simgear/Math/mat3.h

/* Copyright 1988, Brown Computer Graphics Group.  All Rights Reserved. */

/* -------------------------------------------------------------------------
		       Public MAT3 include file
   ------------------------------------------------------------------------- */

#ifndef MAT3_HAS_BEEN_INCLUDED
#define MAT3_HAS_BEEN_INCLUDED

/* -----------------------------  Constants  ------------------------------ */

/*
 * Make sure the math library .h file is included, in case it wasn't.
 */

#ifndef HUGE
#include <math.h>
#endif
#include <stdio.h>

#include <string.h>
#include "Include/fg_memory.h"

#ifdef __cplusplus                                                          
extern "C" {                            
#endif                                   


#define MAT3_DET0	-1			/* Indicates singular mat */
#define MAT3_EPSILON	1e-12			/* Close enough to zero   */

#ifdef M_PI
#  define  MAT3_PI    M_PI
#else
#  define  MAT3_PI    3.14159265358979323846
#endif

#define USE_XTRA_MAT3_INLINES

/* ------------------------------  Types  --------------------------------- */

typedef double MAT3mat[4][4];		/* 4x4 matrix			 */
typedef double MAT3vec[3];		/* Vector			 */
typedef double MAT3hvec[4];             /* Vector with homogeneous coord */

/* ------------------------------  Macros  -------------------------------- */

extern MAT3mat identityMatrix;

/* Tests if a number is within EPSILON of zero */
#define MAT3_IS_ZERO(N) 	((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)

/* Sets a vector to the three given values */
#define MAT3_SET_VEC(V,X,Y,Z)	((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))

/* Tests a vector for all components close to zero */
#define MAT3_IS_ZERO_VEC(V)	(MAT3_IS_ZERO((V)[0]) && \
				 MAT3_IS_ZERO((V)[1]) && \
				 MAT3_IS_ZERO((V)[2]))

/* Dot product of two vectors */
#define MAT3_DOT_PRODUCT(V1,V2) \
			((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])

/* Copy one vector to other */
#define MAT3_COPY_VEC(TO,FROM)	((TO)[0] = (FROM)[0], \
				 (TO)[1] = (FROM)[1], \
				 (TO)[2] = (FROM)[2])

/* Normalize vector to unit length, using TEMP as temporary variable.
 * TEMP will be zero if vector has zero length */
#define MAT3_NORMALIZE_VEC(V,TEMP) \
	if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
	   TEMP = 1.0 / TEMP; \
	   MAT3_SCALE_VEC(V,V,TEMP); \
	} else TEMP = 0.0

/* Scale vector by given factor, storing result vector in RESULT_V */
#define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
	MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))

/* Adds vectors V1 and V2, storing result in RESULT_V */
#define MAT3_ADD_VEC(RESULT_V,V1,V2) \
	MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
			       (V1)[2]+(V2)[2])

/* Subtracts vector V2 from V1, storing result in RESULT_V */
#define MAT3_SUB_VEC(RESULT_V,V1,V2) \
	MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
			       (V1)[2]-(V2)[2])

/* Multiplies vectors V1 and V2, storing result in RESULT_V */
#define MAT3_MULT_VEC(RESULT_V,V1,V2) \
	MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
			       (V1)[2]*(V2)[2])

/* Sets RESULT_V to the linear combination of V1 and V2, scaled by
 * SCALE1 and SCALE2, respectively */
#define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
	MAT3_SET_VEC(RESULT_V,	(SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
				(SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
				(SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])

/* Several of the vector macros are useful for homogeneous-coord vectors */
#define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
				  (V)[2]=(Z), (V)[3]=(W))

#define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
				 (TO)[1] = (FROM)[1], \
				 (TO)[2] = (FROM)[2], \
				 (TO)[3] = (FROM)[3])

#define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
	MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
				(V)[2]*(SCALE), (V)[3]*(SCALE))

#define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
	MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
				(V1)[2]+(V2)[2], (V1)[3]+(V2)[3])

#define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
	MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
				(V1)[2]-(V2)[2], (V1)[3]-(V2)[3])

#define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
	MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
				(V1)[2]*(V2)[2], (V1)[3]*(V2)[3])

/* ------------------------------  Entries  ------------------------------- */


#define MAT3identity(mat)    fgmemcpy( mat, identityMatrix, sizeof(MAT3mat) )
#define MAT3zero(mat)        fgmemzero( mat, sizeof(MAT3mat) )
#define MAT3copy(to, from)   fgmemcpy( to, from, sizeof(MAT3mat) )

#if defined( USE_XTRA_MAT3_INLINES )

#  define MAT3mult_vec( result_vec, vec, mat) { \
   MAT3vec tempvec; \
   tempvec[0]=vec[0]*mat[0][0]+vec[1]*mat[1][0]+vec[2]*mat[2][0]+mat[3][0]; \
   tempvec[1]=vec[0]*mat[0][1]+vec[1]*mat[1][1]+vec[2]*mat[2][1]+mat[3][1]; \
   tempvec[2]=vec[0]*mat[0][2]+vec[1]*mat[1][2]+vec[2]*mat[2][2]+mat[3][2]; \
   result_vec[0] = tempvec[0]; \
   result_vec[1] = tempvec[1]; \
   result_vec[2] = tempvec[2]; \
}

#  define MAT3cross_product(result_vec, vec1, vec2)  { \
   MAT3vec tempvec; \
   tempvec[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1]; \
   tempvec[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2]; \
   tempvec[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0]; \
   result_vec[0] = tempvec[0]; \
   result_vec[1] = tempvec[1]; \
   result_vec[2] = tempvec[2]; \
} 

#  define MAT3mult( result_mat,  mat1,  mat2) { \
   register int i, j; \
   MAT3mat	tmp_mat; \
   for (i = 0; i < 4; i++) \
      for (j = 0; j < 4; j++) \
         tmp_mat[i][j] = (mat1[i][0] * mat2[0][j] + \
			  mat1[i][1] * mat2[1][j] + \
			  mat1[i][2] * mat2[2][j] + \
			  mat1[i][3] * mat2[3][j]); \
   fgmemcpy(result_mat, tmp_mat, sizeof(MAT3mat)); \
}

#else // !defined( USE_XTRA_MAT3_INLINES )

/* In MAT3mat.c */
void	MAT3mult(MAT3mat result, MAT3mat, MAT3mat);
void	MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
void	MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);

#endif // defined( USE_XTRA_MAT3_INLINES )

/* In MAT3geom.c */
void	MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
int     MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
void	MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
void	MAT3translate (MAT3mat result_mat, MAT3vec trans);
void	MAT3scale (MAT3mat result_mat, MAT3vec scale);
void	MAT3shear(MAT3mat result_mat, double xshear, double yshear);

void	MAT3transpose (MAT3mat result, MAT3mat);
int	MAT3invert (MAT3mat result, MAT3mat);
void	MAT3print (MAT3mat, FILE *fp);
void	MAT3print_formatted (MAT3mat, FILE *fp, 
			     char *title, char *head, char *format, char *tail);
int	MAT3equal( void );
double  MAT3trace( void );
int	MAT3power( void );
int	MAT3column_reduce( void );
int	MAT3kernel_basis( void );

/* In MAT3vec.c */
int	MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
void	MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);

#ifdef __cplusplus
}
#endif


#endif /* MAT3_HAS_BEEN_INCLUDED */