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nglMatrix.h
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/*
NUI3 - C++ cross-platform GUI framework for OpenGL based applications
Copyright (C) 2002-2003 Sebastien Metrot
licence: see nui3/LICENCE.TXT
*/
/*!
\file nglMatrix.h
\brief Homogeneous matrixes template classes
*/
#ifndef __nglMatrix_h__
#define __nglMatrix_h__
//#include "nui.h"
#include "nglMath.h"
#include "nglVector.h"
//! Homogenous 4x4 matrixes
/*!
This class implements the usual operations on 4x4 homogenous matrixes used
in OpenGL, as a client side counterpart of the OpenGL matrix manipulations
functions. Remember that this implementation can't benefit of any hardware
accelerated TnL, and that you should only perform minimal geometry computing
without OpenGL.
The internal representation is the same as the OpenGL, it is ordered as
column first. Illustration :
\code
// Using the Array field, we have this layout :
//
// Array[0] Array[4] Array[8] Array[12]
// Array[1] Array[5] Array[9] Array[13]
// Array[2] Array[6] Array[10] Array[14]
// Array[3] Array[7] Array[11] Array[15]
// Using the named elements from Elt instead of the array, we have this layout :
//
// Elt.M11 Elt.M12 Elt.M13 Elt.M14
// Elt.M21 Elt.M22 Elt.M23 Elt.M24
// Elt.M31 Elt.M32 Elt.M33 Elt.M34
// Elt.M41 Elt.M42 Elt.M43 Elt.M44
\endcode
*/
template <class T> class nglMatrix
{
public:
union
{
T Array[16];
struct
{
T M11,M21,M31,M41;
T M12,M22,M32,M42;
T M13,M23,M33,M43;
T M14,M24,M34,M44;
} Elt;
};
/// Create an identity matrix (see SetIdentity())
nglMatrix()
{
SetIdentity();
}
/*! Create a matrix from an array
\param pArray flat array (see nglMatrix for conventions), nullify all elements if NULL
*/
nglMatrix(const T pArray[16])
{
if (pArray)
memcpy (Array, pArray, 16*sizeof(T));
else
Nullify();
}
virtual ~nglMatrix()
{
}
/// Set all elements to zero
void Nullify()
{
uint i;
for (i = 0; i < 16; i++)
Array[i] = 0.f;
}
/// Set the matrix to identity
void SetIdentity()
{
Nullify();
Elt.M11 = 1.f;
Elt.M22 = 1.f;
Elt.M33 = 1.f;
Elt.M44 = 1.f;
}
bool IsIdentity() const
{
if (Elt.M11 == 1.0f
&& Elt.M22 == 1.0f
&& Elt.M33 == 1.0f
&& Elt.M44 == 1.0f
&& Elt.M12 == 0.0f
&& Elt.M13 == 0.0f
&& Elt.M14 == 0.0f
&& Elt.M21 == 0.0f
&& Elt.M23 == 0.0f
&& Elt.M24 == 0.0f
&& Elt.M31 == 0.0f
&& Elt.M32 == 0.0f
&& Elt.M34 == 0.0f
&& Elt.M41 == 0.0f
&& Elt.M42 == 0.0f
&& Elt.M43 == 0.0f)
{
return true;
}
return false;
}
/// Transpose the matrix
void Transpose ()
{
T x;
x = Array[1]; Array[1] = Array[4]; Array[4] = x;
x = Array[2]; Array[2] = Array[8]; Array[8] = x;
x = Array[3]; Array[3] = Array[12]; Array[12] = x;
