gim_geometry.h

ODE v0.8 很好用的多平台几何物理模拟库源代码,内含多個示例

   m[2][3] = 0.0;				\
						\
   m[3][0] = 0.0;				\
   m[3][1] = 0.0;				\
   m[3][2] = 0.0;				\
   m[3][3] = 1.0;				\
}\

/*! initialize matrix */
#define ZERO_MATRIX_4X4(m)			\
{						\
   m[0][0] = 0.0;				\
   m[0][1] = 0.0;				\
   m[0][2] = 0.0;				\
   m[0][3] = 0.0;				\
						\
   m[1][0] = 0.0;				\
   m[1][1] = 0.0;				\
   m[1][2] = 0.0;				\
   m[1][3] = 0.0;				\
						\
   m[2][0] = 0.0;				\
   m[2][1] = 0.0;				\
   m[2][2] = 0.0;				\
   m[2][3] = 0.0;				\
						\
   m[3][0] = 0.0;				\
   m[3][1] = 0.0;				\
   m[3][2] = 0.0;				\
   m[3][3] = 0.0;				\
}\

/*! matrix rotation  X */
#define ROTX_CS(m,cosine,sine)		\
{					\
   /* rotation about the x-axis */	\
					\
   m[0][0] = 1.0;			\
   m[0][1] = 0.0;			\
   m[0][2] = 0.0;			\
   m[0][3] = 0.0;			\
					\
   m[1][0] = 0.0;			\
   m[1][1] = (cosine);			\
   m[1][2] = (sine);			\
   m[1][3] = 0.0;			\
					\
   m[2][0] = 0.0;			\
   m[2][1] = -(sine);			\
   m[2][2] = (cosine);			\
   m[2][3] = 0.0;			\
					\
   m[3][0] = 0.0;			\
   m[3][1] = 0.0;			\
   m[3][2] = 0.0;			\
   m[3][3] = 1.0;			\
}\

/*! matrix rotation  Y */
#define ROTY_CS(m,cosine,sine)		\
{					\
   /* rotation about the y-axis */	\
					\
   m[0][0] = (cosine);			\
   m[0][1] = 0.0;			\
   m[0][2] = -(sine);			\
   m[0][3] = 0.0;			\
					\
   m[1][0] = 0.0;			\
   m[1][1] = 1.0;			\
   m[1][2] = 0.0;			\
   m[1][3] = 0.0;			\
					\
   m[2][0] = (sine);			\
   m[2][1] = 0.0;			\
   m[2][2] = (cosine);			\
   m[2][3] = 0.0;			\
					\
   m[3][0] = 0.0;			\
   m[3][1] = 0.0;			\
   m[3][2] = 0.0;			\
   m[3][3] = 1.0;			\
}\

/*! matrix rotation  Z */
#define ROTZ_CS(m,cosine,sine)		\
{					\
   /* rotation about the z-axis */	\
					\
   m[0][0] = (cosine);			\
   m[0][1] = (sine);			\
   m[0][2] = 0.0;			\
   m[0][3] = 0.0;			\
					\
   m[1][0] = -(sine);			\
   m[1][1] = (cosine);			\
   m[1][2] = 0.0;			\
   m[1][3] = 0.0;			\
					\
   m[2][0] = 0.0;			\
   m[2][1] = 0.0;			\
   m[2][2] = 1.0;			\
   m[2][3] = 0.0;			\
					\
   m[3][0] = 0.0;			\
   m[3][1] = 0.0;			\
   m[3][2] = 0.0;			\
   m[3][3] = 1.0;			\
}\

/*! matrix copy */
#define COPY_MATRIX_2X2(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[0][1];		\
				\
   b[1][0] = a[1][0];		\
   b[1][1] = a[1][1];		\
				\
}\


/*! matrix copy */
#define COPY_MATRIX_2X3(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[0][1];		\
   b[0][2] = a[0][2];		\
				\
   b[1][0] = a[1][0];		\
   b[1][1] = a[1][1];		\
   b[1][2] = a[1][2];		\
}\


/*! matrix copy */
#define COPY_MATRIX_3X3(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[0][1];		\
   b[0][2] = a[0][2];		\
				\
   b[1][0] = a[1][0];		\
   b[1][1] = a[1][1];		\
   b[1][2] = a[1][2];		\
				\
   b[2][0] = a[2][0];		\
   b[2][1] = a[2][1];		\
   b[2][2] = a[2][2];		\
}\


/*! matrix copy */
#define COPY_MATRIX_4X4(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[0][1];		\
   b[0][2] = a[0][2];		\
   b[0][3] = a[0][3];		\
				\
   b[1][0] = a[1][0];		\
   b[1][1] = a[1][1];		\
   b[1][2] = a[1][2];		\
   b[1][3] = a[1][3];		\
				\
   b[2][0] = a[2][0];		\
   b[2][1] = a[2][1];		\
   b[2][2] = a[2][2];		\
   b[2][3] = a[2][3];		\
				\
   b[3][0] = a[3][0];		\
   b[3][1] = a[3][1];		\
   b[3][2] = a[3][2];		\
   b[3][3] = a[3][3];		\
}\


