity();
else
std::fill_n(m, 16, 0);
}
inline MatrixF::MatrixF( const EulerF &e )
{
set(e);
}
inline MatrixF::MatrixF( const EulerF &e, const Point3F& p )
{
set(e,p);
}
inline MatrixF& MatrixF::set( const EulerF &e)
{
m_matF_set_euler( e, *this );
return (*this);
}
inline MatrixF& MatrixF::set( const EulerF &e, const Point3F& p)
{
m_matF_set_euler_point( e, p, *this );
return (*this);
}
inline MatrixF& MatrixF::setCrossProduct( const Point3F &p)
{
m[1] = -(m[4] = p.z);
m[8] = -(m[2] = p.y);
m[6] = -(m[9] = p.x);
m[0] = m[3] = m[5] = m[7] = m[10] = m[11] =
m[12] = m[13] = m[14] = 0.0f;
m[15] = 1;
return (*this);
}
inline MatrixF& MatrixF::setTensorProduct( const Point3F &p, const Point3F &q)
{
m[0] = p.x * q.x;
m[1] = p.x * q.y;
m[2] = p.x * q.z;
m[4] = p.y * q.x;
m[5] = p.y * q.y;
m[6] = p.y * q.z;
m[8] = p.z * q.x;
m[9] = p.z * q.y;
m[10] = p.z * q.z;
m[3] = m[7] = m[11] = m[12] = m[13] = m[14] = 0.0f;
m[15] = 1.0f;
return (*this);
}
inline bool MatrixF::isIdentity() const
{
return
m[0] == 1.0f &&
m[1] == 0.0f &&
m[2] == 0.0f &&
m[3] == 0.0f &&
m[4] == 0.0f &&
m[5] == 1.0f &&
m[6] == 0.0f &&
m[7] == 0.0f &&
m[8] == 0.0f &&
m[9] == 0.0f &&
m[10] == 1.0f &&
m[11] == 0.0f &&
m[12] == 0.0f &&
m[13] == 0.0f &&
m[14] == 0.0f &&
m[15] == 1.0f;
}
inline MatrixF& MatrixF::identity()
{
m[0] = 1.0f;
m[1] = 0.0f;
m[2] = 0.0f;
m[3] = 0.0f;
m[4] = 0.0f;
m[5] = 1.0f;
m[6] = 0.0f;
m[7] = 0.0f;
m[8] = 0.0f;
m[9] = 0.0f;
m[10] = 1.0f;
m[11] = 0.0f;
m[12] = 0.0f;
m[13] = 0.0f;
m[14] = 0.0f;
m[15] = 1.0f;
return (*this);
}
inline MatrixF& MatrixF::inverse()
{
m_matF_inverse(m);
return (*this);
}
inline void MatrixF::invertTo( MatrixF *out )
{
m_matF_invert_to(m,*out);
}
inline MatrixF& MatrixF::affineInverse()
{
// AssertFatal(isAffine() == true, "Error, this matrix is not an affine transform");
m_matF_affineInverse(m);
return (*this);
}
inline MatrixF& MatrixF::transpose()
{
m_matF_transpose(m);
return (*this);
}
inline MatrixF& MatrixF::scale(const Point3F& p)
{
m_matF_scale(m,p);
return *this;
}
inline Point3F MatrixF::getScale() const
{
Point3F scale;
scale.x = mSqrt(m[0]*m[0] + m[4] * m[4] + m[8] * m[8]);
scale.y = mSqrt(m[1]*m[1] + m[5] * m[5] + m[9] * m[9]);
scale.z = mSqrt(m[2]*m[2] + m[6] * m[6] + m[10] * m[10]);
return scale;
}
inline void MatrixF::normalize()
{
m_matF_normalize(m);
}
inline MatrixF& MatrixF::mul( const MatrixF &a )
{ // M * a -> M
AssertFatal(&a != this, "MatrixF::mul - a.mul(a) is invalid!");
MatrixF tempThis(*this);
m_matF_x_matF(tempThis, a, *this);
return (*this);
}
inline MatrixF& MatrixF::mulL( const MatrixF &a )
{ // a * M -> M
AssertFatal(&a != this, "MatrixF::mulL - a.mul(a) is invalid!");
MatrixF tempThis(*this);
m_matF_x_matF(a, tempThis, *this);
return (*this);
}
inline MatrixF& MatrixF::mul( const MatrixF &a, const MatrixF &b )
{ // a * b -> M
AssertFatal((&a != this) && (&b != this), "MatrixF::mul - a.mul(a, b) a.mul(b, a) a.mul(a, a) is invalid!");
m_matF_x_matF(a, b, *this);
return (*this);
}
inline MatrixF& MatrixF::mul(const F32 a)
{
for (U32 i = 0; i < 16; i++)
m[i] *= a;
return *this;
}
inline MatrixF& MatrixF::mul(const MatrixF &a, const F32 b)
{
*this = a;
mul(b);
return *this;
}
inline void MatrixF::mul( Point4F& p ) const
{
Point4F temp;
m_matF_x_point4F(*this, &p.x, &temp.x);
p = temp;
}
inline void MatrixF::mulP( Point3F& p) const
{
// M * p -> d
Point3F d;
m_matF_x_point3F(*this, &p.x, &d.x);
p = d;
}
inline void MatrixF::mulP( const Point3F &p, Point3F *d) const
{
// M * p -> d
m_matF_x_point3F(*this, &p.x, &d->x);
}
inline void MatrixF::mulV( VectorF& v) const
{
// M * v -> v
VectorF temp;
m_matF_x_vectorF(*this, &v.x, &temp.x);
v = temp;
}
inline void MatrixF::mulV( const VectorF &v, Point3F *d) const
{
// M * v -> d
m_matF_x_vectorF(*this, &v.x, &d->x);
}
inline void MatrixF::mul(Box3F& b) const
{
m_matF_x_box3F(*this, &b.minExtents.x, &b.maxExtents.x);
}
inline MatrixF& MatrixF::add( const MatrixF& a )
{
for( U32 i = 0; i < 16; ++ i )
m[ i ] += a.m[ i ];
return *this;
}
inline void MatrixF::LookAt(const VectorF& eye, const VectorF& target, const VectorF& up)
{
// Calculate the forward vector (camera direction).
VectorF zAxis = target; // Camera looks towards the target
zAxis.normalize();
// Calculate the right vector.
VectorF xAxis = mCross(up, zAxis);
xAxis.normalize();
// Recalculate the up vector.