x = Array[6]; Array[6] = Array[9]; Array[9] = x;
x = Array[7]; Array[7] = Array[13]; Array[13] = x;
x = Array[11]; Array[11] = Array[14]; Array[14] = x;
}
/// Compute the determinant
T Determinant () const
{
return
(Elt.M11*Elt.M22 - Elt.M12*Elt.M21)*(Elt.M33*Elt.M44 - Elt.M34*Elt.M43)
-(Elt.M11*Elt.M23 - Elt.M13*Elt.M21)*(Elt.M32*Elt.M44 - Elt.M34*Elt.M42)
+(Elt.M11*Elt.M24 - Elt.M14*Elt.M21)*(Elt.M32*Elt.M43 - Elt.M33*Elt.M42)
+(Elt.M12*Elt.M23 - Elt.M13*Elt.M22)*(Elt.M31*Elt.M44 - Elt.M34*Elt.M41)
-(Elt.M12*Elt.M24 - Elt.M14*Elt.M22)*(Elt.M31*Elt.M43 - Elt.M33*Elt.M41)
+(Elt.M13*Elt.M24 - Elt.M14*Elt.M23)*(Elt.M31*Elt.M42 - Elt.M32*Elt.M41);
}
/// Invert matrix (does not check orthogonality)
void Invert ()
{
T det = Determinant();
if (det == 0.f) return;
nglMatrix<T> result;
det = 1.f / det;
result.Elt.M11 = det * (Elt.M22*(Elt.M33*Elt.M44 - Elt.M34*Elt.M43) + Elt.M23*(Elt.M34*Elt.M42 - Elt.M32*Elt.M44) + Elt.M24*(Elt.M32*Elt.M43 - Elt.M33*Elt.M42));
result.Elt.M12 = det * (Elt.M32*(Elt.M13*Elt.M44 - Elt.M14*Elt.M43) + Elt.M33*(Elt.M14*Elt.M42 - Elt.M12*Elt.M44) + Elt.M34*(Elt.M12*Elt.M43 - Elt.M13*Elt.M42));
result.Elt.M13 = det * (Elt.M42*(Elt.M13*Elt.M24 - Elt.M14*Elt.M23) + Elt.M43*(Elt.M14*Elt.M22 - Elt.M12*Elt.M24) + Elt.M44*(Elt.M12*Elt.M23 - Elt.M13*Elt.M22));
result.Elt.M14 = det * (Elt.M12*(Elt.M24*Elt.M33 - Elt.M23*Elt.M34) + Elt.M13*(Elt.M22*Elt.M34 - Elt.M24*Elt.M32) + Elt.M14*(Elt.M23*Elt.M32 - Elt.M22*Elt.M33));
result.Elt.M21 = det * (Elt.M23*(Elt.M31*Elt.M44 - Elt.M34*Elt.M41) + Elt.M24*(Elt.M33*Elt.M41 - Elt.M31*Elt.M43) + Elt.M21*(Elt.M34*Elt.M43 - Elt.M33*Elt.M44));
result.Elt.M22 = det * (Elt.M33*(Elt.M11*Elt.M44 - Elt.M14*Elt.M41) + Elt.M34*(Elt.M13*Elt.M41 - Elt.M11*Elt.M43) + Elt.M31*(Elt.M14*Elt.M43 - Elt.M13*Elt.M44));
result.Elt.M23 = det * (Elt.M43*(Elt.M11*Elt.M24 - Elt.M14*Elt.M21) + Elt.M44*(Elt.M13*Elt.M21 - Elt.M11*Elt.M23) + Elt.M41*(Elt.M14*Elt.M23 - Elt.M13*Elt.M24));
result.Elt.M24 = det * (Elt.M13*(Elt.M24*Elt.M31 - Elt.M21*Elt.M34) + Elt.M14*(Elt.M21*Elt.M33 - Elt.M23*Elt.M31) + Elt.M11*(Elt.M23*Elt.M34 - Elt.M24*Elt.M33));
result.Elt.M31 = det * (Elt.M24*(Elt.M31*Elt.M42 - Elt.M32*Elt.M41) + Elt.M21*(Elt.M32*Elt.M44 - Elt.M34*Elt.M42) + Elt.M22*(Elt.M34*Elt.M41 - Elt.M31*Elt.M44));
result.Elt.M32 = det * (Elt.M34*(Elt.M11*Elt.M42 - Elt.M12*Elt.M41) + Elt.M31*(Elt.M12*Elt.M44 - Elt.M14*Elt.M42) + Elt.M32*(Elt.M14*Elt.M41 - Elt.M11*Elt.M44));
result.Elt.M33 = det * (Elt.M44*(Elt.M11*Elt.M22 - Elt.M12*Elt.M21) + Elt.M41*(Elt.M12*Elt.M24 - Elt.M14*Elt.M22) + Elt.M42*(Elt.M14*Elt.M21 - Elt.M11*Elt.M24));
