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glMatrix.cpp
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glMatrix.cpp
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/*-----------------------------------------------------------------------------
glMatrix.cpp
2006 Shamus Young
-------------------------------------------------------------------------------
Functions useful for manipulating the Matrix struct
-----------------------------------------------------------------------------*/
#define M(e,x,y) (e.elements[x][y])
/*** Order type constants, constructors, extractors ***/
/* There are 24 possible conventions, designated by: */
/* o EulAxI = axis used initially */
/* o EulPar = parity of axis permutation */
/* o EulRep = repetition of initial axis as last */
/* o EulFrm = frame from which axes are taken */
/* Axes I,J,K will be a permutation of X,Y,Z. */
/* Axis H will be either I or K, depending on EulRep. */
/* Frame S takes axes from initial static frame. */
/* If ord = (AxI=X, Par=Even, Rep=No, Frm=S), then */
/* {a,b,c,ord} means Rz(c)Ry(b)Rx(a), where Rz(c)v */
/* rotates v around Z by c radians. */
#define EulFrmS 0
#define EulFrmR 1
#define EulFrm(ord) ((unsigned)(ord)&1)
#define EulRepNo 0
#define EulRepYes 1
#define EulRep(ord) (((unsigned)(ord)>>1)&1)
#define EulParEven 0
#define EulParOdd 1
#define EulPar(ord) (((unsigned)(ord)>>2)&1)
#define EulSafe "\000\001\002\000"
#define EulNext "\001\002\000\001"
#define EulAxI(ord) ((int)(EulSafe[(((unsigned)(ord)>>3)&3)]))
#define EulAxJ(ord) ((int)(EulNext[EulAxI(ord)+(EulPar(ord)==EulParOdd)]))
#define EulAxK(ord) ((int)(EulNext[EulAxI(ord)+(EulPar(ord)!=EulParOdd)]))
#define EulAxH(ord) ((EulRep(ord)==EulRepNo)?EulAxK(ord):EulAxI(ord))
/* EulGetOrd unpacks all useful information about order simultaneously. */
#define EulGetOrd(ord,i,j,k,h,n,s,f) {unsigned o=ord;f=o&1;o>>=1;s=o&1;o>>=1;\
n=o&1;o>>=1;i=EulSafe[o&3];j=EulNext[i+n];k=EulNext[i+1-n];h=s?k:i;}
/* EulOrd creates an order value between 0 and 23 from 4-tuple choices. */
#define EulOrd(i,p,r,f) (((((((i)<<1)+(p))<<1)+(r))<<1)+(f))
/* Static axes */
#define EulOrdXYZs EulOrd(X,EulParEven,EulRepNo,EulFrmS)
#define EulOrdXYXs EulOrd(X,EulParEven,EulRepYes,EulFrmS)
#define EulOrdXZYs EulOrd(X,EulParOdd,EulRepNo,EulFrmS)
#define EulOrdXZXs EulOrd(X,EulParOdd,EulRepYes,EulFrmS)
#define EulOrdYZXs EulOrd(Y,EulParEven,EulRepNo,EulFrmS)
#define EulOrdYZYs EulOrd(Y,EulParEven,EulRepYes,EulFrmS)
#define EulOrdYXZs EulOrd(Y,EulParOdd,EulRepNo,EulFrmS)
#define EulOrdYXYs EulOrd(Y,EulParOdd,EulRepYes,EulFrmS)
#define EulOrdZXYs EulOrd(Z,EulParEven,EulRepNo,EulFrmS)
#define EulOrdZXZs EulOrd(Z,EulParEven,EulRepYes,EulFrmS)
#define EulOrdZYXs EulOrd(Z,EulParOdd,EulRepNo,EulFrmS)
#define EulOrdZYZs EulOrd(Z,EulParOdd,EulRepYes,EulFrmS)
/* Rotating axes */
#define EulOrdZYXr EulOrd(X,EulParEven,EulRepNo,EulFrmR)
#define EulOrdXYXr EulOrd(X,EulParEven,EulRepYes,EulFrmR)
#define EulOrdYZXr EulOrd(X,EulParOdd,EulRepNo,EulFrmR)
