shithub: tinygl

ref: f03aac3fa4e87533f0606b6d28a594504d1b0d1f
dir: /src/zmath.c/

/* Some simple mathematical functions. Don't look for some logic in
   the function names :-) */

#include "zmath.h"
#include <math.h>
#include <stdlib.h>
#include <string.h>

/* ******* Gestion des matrices 4x4 ****** */

void gl_M4_Id(M4* a) {
	GLint i, j;
	for (i = 0; i < 4; i++)
		for (j = 0; j < 4; j++)
			if (i == j)
				a->m[i][j] = 1.0;
			else
				a->m[i][j] = 0.0;
}

int gl_M4_IsId(M4* a) {
	GLint i, j;
	for (i = 0; i < 4; i++)
		for (j = 0; j < 4; j++) {
			if (i == j) {
				if (a->m[i][j] != 1.0)
					return 0;
			} else if (a->m[i][j] != 0.0)
				return 0;
		}
	return 1;
}

void gl_M4_Mul(M4* c, M4* a, M4* b) {
	GLint i, j, k;
	GLfloat s;
	for (i = 0; i < 4; i++)
		for (j = 0; j < 4; j++) {
			s = 0.0;
			for (k = 0; k < 4; k++)
				s += a->m[i][k] * b->m[k][j];
			c->m[i][j] = s;
		}
}

/* c=c*a */
void gl_M4_MulLeft(M4* c, M4* b) {
	GLint i, j, k;
	GLfloat s;
	M4 a;

	/*memcpy(&a, c, 16*sizeof(GLfloat));
	 */
	a = *c;

	for (i = 0; i < 4; i++)
		for (j = 0; j < 4; j++) {
			s = 0.0;
			for (k = 0; k < 4; k++)
				s += a.m[i][k] * b->m[k][j];
			c->m[i][j] = s;
		}
}

void gl_M4_Move(M4* a, M4* b) { memcpy(a, b, sizeof(M4)); }

void gl_MoveV3(V3* a, V3* b) { memcpy(a, b, sizeof(V3)); }

void gl_MulM4V3(V3* a, M4* b, V3* c) {
	a->X = b->m[0][0] * c->X + b->m[0][1] * c->Y + b->m[0][2] * c->Z + b->m[0][3];
	a->Y = b->m[1][0] * c->X + b->m[1][1] * c->Y + b->m[1][2] * c->Z + b->m[1][3];
	a->Z = b->m[2][0] * c->X + b->m[2][1] * c->Y + b->m[2][2] * c->Z + b->m[2][3];
}

void gl_MulM3V3(V3* a, M4* b, V3* c) {
	a->X = b->m[0][0] * c->X + b->m[0][1] * c->Y + b->m[0][2] * c->Z;
	a->Y = b->m[1][0] * c->X + b->m[1][1] * c->Y + b->m[1][2] * c->Z;
	a->Z = b->m[2][0] * c->X + b->m[2][1] * c->Y + b->m[2][2] * c->Z;
}

void gl_M4_MulV4(V4* a, M4* b, V4* c) {
	a->X = b->m[0][0] * c->X + b->m[0][1] * c->Y + b->m[0][2] * c->Z + b->m[0][3] * c->W;
	a->Y = b->m[1][0] * c->X + b->m[1][1] * c->Y + b->m[1][2] * c->Z + b->m[1][3] * c->W;
	a->Z = b->m[2][0] * c->X + b->m[2][1] * c->Y + b->m[2][2] * c->Z + b->m[2][3] * c->W;
	a->W = b->m[3][0] * c->X + b->m[3][1] * c->Y + b->m[3][2] * c->Z + b->m[3][3] * c->W;
}

/* transposition of a 4x4 matrix */
void gl_M4_Transpose(M4* a, M4* b) {
	a->m[0][0] = b->m[0][0];
	a->m[0][1] = b->m[1][0];
	a->m[0][2] = b->m[2][0];
	a->m[0][3] = b->m[3][0];

	a->m[1][0] = b->m[0][1];
	a->m[1][1] = b->m[1][1];
	a->m[1][2] = b->m[2][1];
	a->m[1][3] = b->m[3][1];

	a->m[2][0] = b->m[0][2];
	a->m[2][1] = b->m[1][2];
	a->m[2][2] = b->m[2][2];
	a->m[2][3] = b->m[3][2];

	a->m[3][0] = b->m[0][3];
	a->m[3][1] = b->m[1][3];
	a->m[3][2] = b->m[2][3];
	a->m[3][3] = b->m[3][3];
}

/* inversion of an orthogonal matrix of type Y=M.X+P */
void gl_M4_InvOrtho(M4* a, M4 b) {
	GLint i, j;
	GLfloat s;
	for (i = 0; i < 3; i++)
		for (j = 0; j < 3; j++)
			a->m[i][j] = b.m[j][i];
	a->m[3][0] = 0.0;
	a->m[3][1] = 0.0;
	a->m[3][2] = 0.0;
	a->m[3][3] = 1.0;
	for (i = 0; i < 3; i++) {
		s = 0;
		for (j = 0; j < 3; j++)
			s -= b.m[j][i] * b.m[j][3];
		a->m[i][3] = s;
	}
}