result.Elt.M34 = det * (Elt.M14*(Elt.M22*Elt.M31 - Elt.M21*Elt.M32) + Elt.M11*(Elt.M24*Elt.M32 - Elt.M22*Elt.M34) + Elt.M12*(Elt.M21*Elt.M34 - Elt.M24*Elt.M31));
result.Elt.M41 = det * (Elt.M21*(Elt.M33*Elt.M42 - Elt.M32*Elt.M43) + Elt.M22*(Elt.M31*Elt.M43 - Elt.M33*Elt.M41) + Elt.M23*(Elt.M32*Elt.M41 - Elt.M31*Elt.M42));
result.Elt.M42 = det * (Elt.M31*(Elt.M13*Elt.M42 - Elt.M12*Elt.M43) + Elt.M32*(Elt.M11*Elt.M43 - Elt.M13*Elt.M41) + Elt.M33*(Elt.M12*Elt.M41 - Elt.M11*Elt.M42));
result.Elt.M43 = det * (Elt.M41*(Elt.M13*Elt.M22 - Elt.M12*Elt.M23) + Elt.M42*(Elt.M11*Elt.M23 - Elt.M13*Elt.M21) + Elt.M43*(Elt.M12*Elt.M21 - Elt.M11*Elt.M22));
result.Elt.M44 = det * (Elt.M11*(Elt.M22*Elt.M33 - Elt.M23*Elt.M32) + Elt.M12*(Elt.M23*Elt.M31 - Elt.M21*Elt.M33) + Elt.M13*(Elt.M21*Elt.M32 - Elt.M22*Elt.M31));
*this = result;
}
/// Invert an homogenous transformation matrix (the matrix must only be composed of scaling, rotations and translations.
void InvertHomogenous ()
{
T det = Determinant();
if (det == 0.f) return;
nglMatrix<T> result;
det = 1.f / det;
result.Elt.M11 = det * (Elt.M22*(Elt.M33) + Elt.M23*(-Elt.M32));
result.Elt.M12 = det * (Elt.M32*(Elt.M13) + Elt.M33*(-Elt.M12));
result.Elt.M13 = det * (Elt.M12*Elt.M23 - Elt.M13*Elt.M22);
result.Elt.M14 = det * (Elt.M12*(Elt.M24*Elt.M33 - Elt.M23*Elt.M34) + Elt.M13*(Elt.M22*Elt.M34 - Elt.M24*Elt.M32) + Elt.M14*(Elt.M23*Elt.M32 - Elt.M22*Elt.M33));
result.Elt.M21 = det * (Elt.M23*Elt.M31 + Elt.M21*(-Elt.M33));
result.Elt.M22 = det * (Elt.M33*Elt.M11 + Elt.M31*(-Elt.M13));
result.Elt.M23 = det * (Elt.M13*Elt.M21 - Elt.M11*Elt.M23);
result.Elt.M24 = det * (Elt.M13*(Elt.M24*Elt.M31 - Elt.M21*Elt.M34) + Elt.M14*(Elt.M21*Elt.M33 - Elt.M23*Elt.M31) + Elt.M11*(Elt.M23*Elt.M34 - Elt.M24*Elt.M33));
result.Elt.M31 = det * (Elt.M21*Elt.M32 + Elt.M22*(-Elt.M31));
result.Elt.M32 = det * (Elt.M31*Elt.M12 + Elt.M32*(-Elt.M11));
result.Elt.M33 = det * (Elt.M11*Elt.M22 - Elt.M12*Elt.M21);
result.Elt.M34 = det * (Elt.M14*(Elt.M22*Elt.M31 - Elt.M21*Elt.M32) + Elt.M11*(Elt.M24*Elt.M32 - Elt.M22*Elt.M34) + Elt.M12*(Elt.M21*Elt.M34 - Elt.M24*Elt.M31));
result.Elt.M41 = 0;
result.Elt.M42 = 0;
result.Elt.M43 = 0;
result.Elt.M44 = det * (Elt.M11*(Elt.M22*Elt.M33 - Elt.M23*Elt.M32) + Elt.M12*(Elt.M23*Elt.M31 - Elt.M21*Elt.M33) + Elt.M13*(Elt.M21*Elt.M32 - Elt.M22*Elt.M31));
*this = result;
}
/// Setup a translation matrix
void SetTranslation (const nglVector<T>& rDelta)
{
SetTranslation(rDelta[0], rDelta[1], rDelta[2]);
}
/// Setup a translation matrix
void SetTranslation (T X, T Y, T Z)
{
SetIdentity();
Elt.M14 = X;
Elt.M24 = Y;
Elt.M34 = Z;
}
/// Compose with a translation
