?? xmatrixfunc.cpp
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/********************************************************************************
聲明：
這里的代碼版權歸潘李亮所有．你可以自由使用分發這些代碼．但是不得用于商業用途．
如有需要請于作者聯系．
在你使用本代碼時候，請務必保留本聲明
潘李亮 2003-10
Stanly Lee. 2003-10
Email : xheartblue@etang.com
提供矩陣和向量等類的操作函數．這些函數不屬于任何一個類．
使用這些類可以加快運算速度．函數不需要返回．參數以引用
的方式傳遞．
*******************************************************************************/
#include "XMathLib.h"
namespace XMathLib
{
void XMatrix3x3::From(XMatrix& _m)
{
for( int r = 0 ; r< 3; r++)
for(int c = 0 ; c < 3 ; c++)
{
m[r][c] = _m.m[r][c];
}
}
void XMatrix::From(XMatrix3x3& _m)
{
//效率不高。要改。但是必要不大
LoadIdentity();
for( int r = 0 ; r< 3; r++)
for(int c = 0 ; c < 3 ; c++)
{
m[r][c] = _m.m[r][c];
}
}
bool _MATH_LIB_EXPORT_ XMatrix_Inv(XMatrix3x3& m1 , XMatrix3x3& mOut)
{
XMatrix3x3 m = m1;
int max_r;
//int max_c;
float pivot = 1.0;
mOut.LoadIdentity();
for(int row = 0 ; row < 3 ; row++ )
{
//選主元．
pivot = m.m[row][row];
max_r = row;
for( int i = row ; i < 3 ; i++ )
{
float t = (float)fabs(m.m[i][row]);
if( t > fabs(pivot))
{
pivot = m.m[i][row];
max_r = i;
}
}
//主元選定．
if(pivot == 0)
return false;
//交換行
if(max_r != row)
{
XM_Swap(m.m[max_r][0],m.m[row][0]); XM_Swap(mOut.m[max_r][0],mOut.m[row][0]);
XM_Swap(m.m[max_r][1],m.m[row][1]); XM_Swap(mOut.m[max_r][1],mOut.m[row][1]);
XM_Swap(m.m[max_r][2],m.m[row][2]); XM_Swap(mOut.m[max_r][2],mOut.m[row][2]);
}
//歸一化到1
for( int x = 0 ; x < 3 ; x ++)
{
mOut.m[row][x] /= pivot;
m.m[row][x] /= pivot;
}
//消去當前列，除了當前行上的以外。該列全部成為0
for(int y = 0 ; y < 3 ; y ++)
{
if(y == row )
continue;
float times = m.m[y][row];
//消去。
for (int x = 0 ; x < 3 ; x ++)
{
m.m[y][x] -= m.m[row][x] * times;
mOut.m[y][x] -= mOut.m[row][x] * times;
}
}
}
return true;
}
/*
* 逆矩陣，采用高斯消去法．
*/
/*******************************************************************************
This function is tested by Stanly Lee at 2003-11
*******************************************************************************/
bool _MATH_LIB_EXPORT_ XMatrix_Inv(XMatrix&m1 , XMatrix& mOut)
{
XMatrix m = m1;
int max_r;
//int max_c;
float pivot = 1.0;
mOut.LoadIdentity();
for(int row = 0 ; row < 4 ; row++ )
{
//選主元．
pivot = m.m[row][row];
max_r = row;
for( int i = row ; i < 4 ; i++ )
{
float t = (float)fabs(m.m[i][row]);
if( t > fabs(pivot))
{
pivot = m.m[i][row];
max_r = i;
}
}
//主元選定．
if(pivot == 0)
return false;
//交換行
if(max_r != row)
{
XM_Swap(m.m[max_r][0],m.m[row][0]); XM_Swap(mOut.m[max_r][0],mOut.m[row][0]);
XM_Swap(m.m[max_r][1],m.m[row][1]); XM_Swap(mOut.m[max_r][1],mOut.m[row][1]);
XM_Swap(m.m[max_r][2],m.m[row][2]); XM_Swap(mOut.m[max_r][2],mOut.m[row][2]);
XM_Swap(m.m[max_r][3],m.m[row][3]); XM_Swap(mOut.m[max_r][3],mOut.m[row][3]);
}
//歸一化到1
for( int x = 0 ; x < 4 ; x ++)
{
mOut.m[row][x] /= pivot;
m.m[row][x] /= pivot;
}
//消去當前列，除了當前行上的以外。該列全部成為0
for(int y = 0 ; y < 4 ; y ++)
{
if(y == row )
continue;
float times = m.m[y][row];
//消去。
for (int x = 0 ; x < 4 ; x ++)
{
m.m[y][x] -= m.m[row][x] * times;
mOut.m[y][x] -= mOut.m[row][x] * times;
}
}
}
return true;
}
/*
* 轉置
*/
void _MATH_LIB_EXPORT_ XMatrix_Transpos(XMatrix&m , XMatrix& mOut)
{
for(int r = 0 ; r < 4 ; r ++)
{
mOut.m[0][r] = m.m[r][0];