VectorF yAxis = mCross(zAxis, xAxis);
// Set the rotation part of the matrix (camera axes).
setColumn(0, xAxis); // Right
setColumn(1, zAxis); // Forward
setColumn(2, yAxis); // Up
// Set the translation part (camera position).
setPosition(eye);
}
inline void MatrixF::getColumn(S32 col, Point4F *cptr) const
{
cptr->x = m[col];
cptr->y = m[col+4];
cptr->z = m[col+8];
cptr->w = m[col+12];
}
inline void MatrixF::getColumn(S32 col, Point3F *cptr) const
{
cptr->x = m[col];
cptr->y = m[col+4];
cptr->z = m[col+8];
}
inline void MatrixF::setColumn(S32 col, const Point4F &cptr)
{
m[col] = cptr.x;
m[col+4] = cptr.y;
m[col+8] = cptr.z;
m[col+12]= cptr.w;
}
inline void MatrixF::setColumn(S32 col, const Point3F &cptr)
{
m[col] = cptr.x;
m[col+4] = cptr.y;
m[col+8] = cptr.z;
}
inline void MatrixF::getRow(S32 col, Point4F *cptr) const
{
col *= 4;
cptr->x = m[col++];
cptr->y = m[col++];
cptr->z = m[col++];
cptr->w = m[col];
}
inline void MatrixF::getRow(S32 col, Point3F *cptr) const
{
col *= 4;
cptr->x = m[col++];
cptr->y = m[col++];
cptr->z = m[col];
}
inline void MatrixF::setRow(S32 col, const Point4F &cptr)
{
col *= 4;
m[col++] = cptr.x;
m[col++] = cptr.y;
m[col++] = cptr.z;
m[col] = cptr.w;
}
inline void MatrixF::setRow(S32 col, const Point3F &cptr)
{
col *= 4;
m[col++] = cptr.x;
m[col++] = cptr.y;
m[col] = cptr.z;
}
inline Point3F MatrixF::getPosition() const
{
return Point3F( m[3], m[3+4], m[3+8] );
}
inline void MatrixF::displace( const Point3F &delta )
{
m[3] += delta.x;
m[3+4] += delta.y;
m[3+8] += delta.z;
}
inline VectorF MatrixF::getForwardVector() const
{
VectorF vec;
getColumn( 1, &vec );
return vec;
}
inline VectorF MatrixF::getRightVector() const
{
VectorF vec;
getColumn( 0, &vec );
return vec;
}
inline VectorF MatrixF::getUpVector() const
{
VectorF vec;
getColumn( 2, &vec );
return vec;
}
//------------------------------------
// Math operator overloads
//------------------------------------
inline MatrixF operator * ( const MatrixF &m1, const MatrixF &m2 )
{
// temp = m1 * m2
MatrixF temp;
m_matF_x_matF(m1, m2, temp);
return temp;
}
inline MatrixF& MatrixF::operator *= ( const MatrixF &m1 )
{
MatrixF tempThis(*this);
m_matF_x_matF(tempThis, m1, *this);
return (*this);
}
inline MatrixF &MatrixF::operator = (const MatrixF &m1)
{
for (U32 i=0;i<16;i++)
this->m[i] = m1.m[i];
return (*this);
}
inline bool MatrixF::isNaN()
{
bool isaNaN = false;
for (U32 i = 0; i < 16; i++)
if (mIsNaN_F(m[i]))
isaNaN = true;
return isaNaN;
}
//------------------------------------
// Non-member methods
//------------------------------------
inline void mTransformPlane(const MatrixF& mat, const Point3F& scale, const PlaneF& plane, PlaneF * result)
{
m_matF_x_scale_x_planeF(mat, &scale.x, &plane.x, &result->x);
}
#else // !USE_TEMPLATE_MATRIX
//------------------------------------
// Templatized matrix class to replace MATRIXF above
//------------------------------------
template<typename DATA_TYPE, U32 rows, U32 cols>
class Matrix {
friend class MatrixTemplateExport;
private:
DATA_TYPE data[rows * cols];
public:
static_assert(rows >= 2 && cols >= 2, "Matrix must have at least 2 rows and 2 cols.");
// ------ Setters and initializers ------
explicit Matrix(bool identity = false) {
std::fill(data, data + (rows * cols), DATA_TYPE(0));
if (identity) {
for (U32 i = 0; i < rows; i++) {
for (U32 j = 0; j < cols; j++) {
// others already get filled with 0
if (j == i)
(*this)(i, j) = static_cast<DATA_TYPE>(1);
}
}
}
}
explicit Matrix(const EulerF& e) {
set(e);
}
~Matrix() = default;
/// Make this an identity matrix.
Matrix<DATA_TYPE, rows, cols>& identity();
void reverseProjection();
void normalize();
Matrix<DATA_TYPE, rows, cols>& set(const EulerF& e);
Matrix(const EulerF& e, const Point3F p);
Matrix<DATA_TYPE, rows, cols>& set(const EulerF& e, const Point3F p);
Matrix<DATA_TYPE, rows, cols>& inverse();
Matrix<DATA_TYPE, rows, cols>& transpose();
void invert();
Matrix<DATA_TYPE, rows, cols>& setCrossProduct(const Point3F& p);
Matrix<DATA_TYPE, rows, cols>& setTensorProduct(const Point3F& p, const Point3F& q);
/// M * Matrix(p) -> M
Matrix<DATA_TYPE, rows, cols>& scale(const Point3F& s);
Matrix<DATA_TYPE, rows, cols>& scale(DATA_TYPE s) { return scale(Point3F(s, s, s)); }
void setColumn(S32 col, const Point4F& cptr);
void setColumn(S32 col, const Point3F& cptr);
void setRow(S32 row, const Point4F& cptr);
void setRow(S32 row, const Point3F& cptr);
void displace(const Point3F& delta);
bool fullInverse();
void setPosition(const Point3F& pos) { setColumn(3, pos); }
DATA_TYPE determinant() const {
AssertFatal(rows == cols, "Determinant is only defined for square matrices.");
// For simplicity, only implement for 3x3 matrices
AssertFatal(rows >= 3 && cols >= 3, "Determinant only for 3x3 or more"); // Ensure the matrix is 3x3
return (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(1, 2) * (*this)(2, 1)) +
(*this)(1, 0) * ((*this)(0, 2) * (*this)(2, 1) - (*this)(0, 1) * (*this)(2, 2)) +
(*this)(2, 0) * ((*this)(0, 1) * (*this)(1, 2) - (*this)(0, 2) * (*this)(1, 1));
}
///< M * a -> M
Matrix<DATA_TYPE, rows, cols>& mul(const Matrix<DATA_TYPE, rows, cols>& a)
{ return *this = *this * a; }
///< a * M -> M
Matrix<DATA_TYPE, rows, cols>& mulL(const Matrix<DATA_TYPE, rows, cols>& a)
{ return *this = a * *this; }
///< a * b -> M
Matrix<DATA_TYPE, rows, cols>& mul(const Matrix<DATA_TYPE, rows, cols>& a, const Matrix<DATA_TYPE, rows, cols>& b)
{ return *this = a * b; }
///< M * a -> M
Matrix<DATA_TYPE, rows, cols>& mul(const F32 a)
{ return *this = *this * a; }
///< a * b -> M
Matrix<DATA_TYPE, rows, cols>& mul(const Matrix<DATA_TYPE, rows, cols>& a, const F32 b)
{ return *this = a * b; }
Matrix<DATA_TYPE, rows, cols>& add(const Matrix<DATA_TYPE, rows, cols>& a)
{
return *this = *this += a;
}
///< M * p -> p (full [4x4] * [1x4])
void mul(Point4F& p) const { p = *this * p; }
///< M * p -> p (assume w = 1.0f)
void mulP(Point3F& p) const {
Point3F result;
result.x = (*this)(0, 0) * p.x + (*this)(0, 1) * p.y + (*this)(0, 2) * p.z + (*this)(0, 3);
result.y = (*this)(1, 0) * p.x + (*this)(1, 1) * p.y + (*this)(1, 2) * p.z + (*this)(1, 3);
result.z = (*this)(2, 0) * p.x + (*this)(2, 1) * p.y + (*this)(2, 2) * p.z + (*this)(2, 3);
p = result;
}
///< M * p -> d (assume w = 1.0f)
void mulP(const Point3F& p, Point3F* d) const { *d = *this * p; }
///< M * v -> v (assume w = 0.0f)
void mulV(VectorF& v) const
{
AssertFatal(rows == 4 && cols == 4, "Multiplying VectorF with matrix requires 4x4");
VectorF result(
(*this)(0, 0) * v.x + (*this)(0, 1) * v.y + (*this)(0, 2) * v.z,
(*this)(1, 0) * v.x + (*this)(1, 1) * v.y + (*this)(1, 2) * v.z,
(*this)(2, 0) * v.x + (*this)(2, 1) * v.y + (*this)(2, 2) * v.z
);
v = result;
}
///< M * v -> d (assume w = 0.0f)
void mulV(const VectorF& v, Point3F* d) const
{
AssertFatal(rows == 4 && cols == 4, "Multiplying VectorF with matrix requires 4x4");
VectorF result(
(*this)(0, 0) * v.x + (*this)(0, 1) * v.y + (*this)(0, 2) * v.z,
(*this)(1, 0) * v.x + (*this)(1, 1) * v.y + (*this)(1, 2) * v.z,
(*this)(2, 0) * v.x + (*this)(2, 1) * v.y + (*this)(2, 2) * v.z
);
d->x = result.x;
d->y = result.y;
d->z = result.z;
}
///< Axial box -> Axial Box (too big a function to be inline)
void mul(Box3F& box) const;
// ------ Getters ------
bool isNaN() {
for (U32 i = 0; i < rows; i++) {
for (U32 j = 0; j < cols; j++) {
if (mIsNaN_F((*this)(i, j)))
return true;
}
}
return false;
}
// row + col * cols
static U32 idx(U32 i, U32 j) { return (i + j * cols); }
bool isAffine() const;
bool isIdentity() const;
/// Take inverse of matrix assuming it is affine (rotation,
/// scale, sheer, translation only).