void Translate (const nglVector<T>& rDelta)
{
Translate(rDelta[0], rDelta[1], rDelta[2]);
}
/// Compose with a translation
void Translate (T X, T Y, T Z)
{
nglMatrix<T> m;
m.SetTranslation(X, Y, Z);
*this *= m;
}
/// Setup a scaling transformation (homothetia)
void SetScaling (const nglVector<T>& rVector)
{
Nullify();
Elt.M11 = rVector[0];
Elt.M22 = rVector[1];
Elt.M33 = rVector[2];
Elt.M44 = 1;
}
/// Setup a scaling transformation (homothetia)
void SetScaling (T X, T Y, T Z)
{
Nullify();
Elt.M11 = X;
Elt.M22 = Y;
Elt.M33 = Z;
Elt.M44 = 1;
}
/// Apply a scaling transformation
void Scale (T X, T Y, T Z)
{
nglMatrix<T> m;
m.SetScaling(X, Y, Z);
*this *= m;
}
/// Apply a scaling transformation
void Scale (const nglVector<T>& rVector)
{
SetScaling(rVector[0], rVector[1], rVector[2]);
}
/// Setup a rotation matrix of \a Angle degrees around \a rAxis (using right hand convention)
void SetRotation (T Angle, const nglVector<T>& rAxis)
{
nglVector<T> axis = rAxis;
axis.Normalize();
T a = (T) DEG2RAD(Angle);
T s = (T) sin (a);
T c = (T) cos (a);
T t = (T) 1.0 - c;
T x = axis[0];
T y = axis[1];
T z = axis[2];
T xy = x * y;
T xz = x * z;
T yz = y * z;
Elt.M11 = t * x * x + c;
Elt.M12 = t * xy - s * z;
Elt.M13 = t * xz + s * y;
Elt.M14 = 0.f;
Elt.M21 = t * xy + s * z;
Elt.M22 = t * y * y + c;
Elt.M23 = t * yz - s * x;
Elt.M24 = 0.f;
Elt.M31 = t * xz - s * y;
Elt.M32 = t * yz + s * x;
Elt.M33 = t * z * z + c;
Elt.M34 = 0.f;
Elt.M41 = 0.f;
Elt.M42 = 0.f;
Elt.M43 = 0.f;
Elt.M44 = 1.f;
}
/// Setup a rotation matrix of \a Angle degrees around the axis which coordinates are \a X, \a Y and \a Z
void SetRotation (T Angle, T X, T Y, T Z)
{
SetRotation(Angle, nglVector<T>(X, Y, Z));
}
/// Compose with a rotation of \a Angle degrees around \a rAxis
void Rotate (T Angle, const nglVector<T>& rAxis)
{
nglMatrix<T> trans;
trans.SetRotation(Angle, rAxis);
*this *= trans;
}
/// Compose with a rotation of \a Angle degrees around the axis which coordinates are \a X, \a Y and \a Z
void Rotate (T Angle, T X, T Y, T Z)
{
nglMatrix<T> trans;
trans.SetRotation(Angle, X, Y, Z);
*this *= trans;
}
/// Setup a camera matrix, given eye and target position and up direction
void LookAt (T EyeX, T EyeY, T EyeZ, T TargetX, T TargetY, T TargetZ, T UpX, T UpY, T UpZ)
{
LookAt(nglVector<T>(EyeX, EyeY, EyeZ),
nglVector<T>(TargetX, TargetY, TargetZ),
nglVector<T>(UpX, UpY, UpZ));
}
/// Setup a camera matrix, given eye and target position and up direction
void LookAt (const nglVector<T>& rEye, const nglVector<T>& rTarget, const nglVector<T>& rUp)
{
nglVector<T> forward = rTarget - rEye;
forward.Normalize();
/* Side = forward x up */