mOut.m[1][r] = m.m[r][1];
mOut.m[2][r] = m.m[r][2];
mOut.m[3][r] = m.m[r][3];
}
return;
}
/*
* 經過該投影矩陣投影后，投影體為一個范體，
x( -1 , 1 )
y( -1 , 1 )
z( -1 , 1 )
*/
void _MATH_LIB_EXPORT_ XM_Perspective(XMatrix& mOut,float fov_angle,float aspect,float Znear,float Zfar)
{
float dz = Zfar - Znear;
float yp = XM_CosD(fov_angle / 2 ) / XM_SinD(fov_angle / 2 ) ;
float xp = yp / aspect;
float z1 = - (Zfar + Znear) / dz;
float z2 = - 2*Zfar * Znear / dz ;
mOut.m[0][0] = xp ; mOut.m[0][1] = 0 ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = yp ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = 0 ; mOut.m[2][2] = z1 ; mOut.m[2][3] = -1;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = z2 ; mOut.m[3][3] = 0;
return ;
}
/*
* 正交投影
經過該投影矩陣后，物體大小不會變形．
x = x/w + dx;
y = y/h + dy;
注意投影后的范體是(-1,1);
*/
void _MATH_LIB_EXPORT_ XM_Ortho3D(XMatrix& mOut,float Znear ,float Zfar ,float top,float bottom ,float left ,float right)
{
float cx = (right + left) / 2.0f ;
float cy = (top + bottom) / 2.0f ;
float w = (float)fabs(right - left) / 2.0f ;
float h = (float)fabs(top - bottom) / 2.0f ;
float x = 1.0f/w;
float dx = -cx/w;
float y = 1.0f/h;
float dy = -cy/h;
float z = -2.0f/(Zfar - Znear);
float dz = -((Zfar + Znear)) / (Zfar - Znear);
mOut.m[0][0] = x ; mOut.m[0][1] = 0 ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = y ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = 0 ; mOut.m[2][2] = z ; mOut.m[2][3] = 0;
mOut.m[3][0] = dx ; mOut.m[3][1] = dy ; mOut.m[3][2] = dz ; mOut.m[3][3] = 1;
return ;
}
void _MATH_LIB_EXPORT_ XM_Transform(XMatrix& mOut,float tx,float ty,float tz)
{
mOut.m[0][0] = 1 ; mOut.m[0][1] = 0 ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = 1 ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = 0 ; mOut.m[2][2] = 1 ; mOut.m[2][3] = 0;
mOut.m[3][0] = tx ; mOut.m[3][1] = ty ; mOut.m[3][2] = tz ; mOut.m[3][3] = 1;
return ;
}
void _MATH_LIB_EXPORT_ XM_Scale(XMatrix& mOut,float sx,float sy,float sz)
{
mOut.m[0][0] = sx ; mOut.m[0][1] = 0 ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = sy ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = 0 ; mOut.m[2][2] = sz ; mOut.m[2][3] = 0;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = 0 ; mOut.m[3][3] = 1;
return ;
}
void _MATH_LIB_EXPORT_ XM_RotateX(XMatrix& mOut,float angle)
{
float c = XM_CosD(angle);
float s = XM_SinD(angle);
mOut.m[0][0] = 1 ; mOut.m[0][1] = 0 ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = c ; mOut.m[1][2] = s ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = -s ; mOut.m[2][2] = c ; mOut.m[2][3] = 0;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = 0 ; mOut.m[3][3] = 1;
return ;
}
void _MATH_LIB_EXPORT_ XM_RotateY(XMatrix& mOut,float angle)
{
float c = XM_CosD(angle);
float s = XM_SinD(angle);
mOut.m[0][0] = c ; mOut.m[0][1] = 0 ; mOut.m[0][2] = -s ; mOut.m[0][3] = 0;
mOut.m[1][0] = 0 ; mOut.m[1][1] = 1 ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = s ; mOut.m[2][1] = 0 ; mOut.m[2][2] = c ; mOut.m[2][3] = 0;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = 0 ; mOut.m[3][3] = 1;
return ;
}
void _MATH_LIB_EXPORT_ XM_RotateZ(XMatrix& mOut,float angle)
{
float c = XM_CosD(angle);
float s = XM_SinD(angle);