/* Inversion of a general nxn matrix.
   Note : m is destroyed */

int Matrix_Inv(GLfloat* r, GLfloat* m, GLint n) {
	GLint i, j, k, l;
	GLfloat max, tmp, t;

	/* identit�e dans r */
	for (i = 0; i < n * n; i++)
		r[i] = 0;
	for (i = 0; i < n; i++)
		r[i * n + i] = 1;

	for (j = 0; j < n; j++) {

		/* recherche du nombre de plus grand module sur la colonne j */
		max = m[j * n + j];
		k = j;
		for (i = j + 1; i < n; i++)
			if (fabs(m[i * n + j]) > fabs(max)) {
				k = i;
				max = m[i * n + j];
			}

		/* non GLintersible matrix */
		if (max == 0)
			return 1;

		/* permutation des lignes j et k */
		if (k != j) {
			for (i = 0; i < n; i++) {
				tmp = m[j * n + i];
				m[j * n + i] = m[k * n + i];
				m[k * n + i] = tmp;

				tmp = r[j * n + i];
				r[j * n + i] = r[k * n + i];
				r[k * n + i] = tmp;
			}
		}

		/* multiplication de la ligne j par 1/max */
		max = 1 / max;
		for (i = 0; i < n; i++) {
			m[j * n + i] *= max;
			r[j * n + i] *= max;
		}

		for (l = 0; l < n; l++)
			if (l != j) {
				t = m[l * n + j];
				for (i = 0; i < n; i++) {
					m[l * n + i] -= m[j * n + i] * t;
					r[l * n + i] -= r[j * n + i] * t;
				}
			}
	}

	return 0;
}

/* inversion of a 4x4 matrix */

void gl_M4_Inv(M4* a, M4* b) {
	M4 tmp;
	memcpy(&tmp, b, 16 * sizeof(GLfloat));
	/*tmp=*b;*/
	Matrix_Inv(&a->m[0][0], &tmp.m[0][0], 4);
}

void gl_M4_Rotate(M4* a, GLfloat t, GLint u) {
	GLfloat s, c;
	GLint v, w;
	if ((v = u + 1) > 2)
		v = 0;
	if ((w = v + 1) > 2)
		w = 0;
	s = sin(t);
	c = cos(t);
	gl_M4_Id(a);
	a->m[v][v] = c;
	a->m[v][w] = -s;
	a->m[w][v] = s;
	a->m[w][w] = c;
}

/* inverse of a 3x3 matrix */
void gl_M3_Inv(M3* a, M3* m) {
	GLfloat det;

	det = m->m[0][0] * m->m[1][1] * m->m[2][2] - m->m[0][0] * m->m[1][2] * m->m[2][1] - m->m[1][0] * m->m[0][1] * m->m[2][2] +
		  m->m[1][0] * m->m[0][2] * m->m[2][1] + m->m[2][0] * m->m[0][1] * m->m[1][2] - m->m[2][0] * m->m[0][2] * m->m[1][1];

	a->m[0][0] = (m->m[1][1] * m->m[2][2] - m->m[1][2] * m->m[2][1]) / det;
	a->m[0][1] = -(m->m[0][1] * m->m[2][2] - m->m[0][2] * m->m[2][1]) / det;
	a->m[0][2] = -(-m->m[0][1] * m->m[1][2] + m->m[0][2] * m->m[1][1]) / det;

	a->m[1][0] = -(m->m[1][0] * m->m[2][2] - m->m[1][2] * m->m[2][0]) / det;
	a->m[1][1] = (m->m[0][0] * m->m[2][2] - m->m[0][2] * m->m[2][0]) / det;
	a->m[1][2] = -(m->m[0][0] * m->m[1][2] - m->m[0][2] * m->m[1][0]) / det;

	a->m[2][0] = (m->m[1][0] * m->m[2][1] - m->m[1][1] * m->m[2][0]) / det;
	a->m[2][1] = -(m->m[0][0] * m->m[2][1] - m->m[0][1] * m->m[2][0]) / det;
	a->m[2][2] = (m->m[0][0] * m->m[1][1] - m->m[0][1] * m->m[1][0]) / det;
}

/* vector arithmetic */

int gl_V3_Norm(V3* a) {
	GLfloat n;
	n = sqrt(a->X * a->X + a->Y * a->Y + a->Z * a->Z);
	if (n == 0)
		return 1;
	a->X /= n;
	a->Y /= n;
	a->Z /= n;
	return 0;
}

V3 gl_V3_New(GLfloat x, GLfloat y, GLfloat z) {
	V3 a;
	a.X = x;
	a.Y = y;
	a.Z = z;
	return a;
}

V4 gl_V4_New(GLfloat x, GLfloat y, GLfloat z, GLfloat w) {
	V4 a;
	a.X = x;
	a.Y = y;
	a.Z = z;
	a.W = w;
	return a;
}