nglVector<T> side = forward ^ rUp;
side.Normalize();
/* Recompute up as : up = side x forward */
nglVector<T> up = side ^ forward;
Elt.M11 = side[0];
Elt.M12 = side[1];
Elt.M13 = side[2];
Elt.M14 = -rEye[0];
Elt.M21 = up[0];
Elt.M22 = up[1];
Elt.M23 = up[2];
Elt.M24 = -rEye[1];
Elt.M31 = -forward[0];
Elt.M32 = -forward[1];
Elt.M33 = -forward[2];
Elt.M34 = -rEye[2];
Elt.M41 = 0.f;
Elt.M42 = 0.f;
Elt.M43 = 0.f;
Elt.M44 = 1.f;
}
/*! Interpret the matrix as a rotation matrix with \a pAlpha, \a pBeta and \a pGama Euler angles
Only return valid results if the matrix determinant is 1
*/
void GetEulerAngles (T* pAlpha, T* pBeta, T* pGamma) const
{
if (Elt.M21 != 0.f)
{
if (pAlpha) *pAlpha = (T)asin(Elt.M32);
if (pBeta) *pBeta = (T)atan2(-Elt.M31, Elt.M33);
if (pGamma) *pGamma = (T)atan2(-Elt.M21, Elt.M22);
}
else
{
if (pAlpha) *pAlpha = (T)asin(Elt.M32);
if (pBeta) *pBeta = 0.f;
if (pGamma) *pGamma = (T)atan2(-Elt.M21,Elt.M11);
}
}
/// Setup an orthogonal projection matrix given a clipping cube
bool SetOrtho (T Left, T Right, T Bottom, T Top, T Near, T Far)
{
T deltax, deltay, deltaz;
deltax = Right - Left;
deltay = Top - Bottom;
deltaz = Far - Near;
if ((deltax == 0.) || (deltay == 0.f) || (deltaz == 0.f))
return false;
Nullify();
Elt.M11 = (T)(2.f / deltax);
Elt.M14 = (T)(-(Right + Left) / deltax);
Elt.M22 = (T)(2.f / deltay);
Elt.M24 = (T)(-(Top + Bottom) / deltay);
Elt.M33 = (T)(-2.f / deltaz);
Elt.M34 = (T)(-(Far + Near) / deltaz);
Elt.M44 = 1.f;
return true;
}
/// Setup an orthogonal projection matrix, with near and far Z planes set to -1 and 1 respectively
bool SetOrtho (T Left, T Right, T Bottom, T Top)
{
return SetOrtho(Left, Right, Bottom, Top, -1.f, 1.f);
}
/*! Setup a perspective projection matrix
\param FovY field of view in degree, in the vertical (Y) direction
\param Aspect ratio, ie. width / height using viewport dimensions
\param Near smaller Z value (positive)
\param Far greater Z value (positive)
*/
bool SetPerspective (T FovY, T Aspect, T Near, T Far)
{
T sine, cotangent, deltaZ;
T angle = (T)DEG2RAD(FovY);
deltaZ = Far - Near;
sine = (T)sin(angle);
if ((deltaZ == 0.f) || (sine == 0.f) || (Aspect == 0.f))
return false;
cotangent = (T)cos(angle) / sine;
Nullify();
Elt.M11 = (T)(cotangent / Aspect);
Elt.M22 = (T)cotangent;
Elt.M33 = (T)(-(Far + Near) / deltaZ);
Elt.M43 = -1.f;
Elt.M34 = (T)(-2.f * Near * Far / deltaZ);
return true;
}
/*! Setup a perspective projection matrix
\param Left smaller X value (left plane)
\param Right greater X value (right plane)
\param Bottom smaller Y value (bottom plane)
\param Top greater Y value (top plane)