/*! matrix transpose */
#define TRANSPOSE_MATRIX_2X2(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[1][0];		\
				\
   b[1][0] = a[0][1];		\
   b[1][1] = a[1][1];		\
}\


/*! matrix transpose */
#define TRANSPOSE_MATRIX_3X3(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[1][0];		\
   b[0][2] = a[2][0];		\
				\
   b[1][0] = a[0][1];		\
   b[1][1] = a[1][1];		\
   b[1][2] = a[2][1];		\
				\
   b[2][0] = a[0][2];		\
   b[2][1] = a[1][2];		\
   b[2][2] = a[2][2];		\
}\


/*! matrix transpose */
#define TRANSPOSE_MATRIX_4X4(b,a)	\
{				\
   b[0][0] = a[0][0];		\
   b[0][1] = a[1][0];		\
   b[0][2] = a[2][0];		\
   b[0][3] = a[3][0];		\
				\
   b[1][0] = a[0][1];		\
   b[1][1] = a[1][1];		\
   b[1][2] = a[2][1];		\
   b[1][3] = a[3][1];		\
				\
   b[2][0] = a[0][2];		\
   b[2][1] = a[1][2];		\
   b[2][2] = a[2][2];		\
   b[2][3] = a[3][2];		\
				\
   b[3][0] = a[0][3];		\
   b[3][1] = a[1][3];		\
   b[3][2] = a[2][3];		\
   b[3][3] = a[3][3];		\
}\


/*! multiply matrix by scalar */
#define SCALE_MATRIX_2X2(b,s,a)		\
{					\
   b[0][0] = (s) * a[0][0];		\
   b[0][1] = (s) * a[0][1];		\
					\
   b[1][0] = (s) * a[1][0];		\
   b[1][1] = (s) * a[1][1];		\
}\


/*! multiply matrix by scalar */
#define SCALE_MATRIX_3X3(b,s,a)		\
{					\
   b[0][0] = (s) * a[0][0];		\
   b[0][1] = (s) * a[0][1];		\
   b[0][2] = (s) * a[0][2];		\
					\
   b[1][0] = (s) * a[1][0];		\
   b[1][1] = (s) * a[1][1];		\
   b[1][2] = (s) * a[1][2];		\
					\
   b[2][0] = (s) * a[2][0];		\
   b[2][1] = (s) * a[2][1];		\
   b[2][2] = (s) * a[2][2];		\
}\


/*! multiply matrix by scalar */
#define SCALE_MATRIX_4X4(b,s,a)		\
{					\
   b[0][0] = (s) * a[0][0];		\
   b[0][1] = (s) * a[0][1];		\
   b[0][2] = (s) * a[0][2];		\
   b[0][3] = (s) * a[0][3];		\
					\
   b[1][0] = (s) * a[1][0];		\
   b[1][1] = (s) * a[1][1];		\
   b[1][2] = (s) * a[1][2];		\
   b[1][3] = (s) * a[1][3];		\
					\
   b[2][0] = (s) * a[2][0];		\
   b[2][1] = (s) * a[2][1];		\
   b[2][2] = (s) * a[2][2];		\
   b[2][3] = (s) * a[2][3];		\
					\
   b[3][0] = s * a[3][0];		\
   b[3][1] = s * a[3][1];		\
   b[3][2] = s * a[3][2];		\
   b[3][3] = s * a[3][3];		\
}\


/*! multiply matrix by scalar */
#define ACCUM_SCALE_MATRIX_2X2(b,s,a)		\
{					\
   b[0][0] += (s) * a[0][0];		\
   b[0][1] += (s) * a[0][1];		\
					\
   b[1][0] += (s) * a[1][0];		\
   b[1][1] += (s) * a[1][1];		\
}\


/*! multiply matrix by scalar */
#define ACCUM_SCALE_MATRIX_3X3(b,s,a)		\
{					\
   b[0][0] += (s) * a[0][0];		\
   b[0][1] += (s) * a[0][1];		\
   b[0][2] += (s) * a[0][2];		\
					\
   b[1][0] += (s) * a[1][0];		\
   b[1][1] += (s) * a[1][1];		\
   b[1][2] += (s) * a[1][2];		\
					\
   b[2][0] += (s) * a[2][0];		\
   b[2][1] += (s) * a[2][1];		\
   b[2][2] += (s) * a[2][2];		\
}\


/*! multiply matrix by scalar */
#define ACCUM_SCALE_MATRIX_4X4(b,s,a)		\
{					\
   b[0][0] += (s) * a[0][0];		\
   b[0][1] += (s) * a[0][1];		\
   b[0][2] += (s) * a[0][2];		\
   b[0][3] += (s) * a[0][3];		\
					\
   b[1][0] += (s) * a[1][0];		\
   b[1][1] += (s) * a[1][1];		\
   b[1][2] += (s) * a[1][2];		\
   b[1][3] += (s) * a[1][3];		\
					\
   b[2][0] += (s) * a[2][0];		\
   b[2][1] += (s) * a[2][1];		\
   b[2][2] += (s) * a[2][2];		\
   b[2][3] += (s) * a[2][3];		\
					\
   b[3][0] += (s) * a[3][0];		\
   b[3][1] += (s) * a[3][1];		\
   b[3][2] += (s) * a[3][2];		\
   b[3][3] += (s) * a[3][3];		\
}\

