urot.c

图形处理算法合集3：包括图形处理、帧缓存技术、渲染、矩阵运算、建模方法

/* urot.c */
/* Generates a uniform random rotation */
/* Ken Shoemake, September 1991 */

#include <stdlib.h>
#include <math.h>
#include "GraphicsGems.h"

/* Define an INT32 value to be a 32 bit signed integer */
typedef int INT32;

typedef struct {float x, y, z, w;} Quat;
enum QuatPart {X, Y, Z, W, QuatLen, V=0};

/* * * * * *  Utility for quaternion conversion * * * * * */

/** Qt_ToMatrix
 *  Construct rotation matrix from quaternion (unit or not).
 *  Assumes matrix is used to multiply row vector on the right:
 *  vnew = vold mat.  Works correctly for right-handed coordinate system
 *  and right-handed rotations. For column vectors or for left-handed
 *  coordinate systems, transpose the matrix.
 */
void Qt_ToMatrix(Quat q, Matrix3 *out)
{
	double norm = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
	double s = (norm > 0.0) ? 2.0/norm : 0.0;
	double xs = q.x*s,		ys = q.y*s,		zs = q.z*s;
	double wx = q.w*xs,	wy = q.w*ys,	wz = q.w*zs,
		 	xx = q.x*xs,	xy = q.x*ys,	xz = q.x*zs,
		 	yy = q.y*ys,	yz = q.y*zs,	zz = q.z*zs;
	double (*mat)[3] = out->element;
	mat[X][X] = 1.0 - (yy + zz); mat[X][Y] = xy + wz; mat[X][Z] = xz - wy;
	mat[Y][X] = xy - wz; mat[Y][Y] = 1.0 - (xx + zz); mat[Y][Z] = yz + wx;
	mat[Z][X] = xz + wy; mat[Z][Y] = yz - wx; mat[Z][Z] = 1.0 - (xx + yy);
} /* Qt_ToMatrix */


/* * * * * *  How to do it using gaussians * * * * * */

/** Qt_RandomG
 *  Generate uniform random unit quaternion from random seed.
 */
Quat Qt_RandomG(INT32 *argseed)
{
/*  This algorithm generates a gaussian deviate for each coordinate, so
 *  the total effect is to generate a symmetric 4-D gaussian distribution,
 *  by separability. Projecting onto the surface of the hypersphere gives
 *  a uniform distribution.
 */
	Quat q;
	/* uurand generates doubles uniformly distributed between