mOut.m[0][0] = c ; mOut.m[0][1] = s ; mOut.m[0][2] = 0 ; mOut.m[0][3] = 0;
mOut.m[1][0] = -s ; mOut.m[1][1] = c ; mOut.m[1][2] = 0 ; mOut.m[1][3] = 0;
mOut.m[2][0] = 0 ; mOut.m[2][1] = 0 ; mOut.m[2][2] = 1 ; mOut.m[2][3] = 0;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = 0 ; mOut.m[3][3] = 1;
return ;
}
/*******************************************************************************
This function is tested by Stanly Lee at 2003-11
*******************************************************************************/
void _MATH_LIB_EXPORT_ XM_RotatePV(XMatrix& mOut,XVector& v , float angle)
{
float vsin = XM_SinD(angle);
float vcos = XM_CosD(angle);
float a = v.x * vsin;
float b = v.y * vsin;
float c = v.z * vsin;
mOut.m[0][0] = vcos ; mOut.m[0][1] = c ; mOut.m[0][2] = -b ; mOut.m[0][3] = 0;
mOut.m[1][0] = -c ; mOut.m[1][1] = vcos ; mOut.m[1][2] = a ; mOut.m[1][3] = 0;
mOut.m[2][0] = b ; mOut.m[2][1] = -a ; mOut.m[2][2] = vcos ; mOut.m[2][3] = 0;
mOut.m[3][0] = 0 ; mOut.m[3][1] = 0 ; mOut.m[3][2] = 0 ; mOut.m[3][3] = 1;
return ;
}
/*******************************************************************************
This function is tested by Stanly Lee at 2003-11
*******************************************************************************/
void _MATH_LIB_EXPORT_ XM_Rotate(XMatrix& mOut,XVector& v , float angle)
{
//This code and algrithm is copy from the mesaLib4.0
float xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
float x = v.x;
float y = v.y;
float z = v.z;
s = (float) XM_SinD( angle );
c = (float) XM_CosD( angle );
mOut.LoadIdentity();
#define M(row,col) mOut.m [row ] [ col ]
float mag = (float) sqrt(x * x + y * y + z * z);
if (mag <= 1.0e-4)
{
/* no rotation, leave mat as-is */
return;
}
x /= mag;
y /= mag;
z /= mag;
xx = x * x; yy = y * y;
zz = z * z; xy = x * y;
yz = y * z; zx = z * x;
xs = x * s; ys = y * s;
zs = z * s; one_c = 1.0F - c;
/* We already hold the identity-matrix so we can skip some statements */
M(0,0) = (one_c * xx) + c;
M(1,0) = (one_c * xy) - zs;
M(2,0) = (one_c * zx) + ys;
/* M(3,0) = 0.0F; */
M(0,1) = (one_c * xy) + zs;
M(1,1) = (one_c * yy) + c;
M(2,1) = (one_c * yz) - xs;
/* M(3,1) = 0.0F; */
M(0,2) = (one_c * zx) - ys;
M(1,2) = (one_c * yz) + xs;
M(2,2) = (one_c * zz) + c;
/* M(3,2) = 0.0F; */
/*
M(0,3) = 0.0F;
M(1,3) = 0.0F;
M(2,3) = 0.0F;
M(3,3) = 1.0F;
*/
#undef M
}
/*******************************************************************************
This function is tested by Stanly Lee at 2003-11
*******************************************************************************/
void _MATH_LIB_EXPORT_ XM_LookAt(XMatrix& mOut,XVector& eyeAt,XVector eyeTarget,XVector& upDir)
{
XVector vZ = eyeAt - eyeTarget;//注意這里是因為OpenGL用的you手系．默認的方向是向著Z的負方向．
XVector vX = upDir.cp(vZ);
vX.normalize();
vZ.normalize();
XVector vY = vZ.cp(vX);//重新計算向上的方向．我們可以保證vY也是個單位向量，就不需要再做單位化了。
#define M(row,col) mOut.m[row ] [ col ]
M(0,0) = vX.x;
M(1,0) = vX.y;
M(2,0) = vX.z;
M(3,0) = - vX.dp3(eyeAt) ;
M(0,1) = vY.x;
M(1,1) = vY.y;
M(2,1) = vY.z;
M(3,1) = -vY.dp3(eyeAt) ;
M(0,2) = vZ.x;
M(1,2) = vZ.y;
M(2,2) = vZ.z;
M(3,2) = -vZ.dp3(eyeAt) ;
M(0,3) = 0;
M(1,3) = 0;
M(2,3) = 0;
M(3,3) = 1;
#undef M
}
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