/*! matrix product */
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
#define MATRIX_PRODUCT_2X2(c,a,b)		\
{						\
   c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0];	\
   c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1];	\
						\
   c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0];	\
   c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1];	\
						\
}\

/*! matrix product */
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
#define MATRIX_PRODUCT_3X3(c,a,b)				\
{								\
   c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0];	\
   c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1];	\
   c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2];	\
								\
   c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0];	\
   c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1];	\
   c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2];	\
								\
   c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0];	\
   c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1];	\
   c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2];	\
}\


/*! matrix product */
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
#define MATRIX_PRODUCT_4X4(c,a,b)		\
{						\
   c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]+a[0][3]*b[3][0];\
   c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]+a[0][3]*b[3][1];\
   c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]+a[0][3]*b[3][2];\
   c[0][3] = a[0][0]*b[0][3]+a[0][1]*b[1][3]+a[0][2]*b[2][3]+a[0][3]*b[3][3];\
						\
   c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]+a[1][3]*b[3][0];\
   c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]+a[1][3]*b[3][1];\
   c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]+a[1][3]*b[3][2];\
   c[1][3] = a[1][0]*b[0][3]+a[1][1]*b[1][3]+a[1][2]*b[2][3]+a[1][3]*b[3][3];\
						\
   c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]+a[2][3]*b[3][0];\
   c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]+a[2][3]*b[3][1];\
   c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]+a[2][3]*b[3][2];\
   c[2][3] = a[2][0]*b[0][3]+a[2][1]*b[1][3]+a[2][2]*b[2][3]+a[2][3]*b[3][3];\
						\
   c[3][0] = a[3][0]*b[0][0]+a[3][1]*b[1][0]+a[3][2]*b[2][0]+a[3][3]*b[3][0];\
   c[3][1] = a[3][0]*b[0][1]+a[3][1]*b[1][1]+a[3][2]*b[2][1]+a[3][3]*b[3][1];\
   c[3][2] = a[3][0]*b[0][2]+a[3][1]*b[1][2]+a[3][2]*b[2][2]+a[3][3]*b[3][2];\
   c[3][3] = a[3][0]*b[0][3]+a[3][1]*b[1][3]+a[3][2]*b[2][3]+a[3][3]*b[3][3];\
}\


/*! matrix times vector */
#define MAT_DOT_VEC_2X2(p,m,v)					\
{								\
   p[0] = m[0][0]*v[0] + m[0][1]*v[1];				\
   p[1] = m[1][0]*v[0] + m[1][1]*v[1];				\
}\


/*! matrix times vector */
#define MAT_DOT_VEC_3X3(p,m,v)					\
{								\
   p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];		\
   p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];		\
   p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];		\
}\


/*! matrix times vector
v is a vec4f
*/
#define MAT_DOT_VEC_4X4(p,m,v)					\
{								\
   p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]*v[3];	\
   p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]*v[3];	\
   p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]*v[3];	\
   p[3] = m[3][0]*v[0] + m[3][1]*v[1] + m[3][2]*v[2] + m[3][3]*v[3];	\
}\

/*! matrix times vector
v is a vec3f
and m is a mat4f<br>
Last column is added as the position
*/
#define MAT_DOT_VEC_3X4(p,m,v)					\
{								\
   p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3];	\
   p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3];	\
   p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3];	\
}\

/*! vector transpose times matrix */
/*! p[j] = v[0]*m[0][j] + v[1]*m[1][j] + v[2]*m[2][j]; */
#define VEC_DOT_MAT_3X3(p,v,m)					\
{								\
   p[0] = v[0]*m[0][0] + v[1]*m[1][0] + v[2]*m[2][0];		\
   p[1] = v[0]*m[0][1] + v[1]*m[1][1] + v[2]*m[2][1];		\
   p[2] = v[0]*m[0][2] + v[1]*m[1][2] + v[2]*m[2][2];		\
}\


/*! affine matrix times vector */
/** The matrix is assumed to be an affine matrix, with last two
 * entries representing a translation */
#define MAT_DOT_VEC_2X3(p,m,v)					\
{								\
   p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2];		\
   p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2];		\
}\


/** inverse transpose of matrix times vector
 *
 * This macro computes inverse transpose of matrix m,
 * and multiplies vector v into it, to yeild vector p
 *
 * DANGER !!! Do Not use this on normal vectors!!!
 * It will leave normals the wrong length !!!
 * See macro below for use on normals.
 */
#define INV_TRANSP_MAT_DOT_VEC_2X2(p,m,v)			\
{								\
   GREAL det;						\
								\
   det = m[0][0]*m[1][1] - m[0][1]*m[1][0];			\
   p[0] = m[1][1]*v[0] - m[1][0]*v[1];				\
   p[1] = - m[0][1]*v[0] + m[0][0]*v[1];			\
								\
   /* if matrix not singular, and not orthonormal, then renormalize */ \