#define EulOrdXZXr EulOrd(X,EulParOdd,EulRepYes,EulFrmR)
#define EulOrdXZYr EulOrd(Y,EulParEven,EulRepNo,EulFrmR)
#define EulOrdYZYr EulOrd(Y,EulParEven,EulRepYes,EulFrmR)
#define EulOrdZXYr EulOrd(Y,EulParOdd,EulRepNo,EulFrmR)
#define EulOrdYXYr EulOrd(Y,EulParOdd,EulRepYes,EulFrmR)
#define EulOrdYXZr EulOrd(Z,EulParEven,EulRepNo,EulFrmR)
#define EulOrdZXZr EulOrd(Z,EulParEven,EulRepYes,EulFrmR)
#define EulOrdXYZr EulOrd(Z,EulParOdd,EulRepNo,EulFrmR)
#define EulOrdZYZr EulOrd(Z,EulParOdd,EulRepYes,EulFrmR)
#include <math.h>
#include <float.h>
#include "macro.h"
#include "glTypes.h"
static float identity[4][4] =
{
{1.0f, 0.0f, 0.0f, 0.0f},
{0.0f, 1.0f, 0.0f, 0.0f},
{0.0f, 0.0f, 1.0f, 0.0f},
{0.0f, 0.0f, 0.0f, 1.0f},
};
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
void* glMatrixCreate (void)
{
GLmatrix* m;
int x;
int y;
m = new GLmatrix;
for (x = 0; x < 4; x++) {
for (y = 0; y < 4; y++) {
m -> elements[x][y] = identity[x][y];
}
}
return (void*)m;
}
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
GLmatrix glMatrixIdentity (void)
{
GLmatrix m;
int x;
int y;
for (x = 0; x < 4; x++) {
for (y = 0; y < 4; y++) {
M(m, x, y) = identity[x][y];
}
}
return m;
}
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
void glMatrixElementsSet (GLmatrix* m, float* in)
{
m -> elements[0][0] = in[0];
m -> elements[0][1] = in[1];
m -> elements[0][2] = in[2];
m -> elements[0][3] = in[3];
m -> elements[1][0] = in[4];
m -> elements[1][1] = in[5];
m -> elements[1][2] = in[6];
m -> elements[1][3] = in[7];
m -> elements[2][0] = in[8];
m -> elements[2][1] = in[9];
m -> elements[2][2] = in[10];
m -> elements[2][3] = in[11];
m -> elements[3][0] = in[12];
m -> elements[3][1] = in[13];
m -> elements[3][2] = in[14];
m -> elements[3][3] = in[15];
}
/*---------------------------------------------------------------------------
A matrix multiplication (dot product) of two 4x4 matrices.
---------------------------------------------------------------------------*/
GLmatrix glMatrixMultiply (GLmatrix a, GLmatrix b)
{
GLmatrix result;
M(result, 0,0) = M(a, 0,0) * M(b, 0, 0) + M(a, 1,0) * M(b, 0, 1) + M(a, 2,0) * M(b, 0, 2);
M(result, 1,0) = M(a, 0,0) * M(b, 1, 0) + M(a, 1,0) * M(b, 1, 1) + M(a, 2,0) * M(b, 1, 2);
M(result, 2,0) = M(a, 0,0) * M(b, 2, 0) + M(a, 1,0) * M(b, 2, 1) + M(a, 2,0) * M(b, 2, 2);
M(result, 3,0) = M(a, 0,0) * M(b, 3, 0) + M(a, 1,0) * M(b, 3, 1) + M(a, 2,0) * M(b, 3, 2) + M(a, 3,0);
M(result, 0,1) = M(a, 0,1) * M(b, 0, 0) + M(a, 1,1) * M(b, 0, 1) + M(a, 2,1) * M(b, 0, 2);
M(result, 1,1) = M(a, 0,1) * M(b, 1, 0) + M(a, 1,1) * M(b, 1, 1) + M(a, 2,1) * M(b, 1, 2);
M(result, 2,1) = M(a, 0,1) * M(b, 2, 0) + M(a, 1,1) * M(b, 2, 1) + M(a, 2,1) * M(b, 2, 2);
M(result, 3,1) = M(a, 0,1) * M(b, 3, 0) + M(a, 1,1) * M(b, 3, 1) + M(a, 2,1) * M(b, 3, 2) + M(a, 3,1);
M(result, 0,2) = M(a, 0,2) * M(b, 0, 0) + M(a, 1,2) * M(b, 0, 1) + M(a, 2,2) * M(b, 0, 2);
M(result, 1,2) = M(a, 0,2) * M(b, 1, 0) + M(a, 1,2) * M(b, 1, 1) + M(a, 2,2) * M(b, 1, 2);