Matrix<DATA_TYPE, rows, cols>& affineInverse();
Point3F getScale() const;
EulerF toEuler() const;
Point3F getPosition() const;
void getColumn(S32 col, Point4F* cptr) const;
Point4F getColumn4F(S32 col) const { Point4F ret; getColumn(col, &ret); return ret; }
void getColumn(S32 col, Point3F* cptr) const;
Point3F getColumn3F(S32 col) const { Point3F ret; getColumn(col, &ret); return ret; }
void getRow(S32 row, Point4F* cptr) const;
Point4F getRow4F(S32 row) const { Point4F ret; getRow(row, &ret); return ret; }
void getRow(S32 row, Point3F* cptr) const;
Point3F getRow3F(S32 row) const { Point3F ret; getRow(row, &ret); return ret; }
VectorF getRightVector() const;
VectorF getForwardVector() const;
VectorF getUpVector() const;
DATA_TYPE* getData() {
return data;
}
const DATA_TYPE* getData() const {
return data;
}
void transposeTo(Matrix<DATA_TYPE, cols, rows>& matrix) const {
for (U32 i = 0; i < rows; ++i) {
for (U32 j = 0; j < cols; ++j) {
matrix(j, i) = (*this)(i, j);
}
}
}
void swap(DATA_TYPE& a, DATA_TYPE& b) {
DATA_TYPE temp = a;
a = b;
b = temp;
}
void invertTo(Matrix<DATA_TYPE, cols, rows>* matrix) const;
void dumpMatrix(const char* caption = NULL) const;
// Static identity matrix
static const Matrix Identity;
// ------ Operators ------
friend Matrix<DATA_TYPE, rows, cols> operator*(const Matrix<DATA_TYPE, rows, cols>& m1, const Matrix<DATA_TYPE, rows, cols>& m2) {
Matrix<DATA_TYPE, rows, cols> result;
for (U32 i = 0; i < rows; ++i) {
for (U32 j = 0; j < cols; ++j)
{
result(i, j) = static_cast<DATA_TYPE>(0);
for (U32 k = 0; k < cols; ++k)
{
result(i, j) += m1(i, k) * m2(k, j);
}
}
}
return result;
}
Matrix<DATA_TYPE, rows, cols> operator *= (const Matrix<DATA_TYPE, rows, cols>& other) {
*this = *this * other;
return *this;
}
Matrix<DATA_TYPE, rows, cols> operator+(const Matrix<DATA_TYPE, rows, cols>& m2) {
Matrix<DATA_TYPE, rows, cols> result;
for (U32 i = 0; i < rows; ++i)
{
for (U32 j = 0; j < cols; ++j)
{
result(i, j) = 0; // Initialize result element to 0
result(i, j) = (*this)(i, j) + m2(i, j);
}
}
return result;
}
Matrix<DATA_TYPE, rows, cols> operator+=(const Matrix<DATA_TYPE, rows, cols>& m2) {
for (U32 i = 0; i < rows; ++i)
{
for (U32 j = 0; j < cols; ++j)
{
(*this)(i, j) += m2(i, j);
}
}
return (*this);
}
Matrix<DATA_TYPE, rows, cols> operator * (const DATA_TYPE scalar) const {
Matrix<DATA_TYPE, rows, cols> result;
for (U32 i = 0; i < rows; i++)
{
for (U32 j = 0; j < cols; j++)
{
result(i, j) = (*this)(i, j) * scalar;
}
}
return result;
}
Matrix<DATA_TYPE, rows, cols>& operator *= (const DATA_TYPE scalar) {
for (U32 i = 0; i < rows; i++)
{
for (U32 j = 0; j < cols; j++)
{
(*this)(i, j) *= scalar;
}
}
return *this;
}
Point3F operator*(const Point3F& point) const {
AssertFatal(rows == 4 && cols == 4, "Multiplying point3 with matrix requires 4x4");
Point3F result;
result.x = (*this)(0, 0) * point.x + (*this)(0, 1) * point.y + (*this)(0, 2) * point.z + (*this)(0, 3);
result.y = (*this)(1, 0) * point.x + (*this)(1, 1) * point.y + (*this)(1, 2) * point.z + (*this)(1, 3);
result.z = (*this)(2, 0) * point.x + (*this)(2, 1) * point.y + (*this)(2, 2) * point.z + (*this)(2, 3);
return result;
}
Point4F operator*(const Point4F& point) const {
AssertFatal(rows == 4 && cols == 4, "Multiplying point4 with matrix requires 4x4");
return Point4F(
(*this)(0, 0) * point.x + (*this)(0, 1) * point.y + (*this)(0, 2) * point.z + (*this)(0, 3) * point.w,
(*this)(1, 0) * point.x + (*this)(1, 1) * point.y + (*this)(1, 2) * point.z + (*this)(1, 3) * point.w,
(*this)(2, 0) * point.x + (*this)(2, 1) * point.y + (*this)(2, 2) * point.z + (*this)(2, 3) * point.w,
(*this)(3, 0) * point.x + (*this)(3, 1) * point.y + (*this)(3, 2) * point.z + (*this)(3, 3) * point.w
);
}
Matrix<DATA_TYPE, rows, cols>& operator = (const Matrix<DATA_TYPE, rows, cols>& other) {
if (this != &other) {
std::copy(other.data, other.data + rows * cols, this->data);
}
return *this;
}
bool operator == (const Matrix<DATA_TYPE, rows, cols>& other) const {
for (U32 i = 0; i < rows; i++)
{
for (U32 j = 0; j < cols; j++)
{
if ((*this)(i, j) != other(i, j))
return false;
}
}
return true;
}
bool operator != (const Matrix<DATA_TYPE, rows, cols>& other) const {
return !(*this == other);
}
operator DATA_TYPE* () { return (data); }
operator const DATA_TYPE* () const { return (DATA_TYPE*)(data); }
DATA_TYPE& operator () (U32 row, U32 col) {
if (row >= rows || col >= cols)
AssertFatal(false, "Matrix indices out of range");
return data[idx(col,row)];
}
DATA_TYPE operator () (U32 row, U32 col) const {
if (row >= rows || col >= cols)
AssertFatal(false, "Matrix indices out of range");
return data[idx(col, row)];
}
};
//--------------------------------------------
// INLINE FUNCTIONS
//--------------------------------------------
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::transpose()
{
AssertFatal(rows == cols, "Transpose can only be performed on square matrices.");
swap((*this)(0, 1), (*this)(1, 0));
swap((*this)(0, 2), (*this)(2, 0));
swap((*this)(0, 3), (*this)(3, 0));
swap((*this)(1, 2), (*this)(2, 1));
swap((*this)(1, 3), (*this)(3, 1));
swap((*this)(2, 3), (*this)(3, 2));
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::identity()
{
for (U32 i = 0; i < rows; i++)
{
for (U32 j = 0; j < cols; j++)
{
if (j == i)
(*this)(i, j) = static_cast<DATA_TYPE>(1);
else
(*this)(i, j) = static_cast<DATA_TYPE>(0);
}
}
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::normalize()
{
AssertFatal(rows >= 3 && cols >= 3, "Normalize can only be applied 3x3 or more");
Point3F col0, col1, col2;
getColumn(0, &col0);
getColumn(1, &col1);
mCross(col0, col1, &col2);
mCross(col2, col0, &col1);
col0.normalize();
col1.normalize();
col2.normalize();
setColumn(0, col0);
setColumn(1, col1);
setColumn(2, col2);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::scale(const Point3F& s)
{
// torques scale applies directly, does not create another matrix to multiply with the translation matrix.