\param Near smaller Z value (near plane)
\param Far greater Z value (far plane)
*/
bool SetFrustum (T Left, T Right, T Bottom, T Top, T Near, T Far)
{
T deltaX, deltaY, deltaZ;
deltaX = Right - Left;
deltaY = Top - Bottom;
deltaZ = Far - Near;
if ((Near <= 0.f) || (Far <= 0.f) ||
(deltaX == 0.f) || (deltaY == 0.f) || (deltaZ == 0.f))
return false;
Nullify();
Elt.M11 = (T)(Near * 2.f / deltaX);
Elt.M22 = (T)(Near * 2.f / deltaY);
Elt.M13 = (T)((Right + Left) / deltaX);
Elt.M23 = (T)((Top + Bottom) / deltaY);
Elt.M33 = (T)(-(Far + Near) / deltaZ);
Elt.M43 = (T)(-1.f);
Elt.M34 = (T)(((T) -2.f) * Near * Far / deltaZ);
return true;
}
/*
* Operators
*/
/// Return the value of the element from the i-th line and the j-th column
T operator () (uint i, uint j) const
{
NGL_ASSERT(i < 4 && j < 4);
return Array[i + 4*j];
}
T& operator () (uint i, uint j)
{
NGL_ASSERT(i < 4 && j < 4);
return Array[i + 4*j];
}
nglMatrix<T> operator = (const nglMatrix<T>& rMatrix)
{
memcpy(Array, rMatrix.Array, 16*sizeof(T));
return *this;
}
/*!< Right matrix multiplication. These two lines perform the same operation :
\code
mat1 *= mat2;
mat1 = mat1 * mat2;
\endcode
*/
void operator *= (const nglMatrix<T>& rMatrix)
{
nglMatrix<T> result;
result.Elt.M11 =(Elt.M11 * rMatrix.Elt.M11 + Elt.M12 * rMatrix.Elt.M21 + Elt.M13 * rMatrix.Elt.M31 + Elt.M14 * rMatrix.Elt.M41);
result.Elt.M12 =(Elt.M11 * rMatrix.Elt.M12 + Elt.M12 * rMatrix.Elt.M22 + Elt.M13 * rMatrix.Elt.M32 + Elt.M14 * rMatrix.Elt.M42);
result.Elt.M13 =(Elt.M11 * rMatrix.Elt.M13 + Elt.M12 * rMatrix.Elt.M23 + Elt.M13 * rMatrix.Elt.M33 + Elt.M14 * rMatrix.Elt.M43);
result.Elt.M14 =(Elt.M11 * rMatrix.Elt.M14 + Elt.M12 * rMatrix.Elt.M24 + Elt.M13 * rMatrix.Elt.M34 + Elt.M14 * rMatrix.Elt.M44);
result.Elt.M21 =(Elt.M21 * rMatrix.Elt.M11 + Elt.M22 * rMatrix.Elt.M21 + Elt.M23 * rMatrix.Elt.M31 + Elt.M24 * rMatrix.Elt.M41);
result.Elt.M22 =(Elt.M21 * rMatrix.Elt.M12 + Elt.M22 * rMatrix.Elt.M22 + Elt.M23 * rMatrix.Elt.M32 + Elt.M24 * rMatrix.Elt.M42);
result.Elt.M23 =(Elt.M21 * rMatrix.Elt.M13 + Elt.M22 * rMatrix.Elt.M23 + Elt.M23 * rMatrix.Elt.M33 + Elt.M24 * rMatrix.Elt.M43);
result.Elt.M24 =(Elt.M21 * rMatrix.Elt.M14 + Elt.M22 * rMatrix.Elt.M24 + Elt.M23 * rMatrix.Elt.M34 + Elt.M24 * rMatrix.Elt.M44);
result.Elt.M31 =(Elt.M31 * rMatrix.Elt.M11 + Elt.M32 * rMatrix.Elt.M21 + Elt.M33 * rMatrix.Elt.M31 + Elt.M34 * rMatrix.Elt.M41);
result.Elt.M32 =(Elt.M31 * rMatrix.Elt.M12 + Elt.M32 * rMatrix.Elt.M22 + Elt.M33 * rMatrix.Elt.M32 + Elt.M34 * rMatrix.Elt.M42);
result.Elt.M33 =(Elt.M31 * rMatrix.Elt.M13 + Elt.M32 * rMatrix.Elt.M23 + Elt.M33 * rMatrix.Elt.M33 + Elt.M34 * rMatrix.Elt.M43);