M(result, 2,2) = M(a, 0,2) * M(b, 2, 0) + M(a, 1,2) * M(b, 2, 1) + M(a, 2,2) * M(b, 2, 2);
M(result, 3,2) = M(a, 0,2) * M(b, 3, 0) + M(a, 1,2) * M(b, 3, 1) + M(a, 2,2) * M(b, 3, 2) + M(a, 3,2);
return result;
}
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
GLvector glMatrixTransformPoint (GLmatrix m, GLvector in)
{
GLvector out;
out.x = M(m,0,0) * in.x + M(m,1,0) * in.y + M(m,2,0) * in.z + M(m,3,0);
out.y = M(m,0,1) * in.x + M(m,1,1) * in.y + M(m,2,1) * in.z + M(m,3,1);
out.z = M(m,0,2) * in.x + M(m,1,2) * in.y + M(m,2,2) * in.z + M(m,3,2);
return out;
}
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
GLmatrix glMatrixTranslate (GLmatrix m, GLvector in)
{
GLvector old;
old.x = M(m,3,0);
old.y = M(m,3,1);
old.z = M(m,3,2);
M(m, 3, 0) = 0.0f;
M(m, 3, 1) = 0.0f;
M(m, 3, 2) = 0.0f;
in = glMatrixTransformPoint (m, in);
M(m, 3, 0) = old.x;
M(m, 3, 1) = old.y;
M(m, 3, 2) = old.z;
M(m,3,0) += in.x;
M(m,3,1) += in.y;
M(m,3,2) += in.z;
return m;
}
/*-----------------------------------------------------------------------------
-----------------------------------------------------------------------------*/
GLmatrix glMatrixRotate (GLmatrix m, float theta, float x, float y, float z)
{
GLmatrix r;
float length;
float s, c, t;
GLvector in;
theta *= DEGREES_TO_RADIANS;
r = glMatrixIdentity ();
length = (float)sqrt (x * x + y * y + z * z);
if (length < 0.00001f)
return m;
x /= length;
y /= length;
z /= length;
s = (float)sin (theta);
c = (float)cos (theta);
t = 1.0f - c;
in.x = in.y = in.z = 1.0f;
M(r, 0,0) = t*x*x + c;
M(r, 1,0) = t*x*y - s*z;
M(r, 2,0) = t*x*z + s*y;
M(r, 3,0) = 0;
M(r, 0,1) = t*x*y + s*z;
M(r, 1,1) = t*y*y + c;
M(r, 2,1) = t*y*z - s*x;
M(r, 3,1) = 0;
M(r, 0,2) = t*x*z - s*y;
M(r, 1,2) = t*y*z + s*x;
M(r, 2,2) = t*z*z + c;
M(r, 3,2) = 0;
m = glMatrixMultiply (m, r);
return m;
}
/* Convert matrix to Euler angles (in radians). */
GLvector glMatrixToEuler (GLmatrix mat, int order)
{
GLvector ea;
int i,j,k,h,n,s,f;
EulGetOrd (order,i,j,k,h,n,s,f);
if (s==EulRepYes) {
float sy = (float)sqrt(mat.elements[i][j]*mat.elements[i][j] + mat.elements[i][k]*mat.elements[i][k]);
if (sy > 16 * FLT_EPSILON) {
ea.x = (float)atan2(mat.elements[i][j], mat.elements[i][k]);
ea.y = (float)atan2(sy, mat.elements[i][i]);
ea.z = (float)atan2(mat.elements[j][i], -mat.elements[k][i]);
} else {
ea.x = (float)atan2(-mat.elements[j][k], mat.elements[j][j]);
ea.y = (float)atan2(sy, mat.elements[i][i]);
ea.z = 0;
}
} else {
float cy = (float)sqrt(mat.elements[i][i]*mat.elements[i][i] + mat.elements[j][i]*mat.elements[j][i]);
if (cy > 16*FLT_EPSILON) {
ea.x = (float)atan2(mat.elements[k][j], mat.elements[k][k]);
ea.y = (float)atan2(-mat.elements[k][i], cy);
ea.z = (float)atan2(mat.elements[j][i], mat.elements[i][i]);
} else {
ea.x = (float)atan2(-mat.elements[j][k], mat.elements[j][j]);
ea.y = (float)atan2(-mat.elements[k][i], cy);
ea.z = 0;
}
}
if (n==EulParOdd) {
ea.x = -ea.x;
ea.y = - ea.y;
ea.z = -ea.z;
}
if (f==EulFrmR) {
float t = ea.x;
ea.x = ea.z;
ea.z = t;
}
//ea.w = order;
return (ea);
}