AssertFatal(rows >= 4 && cols >= 4, "Scale can only be applied 4x4 or more");
(*this)(0, 0) *= s.x; (*this)(0, 1) *= s.y; (*this)(0, 2) *= s.z;
(*this)(1, 0) *= s.x; (*this)(1, 1) *= s.y; (*this)(1, 2) *= s.z;
(*this)(2, 0) *= s.x; (*this)(2, 1) *= s.y; (*this)(2, 2) *= s.z;
(*this)(3, 0) *= s.x; (*this)(3, 1) *= s.y; (*this)(3, 2) *= s.z;
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline bool Matrix<DATA_TYPE, rows, cols>::isIdentity() const {
for (U32 i = 0; i < rows; i++)
{
for (U32 j = 0; j < cols; j++)
{
if (j == i)
{
if((*this)(i, j) != static_cast<DATA_TYPE>(1))
{
return false;
}
}
else
{
if((*this)(i, j) != static_cast<DATA_TYPE>(0))
{
return false;
}
}
}
}
return true;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Point3F Matrix<DATA_TYPE, rows, cols>::getScale() const
{
// this function assumes the matrix has scale applied through the scale(const Point3F& s) function.
// for now assume float since we have point3F.
AssertFatal(rows >= 4 && cols >= 4, "Scale can only be applied 4x4 or more");
Point3F scale;
scale.x = mSqrt((*this)(0, 0) * (*this)(0, 0) + (*this)(1, 0) * (*this)(1, 0) + (*this)(2, 0) * (*this)(2, 0));
scale.y = mSqrt((*this)(0, 1) * (*this)(0, 1) + (*this)(1, 1) * (*this)(1, 1) + (*this)(2, 1) * (*this)(2, 1));
scale.z = mSqrt((*this)(0, 2) * (*this)(0, 2) + (*this)(1, 2) * (*this)(1, 2) + (*this)(2, 2) * (*this)(2, 2));
return scale;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Point3F Matrix<DATA_TYPE, rows, cols>::getPosition() const
{
Point3F pos;
getColumn(3, &pos);
return pos;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::getColumn(S32 col, Point4F* cptr) const
{
if (rows >= 2)
{
cptr->x = (*this)(0, col);
cptr->y = (*this)(1, col);
}
if (rows >= 3)
cptr->z = (*this)(2, col);
else
cptr->z = 0.0f;
if (rows >= 4)
cptr->w = (*this)(3, col);
else
cptr->w = 0.0f;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::getColumn(S32 col, Point3F* cptr) const
{
if (rows >= 2)
{
cptr->x = (*this)(0, col);
cptr->y = (*this)(1, col);
}
if (rows >= 3)
cptr->z = (*this)(2, col);
else
cptr->z = 0.0f;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::setColumn(S32 col, const Point4F &cptr) {
if(rows >= 2)
{
(*this)(0, col) = cptr.x;
(*this)(1, col) = cptr.y;
}
if(rows >= 3)
(*this)(2, col) = cptr.z;
if(rows >= 4)
(*this)(3, col) = cptr.w;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::setColumn(S32 col, const Point3F &cptr) {
if(rows >= 2)
{
(*this)(0, col) = cptr.x;
(*this)(1, col) = cptr.y;
}
if(rows >= 3)
(*this)(2, col) = cptr.z;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::getRow(S32 row, Point4F* cptr) const
{
if (cols >= 2)
{
cptr->x = (*this)(row, 0);
cptr->y = (*this)(row, 1);
}
if (cols >= 3)
cptr->z = (*this)(row, 2);
else
cptr->z = 0.0f;
if (cols >= 4)
cptr->w = (*this)(row, 3);
else
cptr->w = 0.0f;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::getRow(S32 row, Point3F* cptr) const
{
if (cols >= 2)
{
cptr->x = (*this)(row, 0);
cptr->y = (*this)(row, 1);
}
if (cols >= 3)
cptr->z = (*this)(row, 2);
else
cptr->z = 0.0f;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline VectorF Matrix<DATA_TYPE, rows, cols>::getRightVector() const
{
VectorF vec;
getColumn(0, &vec);
return vec;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline VectorF Matrix<DATA_TYPE, rows, cols>::getForwardVector() const
{
VectorF vec;
getColumn(1, &vec);
return vec;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline VectorF Matrix<DATA_TYPE, rows, cols>::getUpVector() const
{
VectorF vec;
getColumn(2, &vec);
return vec;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::invertTo(Matrix<DATA_TYPE, cols, rows>* matrix) const
{
Matrix<DATA_TYPE, rows, cols> invMatrix;
for (U32 i = 0; i < rows; ++i)
{
for (U32 j = 0; j < cols; ++j)
{
invMatrix(i, j) = (*this)(i, j);
}
}
invMatrix.inverse();
for (U32 i = 0; i < rows; ++i)
{
for (U32 j = 0; j < cols; ++j)
{
(*matrix)(i, j) = invMatrix(i, j);
}
}
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::setRow(S32 row, const Point4F& cptr) {
if(cols >= 2)
{
(*this)(row, 0) = cptr.x;
(*this)(row, 1) = cptr.y;
}
if(cols >= 3)
(*this)(row, 2) = cptr.z;
if(cols >= 4)
(*this)(row, 3) = cptr.w;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::setRow(S32 row, const Point3F& cptr) {
if(cols >= 2)
{
(*this)(row, 0) = cptr.x;
(*this)(row, 1) = cptr.y;
}
if(cols >= 3)
(*this)(row, 2) = cptr.z;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::displace(const Point3F& delta)
{
(*this)(0, 3) += delta.x;
(*this)(1, 3) += delta.y;
(*this)(2, 3) += delta.z;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::reverseProjection()
{
AssertFatal(rows == 4 && cols == 4, "reverseProjection requires a 4x4 matrix.");