result.Elt.M34 =(Elt.M31 * rMatrix.Elt.M14 + Elt.M32 * rMatrix.Elt.M24 + Elt.M33 * rMatrix.Elt.M34 + Elt.M34 * rMatrix.Elt.M44);
result.Elt.M41 =(Elt.M41 * rMatrix.Elt.M11 + Elt.M42 * rMatrix.Elt.M21 + Elt.M43 * rMatrix.Elt.M31 + Elt.M44 * rMatrix.Elt.M41);
result.Elt.M42 =(Elt.M41 * rMatrix.Elt.M12 + Elt.M42 * rMatrix.Elt.M22 + Elt.M43 * rMatrix.Elt.M32 + Elt.M44 * rMatrix.Elt.M42);
result.Elt.M43 =(Elt.M41 * rMatrix.Elt.M13 + Elt.M42 * rMatrix.Elt.M23 + Elt.M43 * rMatrix.Elt.M33 + Elt.M44 * rMatrix.Elt.M43);
result.Elt.M44 =(Elt.M41 * rMatrix.Elt.M14 + Elt.M42 * rMatrix.Elt.M24 + Elt.M43 * rMatrix.Elt.M34 + Elt.M44 * rMatrix.Elt.M44);
*this = result;
}
/// Matrix multiplication, result is rA * rB
friend nglMatrix<T> operator * (const nglMatrix& rA, const nglMatrix& rB)
{
nglMatrix<T> result = rA;
result *= rB;
return result;
}
/// Left matrix multiplication with a vector, ie. result = matrix * vector
nglVector<T> operator * (const nglVector<T>& rVector) const
{
nglVector<T> result;
T v0, v1, v2, v3;
uint i;
v0 = rVector[0];
v1 = rVector[1];
v2 = rVector[2];
v3 = rVector[3];
for (i = 0; i < 4; i++)
result[i] = v0*Array[i] + v1*Array[4+i] + v2*Array[8+i] + v3*Array[12+i];
return result;
}
/// Scalar multiplication (each element is multiplied by a scalar)
void operator *= (T Scalar)
{
uint i;
for (i = 0; i < 16; i++)
Array[i] *= Scalar;
}
/*
* Debug
*/
/// Display the matrix content in the log
void Dump (uint Level = 0, const nglChar* pTitle = NULL) const
{
uint i;
if (pTitle)
{
NGL_LOG(_T("math"), Level, _T("%ls :"), pTitle);
}
for (i = 0; i < 4; i++)
{
NGL_LOG(_T("math"), Level, _T("[ %8.3f %8.3f %8.3f %8.3f ] "), (T)(*this)(i,0), (T)(*this)(i,1), (T)(*this)(i,2), (T)(*this)(i,3));
}
}
bool operator==(const nglMatrix& rA) const
{
for (int i =0; i< 16; i++)
if (Array[i] != rA.Array[i])
return false;
return true;
}
bool GetValue(nglString& rDump) const
{
rDump.CFormat(_T("{ %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f %8.3f }"),
(T)Array[ 0], (T)Array[ 1], (T)Array[ 2], (T)Array[ 3],
(T)Array[ 4], (T)Array[ 5], (T)Array[ 6], (T)Array[ 7],
(T)Array[ 8], (T)Array[ 9], (T)Array[10], (T)Array[11],
(T)Array[12], (T)Array[13], (T)Array[14], (T)Array[15]
);
return true;
}
bool SetValue(const nglString& rValue)
{
nglString val = rValue;
val.Trim();
val.TrimLeft(_T('{'));
val.TrimRight(_T('}'));
std::vector<nglString> tokens;
val.Tokenize(tokens, _T(' '));
for (uint i = 0; i < MIN(16, tokens.size()); i++)
{
Array[i] = (T)tokens[i].GetCDouble();
}
return true;
}
};
typedef nglMatrix<float> nglMatrixf;
typedef nglMatrix<double> nglMatrixd;
#endif // __nglMatrix_h__