(*this)(2, 0) = (*this)(3, 0) - (*this)(2, 0);
(*this)(2, 1) = (*this)(3, 1) - (*this)(2, 1);
(*this)(2, 2) = (*this)(3, 2) - (*this)(2, 2);
(*this)(2, 3) = (*this)(3, 3) - (*this)(2, 3);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
const Matrix<DATA_TYPE, rows, cols> Matrix<DATA_TYPE, rows, cols>::Identity = []() {
Matrix<DATA_TYPE, rows, cols> identity(true);
return identity;
}();
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::set(const EulerF& e)
{
// when the template refactor is done, euler will be able to be setup in different ways
AssertFatal(rows >= 3 && cols >= 3, "EulerF can only initialize 3x3 or more");
static_assert(std::is_same<DATA_TYPE, float>::value, "Can only initialize eulers with floats for now");
F32 cosPitch, sinPitch;
mSinCos(e.x, sinPitch, cosPitch);
F32 cosYaw, sinYaw;
mSinCos(e.y, sinYaw, cosYaw);
F32 cosRoll, sinRoll;
mSinCos(e.z, sinRoll, cosRoll);
enum {
AXIS_X = (1 << 0),
AXIS_Y = (1 << 1),
AXIS_Z = (1 << 2)
};
U32 axis = 0;
if (e.x != 0.0f) axis |= AXIS_X;
if (e.y != 0.0f) axis |= AXIS_Y;
if (e.z != 0.0f) axis |= AXIS_Z;
switch (axis) {
case 0:
(*this) = Matrix<DATA_TYPE, rows, cols>(true);
break;
case AXIS_X:
(*this)(0, 0) = 1.0f; (*this)(0, 1) = 0.0f; (*this)(0, 2) = 0.0f;
(*this)(1, 0) = 0.0f; (*this)(1, 1) = cosPitch; (*this)(1, 2) = sinPitch;
(*this)(2, 0) = 0.0f; (*this)(2, 1) = -sinPitch; (*this)(2, 2) = cosPitch;
break;
case AXIS_Y:
(*this)(0, 0) = cosYaw; (*this)(1, 0) = 0.0f; (*this)(2, 0) = sinYaw;
(*this)(0, 1) = 0.0f; (*this)(1, 1) = 1.0f; (*this)(2, 1) = 0.0f;
(*this)(0, 2) = -sinYaw; (*this)(1, 2) = 0.0f; (*this)(2, 2) = cosYaw;
break;
case AXIS_Z:
(*this)(0, 0) = cosRoll; (*this)(0, 1) = sinRoll; (*this)(0, 2) = 0.0f;
(*this)(1, 0) = -sinRoll; (*this)(1, 1) = cosRoll; (*this)(1, 2) = 0.0f;
(*this)(2, 0) = 0.0f; (*this)(2, 1) = 0.0f; (*this)(2, 2) = 1.0f;
break;
default:
F32 r1 = cosYaw * cosRoll;
F32 r2 = cosYaw * sinRoll;
F32 r3 = sinYaw * cosRoll;
F32 r4 = sinYaw * sinRoll;
// the matrix looks like this:
// r1 - (r4 * sin(x)) r2 + (r3 * sin(x)) -cos(x) * sin(y)
// -cos(x) * sin(z) cos(x) * cos(z) sin(x)
// r3 + (r2 * sin(x)) r4 - (r1 * sin(x)) cos(x) * cos(y)
//
// where:
// r1 = cos(y) * cos(z)
// r2 = cos(y) * sin(z)
// r3 = sin(y) * cos(z)
// r4 = sin(y) * sin(z)
// init the euler 3x3 rotation matrix.
(*this)(0, 0) = r1 - (r4 * sinPitch); (*this)(0, 1) = r2 + (r3 * sinPitch); (*this)(0, 2) = -cosPitch * sinYaw;
(*this)(1, 0) = -cosPitch * sinRoll; (*this)(1, 1) = cosPitch * cosRoll; (*this)(1, 2) = sinPitch;
(*this)(2, 0) = r3 + (r2 * sinPitch); (*this)(2, 1) = r4 - (r1 * sinPitch); (*this)(2, 2) = cosPitch * cosYaw;
break;
}
if (rows == 4)
{
(*this)(3, 0) = 0.0f;
(*this)(3, 1) = 0.0f;
(*this)(3, 2) = 0.0f;
}
if (cols == 4)
{
(*this)(0, 3) = 0.0f;
(*this)(1, 3) = 0.0f;
(*this)(2, 3) = 0.0f;
}
if (rows == 4 && cols == 4)
{
(*this)(3, 3) = 1.0f;
}
return(*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
Matrix<DATA_TYPE, rows, cols>::Matrix(const EulerF& e, const Point3F p)
{
set(e, p);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::set(const EulerF& e, const Point3F p)
{
AssertFatal(rows >= 3 && cols >= 4, "Euler and Point can only initialize 3x4 or more");
// call set euler, this already sets the last row if it exists.
set(e);
// does this need to multiply with the result of the euler? or are we just setting position.
(*this)(0, 3) = p.x;
(*this)(1, 3) = p.y;
(*this)(2, 3) = p.z;
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::inverse()
{
#if 1
// NOTE: Gauss-Jordan elimination is yielding unpredictable results due to precission handling and
// numbers near 0.0
//
AssertFatal(rows == cols, "Can only perform inverse on square matrices.");
const U32 size = rows - 1;
const DATA_TYPE pivot_eps = static_cast<DATA_TYPE>(1e-20); // Smaller epsilon to handle numerical precision
// Create augmented matrix [this | I]
Matrix<DATA_TYPE, size, rows + size> augmentedMatrix;
for (U32 i = 0; i < size; i++)
{
for (U32 j = 0; j < size; j++)
{
augmentedMatrix(i, j) = (*this)(i, j);
augmentedMatrix(i, j + size) = (i == j) ? static_cast<DATA_TYPE>(1) : static_cast<DATA_TYPE>(0);
}
}
// Apply gauss-joran elimination
for (U32 i = 0; i < size; i++)
{
U32 pivotRow = i;
DATA_TYPE pivotValue = std::abs(augmentedMatrix(i, i));
for (U32 k = i + 1; k < size; k++)
{
DATA_TYPE curValue = std::abs(augmentedMatrix(k, i));
if (curValue > pivotValue) {
pivotRow = k;
pivotValue = curValue;
}
}
// Swap if needed.
if (i != pivotRow)
{
for (U32 j = 0; j < 2 * size; j++)
{
DATA_TYPE temp = augmentedMatrix(i, j);
augmentedMatrix(i, j) = augmentedMatrix(pivotRow, j);
augmentedMatrix(pivotRow, j) = temp;
}
}
// Early out if pivot is 0, return identity matrix.
if (std::abs(augmentedMatrix(i, i)) < pivot_eps)
{
return *this;
}
DATA_TYPE pivotVal = static_cast<DATA_TYPE>(1.0) / augmentedMatrix(i, i);
// scale the pivot
for (U32 j = 0; j < 2 * size; j++)
{
augmentedMatrix(i, j) *= pivotVal;
}
// Eliminate the current column in all other rows
for (U32 k = 0; k < size; k++)
{
if (k != i)
{
DATA_TYPE factor = augmentedMatrix(k, i);
for (U32 j = 0; j < 2 * size; j++)
{
augmentedMatrix(k, j) -= factor * augmentedMatrix(i, j);
}
}
}
}
for (U32 i = 0; i < size; i++)
{
for (U32 j = 0; j < size; j++)
{
(*this)(i, j) = augmentedMatrix(i, j + size);
}
}
#else
AssertFatal(rows == cols, "Can only perform inverse on square matrices.");
AssertFatal(rows >= 3 && cols >= 3, "Must be at least a 3x3 matrix");
DATA_TYPE det = determinant();
// Check if the determinant is non-zero
if (std::abs(det) < static_cast<DATA_TYPE>(1e-10)) {
this->identity(); // Return the identity matrix if the determinant is zero
return *this;
}
DATA_TYPE invDet = DATA_TYPE(1) / det;
Matrix<DATA_TYPE, rows, cols> temp;
// Calculate the inverse of the 3x3 upper-left submatrix using Cramer's rule
temp(0, 0) = ((*this)(1, 1) * (*this)(2, 2) - (*this)(1, 2) * (*this)(2, 1)) * invDet;
temp(0, 1) = ((*this)(2, 1) * (*this)(0, 2) - (*this)(2, 2) * (*this)(0, 1)) * invDet;
temp(0, 2) = ((*this)(0, 1) * (*this)(1, 2) - (*this)(0, 2) * (*this)(1, 1)) * invDet;
temp(1, 0) = ((*this)(1, 2) * (*this)(2, 0) - (*this)(1, 0) * (*this)(2, 2)) * invDet;
temp(1, 1) = ((*this)(2, 2) * (*this)(0, 0) - (*this)(2, 0) * (*this)(0, 2)) * invDet;
temp(1, 2) = ((*this)(0, 2) * (*this)(1, 0) - (*this)(0, 0) * (*this)(1, 2)) * invDet;
temp(2, 0) = ((*this)(1, 0) * (*this)(2, 1) - (*this)(1, 1) * (*this)(2, 0)) * invDet;
temp(2, 1) = ((*this)(2, 0) * (*this)(0, 1) - (*this)(2, 1) * (*this)(0, 0)) * invDet;
temp(2, 2) = ((*this)(0, 0) * (*this)(1, 1) - (*this)(0, 1) * (*this)(1, 0)) * invDet;
// Copy the 3x3 inverse back into this matrix
for (U32 i = 0; i < 3; ++i)
{
for (U32 j = 0; j < 3; ++j)
{
(*this)(i, j) = temp(i, j);
}
}
#endif
Point3F pos = -this->getPosition();
mulV(pos);
this->setPosition(pos);
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline bool Matrix<DATA_TYPE, rows, cols>::fullInverse()
{
#if 1
// NOTE: Gauss-Jordan elimination is yielding unpredictable results due to precission handling and
// numbers near 0.0
AssertFatal(rows == cols, "Can only perform inverse on square matrices.");
const U32 size = rows;
const DATA_TYPE pivot_eps = static_cast<DATA_TYPE>(1e-20); // Smaller epsilon to handle numerical precision
// Create augmented matrix [this | I]
Matrix<DATA_TYPE, size, rows + size> augmentedMatrix;
for (U32 i = 0; i < size; i++)
{
for (U32 j = 0; j < size; j++)
{
augmentedMatrix(i, j) = (*this)(i, j);
augmentedMatrix(i, j + size) = (i == j) ? static_cast<DATA_TYPE>(1) : static_cast<DATA_TYPE>(0);
}
}
// Apply gauss-joran elimination
for (U32 i = 0; i < size; i++)
{
U32 pivotRow = i;
DATA_TYPE pivotValue = std::abs(augmentedMatrix(i, i));
for (U32 k = i + 1; k < size; k++)
{
DATA_TYPE curValue = std::abs(augmentedMatrix(k, i));
if (curValue > pivotValue) {
pivotRow = k;
pivotValue = curValue;
}
}
// Swap if needed.
if (i != pivotRow)
{
for (U32 j = 0; j < 2 * size; j++)
{
DATA_TYPE temp = augmentedMatrix(i, j);
augmentedMatrix(i, j) = augmentedMatrix(pivotRow, j);
augmentedMatrix(pivotRow, j) = temp;
}
}
// Early out if pivot is 0, return identity matrix.
if (std::abs(augmentedMatrix(i, i)) < pivot_eps)
{
return false;
}
DATA_TYPE pivotVal = static_cast<DATA_TYPE>(1.0) / augmentedMatrix(i, i);
// scale the pivot
for (U32 j = 0; j < 2 * size; j++)
{
augmentedMatrix(i, j) *= pivotVal;
}
// Eliminate the current column in all other rows
for (U32 k = 0; k < size; k++)
{
if (k != i)
{
DATA_TYPE factor = augmentedMatrix(k, i);
for (U32 j = 0; j < 2 * size; j++)
{
augmentedMatrix(k, j) -= factor * augmentedMatrix(i, j);
}
}
}
}
for (U32 i = 0; i < size; i++)
{
for (U32 j = 0; j < size; j++)
{
(*this)(i, j) = augmentedMatrix(i, j + size);
}
}
#else
AssertFatal(rows == cols, "Can only perform inverse on square matrices.");
AssertFatal(rows >= 4 && cols >= 4, "Can only perform fullInverse on minimum 4x4 matrix");
Point4F a, b, c, d;
getRow(0, &a);
getRow(1, &b);
getRow(2, &c);
getRow(3, &d);
F32 det = a.x * b.y * c.z * d.w - a.x * b.y * c.w * d.z - a.x * c.y * b.z * d.w + a.x * c.y * b.w * d.z + a.x * d.y * b.z * c.w - a.x * d.y * b.w * c.z
- b.x * a.y * c.z * d.w + b.x * a.y * c.w * d.z + b.x * c.y * a.z * d.w - b.x * c.y * a.w * d.z - b.x * d.y * a.z * c.w + b.x * d.y * a.w * c.z
+ c.x * a.y * b.z * d.w - c.x * a.y * b.w * d.z - c.x * b.y * a.z * d.w + c.x * b.y * a.w * d.z + c.x * d.y * a.z * b.w - c.x * d.y * a.w * b.z
- d.x * a.y * b.z * c.w + d.x * a.y * b.w * c.z + d.x * b.y * a.z * c.w - d.x * b.y * a.w * c.z - d.x * c.y * a.z * b.w + d.x * c.y * a.w * b.z;
if (mFabs(det) < 0.00001f)
return false;
Point4F aa, bb, cc, dd;
aa.x = b.y * c.z * d.w - b.y * c.w * d.z - c.y * b.z * d.w + c.y * b.w * d.z + d.y * b.z * c.w - d.y * b.w * c.z;
aa.y = -a.y * c.z * d.w + a.y * c.w * d.z + c.y * a.z * d.w - c.y * a.w * d.z - d.y * a.z * c.w + d.y * a.w * c.z;
aa.z = a.y * b.z * d.w - a.y * b.w * d.z - b.y * a.z * d.w + b.y * a.w * d.z + d.y * a.z * b.w - d.y * a.w * b.z;
aa.w = -a.y * b.z * c.w + a.y * b.w * c.z + b.y * a.z * c.w - b.y * a.w * c.z - c.y * a.z * b.w + c.y * a.w * b.z;
bb.x = -b.x * c.z * d.w + b.x * c.w * d.z + c.x * b.z * d.w - c.x * b.w * d.z - d.x * b.z * c.w + d.x * b.w * c.z;
bb.y = a.x * c.z * d.w - a.x * c.w * d.z - c.x * a.z * d.w + c.x * a.w * d.z + d.x * a.z * c.w - d.x * a.w * c.z;
bb.z = -a.x * b.z * d.w + a.x * b.w * d.z + b.x * a.z * d.w - b.x * a.w * d.z - d.x * a.z * b.w + d.x * a.w * b.z;
bb.w = a.x * b.z * c.w - a.x * b.w * c.z - b.x * a.z * c.w + b.x * a.w * c.z + c.x * a.z * b.w - c.x * a.w * b.z;
cc.x = b.x * c.y * d.w - b.x * c.w * d.y - c.x * b.y * d.w + c.x * b.w * d.y + d.x * b.y * c.w - d.x * b.w * c.y;
cc.y = -a.x * c.y * d.w + a.x * c.w * d.y + c.x * a.y * d.w - c.x * a.w * d.y - d.x * a.y * c.w + d.x * a.w * c.y;
cc.z = a.x * b.y * d.w - a.x * b.w * d.y - b.x * a.y * d.w + b.x * a.w * d.y + d.x * a.y * b.w - d.x * a.w * b.y;
cc.w = -a.x * b.y * c.w + a.x * b.w * c.y + b.x * a.y * c.w - b.x * a.w * c.y - c.x * a.y * b.w + c.x * a.w * b.y;
dd.x = -b.x * c.y * d.z + b.x * c.z * d.y + c.x * b.y * d.z - c.x * b.z * d.y - d.x * b.y * c.z + d.x * b.z * c.y;
dd.y = a.x * c.y * d.z - a.x * c.z * d.y - c.x * a.y * d.z + c.x * a.z * d.y + d.x * a.y * c.z - d.x * a.z * c.y;
dd.z = -a.x * b.y * d.z + a.x * b.z * d.y + b.x * a.y * d.z - b.x * a.z * d.y - d.x * a.y * b.z + d.x * a.z * b.y;
dd.w = a.x * b.y * c.z - a.x * b.z * c.y - b.x * a.y * c.z + b.x * a.z * c.y + c.x * a.y * b.z - c.x * a.z * b.y;
setRow(0, aa);
setRow(1, bb);
setRow(2, cc);
setRow(3, dd);
mul(1.0f / det);
#endif
return true;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::invert()
{
(*this) = inverse();
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::setCrossProduct(const Point3F& p)
{
AssertFatal(rows == 4 && cols == 4, "Cross product only supported on 4x4 for now");
(*this)(0, 0) = 0;
(*this)(0, 1) = -p.z;
(*this)(0, 2) = p.y;
(*this)(0, 3) = 0;
(*this)(1, 0) = p.z;
(*this)(1, 1) = 0;
(*this)(1, 2) = -p.x;
(*this)(1, 3) = 0;
(*this)(2, 0) = -p.y;
(*this)(2, 1) = p.x;
(*this)(2, 2) = 0;
(*this)(2, 3) = 0;
(*this)(3, 0) = 0;
(*this)(3, 1) = 0;
(*this)(3, 2) = 0;
(*this)(3, 3) = 1;
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::setTensorProduct(const Point3F& p, const Point3F& q)
{
AssertFatal(rows == 4 && cols == 4, "Tensor product only supported on 4x4 for now");
(*this)(0, 0) = p.x * q.x;
(*this)(0, 1) = p.x * q.y;
(*this)(0, 2) = p.x * q.z;
(*this)(0, 3) = 0;
(*this)(1, 0) = p.y * q.x;
(*this)(1, 1) = p.y * q.y;
(*this)(1, 2) = p.y * q.z;
(*this)(1, 3) = 0;
(*this)(2, 0) = p.z * q.x;
(*this)(2, 1) = p.z * q.y;
(*this)(2, 2) = p.z * q.z;
(*this)(2, 3) = 0;
(*this)(3, 0) = 0;
(*this)(3, 1) = 0;
(*this)(3, 2) = 0;
(*this)(3, 3) = 1;
return (*this);
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::mul(Box3F& box) const
{
AssertFatal(rows == 4 && cols == 4, "Multiplying Box3F with matrix requires 4x4");
// Extract the min and max extents
const Point3F& originalMin = box.minExtents;
const Point3F& originalMax = box.maxExtents;
// Array to store transformed corners
Point3F transformedCorners[8];
// Compute all 8 corners of the box
Point3F corners[8] = {
{originalMin.x, originalMin.y, originalMin.z},
{originalMax.x, originalMin.y, originalMin.z},
{originalMin.x, originalMax.y, originalMin.z},
{originalMax.x, originalMax.y, originalMin.z},
{originalMin.x, originalMin.y, originalMax.z},
{originalMax.x, originalMin.y, originalMax.z},
{originalMin.x, originalMax.y, originalMax.z},
{originalMax.x, originalMax.y, originalMax.z}
};
// Transform each corner
for (U32 i = 0; i < 8; ++i)
{
const Point3F& corner = corners[i];
transformedCorners[i].x = (*this)(0, 0) * corner.x + (*this)(0, 1) * corner.y + (*this)(0, 2) * corner.z + (*this)(0, 3);
transformedCorners[i].y = (*this)(1, 0) * corner.x + (*this)(1, 1) * corner.y + (*this)(1, 2) * corner.z + (*this)(1, 3);
transformedCorners[i].z = (*this)(2, 0) * corner.x + (*this)(2, 1) * corner.y + (*this)(2, 2) * corner.z + (*this)(2, 3);
}
// Initialize min and max extents to the transformed values
Point3F newMin = transformedCorners[0];
Point3F newMax = transformedCorners[0];
// Compute the new min and max extents from the transformed corners
for (U32 i = 1; i < 8; ++i)
{
const Point3F& corner = transformedCorners[i];
if (corner.x < newMin.x) newMin.x = corner.x;
if (corner.y < newMin.y) newMin.y = corner.y;
if (corner.z < newMin.z) newMin.z = corner.z;
if (corner.x > newMax.x) newMax.x = corner.x;
if (corner.y > newMax.y) newMax.y = corner.y;
if (corner.z > newMax.z) newMax.z = corner.z;
}
// Update the box with the new min and max extents
box.minExtents = newMin;
box.maxExtents = newMax;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline bool Matrix<DATA_TYPE, rows, cols>::isAffine() const
{
if ((*this)(3, 3) != 1.0f)
{
return false;
}
for (U32 col = 0; col < cols - 1; ++col)
{
if ((*this)(3, col) != 0.0f)
{
return false;
}
}
Point3F one, two, three;
getColumn(0, &one);
getColumn(1, &two);
getColumn(2, &three);
// check columns
{
if (mDot(one, two) > 0.0001f ||
mDot(one, three) > 0.0001f ||
mDot(two, three) > 0.0001f)
return false;
if (mFabs(1.0f - one.lenSquared()) > 0.0001f ||
mFabs(1.0f - two.lenSquared()) > 0.0001f ||
mFabs(1.0f - three.lenSquared()) > 0.0001f)
return false;
}
getRow(0, &one);
getRow(1, &two);
getRow(2, &three);
// check rows
{
if (mDot(one, two) > 0.0001f ||
mDot(one, three) > 0.0001f ||
mDot(two, three) > 0.0001f)
return false;
if (mFabs(1.0f - one.lenSquared()) > 0.0001f ||
mFabs(1.0f - two.lenSquared()) > 0.0001f ||
mFabs(1.0f - three.lenSquared()) > 0.0001f)
return false;
}
return true;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline Matrix<DATA_TYPE, rows, cols>& Matrix<DATA_TYPE, rows, cols>::affineInverse()
{
AssertFatal(rows >= 4 && cols >= 4, "affineInverse requires at least 4x4");
Matrix<DATA_TYPE, rows, cols> temp = *this;
// Transpose rotation part
(*this)(0, 1) = temp(1, 0);
(*this)(0, 2) = temp(2, 0);
(*this)(1, 0) = temp(0, 1);
(*this)(1, 2) = temp(2, 1);
(*this)(2, 0) = temp(0, 2);
(*this)(2, 1) = temp(1, 2);
// Adjust translation part
(*this)(0, 3) = -(temp(0, 0) * temp(0, 3) + temp(1, 0) * temp(1, 3) + temp(2, 0) * temp(2, 3));
(*this)(1, 3) = -(temp(0, 1) * temp(0, 3) + temp(1, 1) * temp(1, 3) + temp(2, 1) * temp(2, 3));
(*this)(2, 3) = -(temp(0, 2) * temp(0, 3) + temp(1, 2) * temp(1, 3) + temp(2, 2) * temp(2, 3));
return *this;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline EulerF Matrix<DATA_TYPE, rows, cols>::toEuler() const
{
AssertFatal(rows >= 3 && cols >= 3, "Euler rotations require at least a 3x3 matrix.");
// like all others assume float for now.
EulerF r;
r.x = mAsin(mClampF((*this)(1,2), -1.0, 1.0));
if (mCos(r.x) != 0.0f)
{
r.y = mAtan2(-(*this)(0, 2), (*this)(2, 2)); // yaw
r.z = mAtan2(-(*this)(1, 0), (*this)(1, 1)); // roll
}
else
{
r.y = 0.0f;
r.z = mAtan2((*this)(0, 1), (*this)(0, 0)); // this rolls when pitch is +90 degrees
}
return r;
}
template<typename DATA_TYPE, U32 rows, U32 cols>
inline void Matrix<DATA_TYPE, rows, cols>::dumpMatrix(const char* caption) const
{
U32 size = (caption == NULL) ? 0 : dStrlen(caption);
FrameTemp<char> spacer(size + 1);
char* spacerRef = spacer;
// is_floating_point should return true for floats and doubles.
const char* formatSpec = std::is_floating_point_v<DATA_TYPE> ? " %-8.4f" : " %d";
dMemset(spacerRef, ' ', size);
// null terminate.
spacerRef[size] = '\0';
/*Con::printf("%s = | %-8.4f %-8.4f %-8.4f %-8.4f |", caption, m[idx(0, 0)], m[idx(0, 1)], m[idx(0, 2)], m[idx(0, 3)]);
Con::printf("%s | %-8.4f %-8.4f %-8.4f %-8.4f |", spacerRef, m[idx(1, 0)], m[idx(1, 1)], m[idx(1, 2)], m[idx(1, 3)]);
Con::printf("%s | %-8.4f %-8.4f %-8.4f %-8.4f |", spacerRef, m[idx(2, 0)], m[idx(2, 1)], m[idx(2, 2)], m[idx(2, 3)]);
Con::printf("%s | %-8.4f %-8.4f %-8.4f %-8.4f |", spacerRef, m[idx(3, 0)], m[idx(3, 1)], m[idx(3, 2)], m[idx(3, 3)]);*/
StringBuilder str;
str.format("%s = |", caption);
for (U32 i = 0; i < rows; i++)
{
if (i > 0)
{
str.append(spacerRef);
}
for (U32 j = 0; j < cols; j++)
{
str.format(formatSpec, (*this)(i, j));
}
str.append(" |\n");
}
Con::printf("%s", str.end().c_str());
}
//------------------------------------
// Non-member methods
//------------------------------------
inline void mTransformPlane(
const MatrixF& mat,
const Point3F& scale,
const PlaneF& plane,
PlaneF* result
) {
// Create the inverse scale matrix
MatrixF invScale(true);
invScale(0, 0) = 1.0f / scale.x;
invScale(1, 1) = 1.0f / scale.y;
invScale(2, 2) = 1.0f / scale.z;
const Point3F shear(mat(0, 3), mat(1, 3), mat(2, 3));
const Point3F row0 = mat.getRow3F(0);
const Point3F row1 = mat.getRow3F(1);
const Point3F row2 = mat.getRow3F(2);
const F32 A = -mDot(row0, shear);
const F32 B = -mDot(row1, shear);
const F32 C = -mDot(row2, shear);
// Compute the inverse transpose of the matrix
MatrixF invTrMatrix(true);
invTrMatrix(0, 0) = mat(0, 0);
invTrMatrix(0, 1) = mat(0, 1);
invTrMatrix(0, 2) = mat(0, 2);
invTrMatrix(1, 0) = mat(1, 0);
invTrMatrix(1, 1) = mat(1, 1);
invTrMatrix(1, 2) = mat(1, 2);
invTrMatrix(2, 0) = mat(2, 0);
invTrMatrix(2, 1) = mat(2, 1);
invTrMatrix(2, 2) = mat(2, 2);
invTrMatrix(3, 0) = A;
invTrMatrix(3, 1) = B;
invTrMatrix(3, 2) = C;
invTrMatrix.mul(invScale);
// Transform the plane normal
Point3F norm(plane.x, plane.y, plane.z);
invTrMatrix.mulP(norm);
norm.normalize();
// Transform the plane point
Point3F point = norm * -plane.d;
MatrixF temp = mat;
point.x *= scale.x;
point.y *= scale.y;
point.z *= scale.z;
temp.mulP(point);
// Recompute the plane distance
PlaneF resultPlane(point, norm);
result->x = resultPlane.x;
result->y = resultPlane.y;
result->z = resultPlane.z;
result->d = resultPlane.d;
}
//--------------------------------------------
// INLINE FUNCTIONS END
//--------------------------------------------
typedef Matrix<F32, 4, 4> MatrixF;
class MatrixTemplateExport
{
public:
template <typename T, U32 rows, U32 cols>
static EngineFieldTable::Field getMatrixField();
};
template<typename T, U32 rows, U32 cols>
inline EngineFieldTable::Field MatrixTemplateExport::getMatrixField()
{
typedef Matrix<T, rows, cols> ThisType;
return _FIELD_AS(T, data, data, rows * cols, "");
}
#endif // !USE_TEMPLATE_MATRIX
#endif //_MMATRIX_H_
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