1 /* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
3 /* -------------------------------------------------------------------------
4 Public MAT3 include file
5 ------------------------------------------------------------------------- */
7 #ifndef MAT3_HAS_BEEN_INCLUDED
8 #define MAT3_HAS_BEEN_INCLUDED
10 /* ----------------------------- Constants ------------------------------ */
13 * Make sure the math library .h file is included, in case it wasn't.
27 #define MAT3_DET0 -1 /* Indicates singular mat */
28 #define MAT3_EPSILON 1e-12 /* Close enough to zero */
29 #define MAT3_PI 3.141592653589793 /* Pi */
31 /* ------------------------------ Types --------------------------------- */
33 typedef double MAT3mat[4][4]; /* 4x4 matrix */
34 typedef double MAT3vec[3]; /* Vector */
35 typedef double MAT3hvec[4]; /* Vector with homogeneous coord */
37 /* ------------------------------ Macros -------------------------------- */
39 /* Tests if a number is within EPSILON of zero */
40 #define MAT3_IS_ZERO(N) ((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)
42 /* Sets a vector to the three given values */
43 #define MAT3_SET_VEC(V,X,Y,Z) ((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))
45 /* Tests a vector for all components close to zero */
46 #define MAT3_IS_ZERO_VEC(V) (MAT3_IS_ZERO((V)[0]) && \
47 MAT3_IS_ZERO((V)[1]) && \
50 /* Dot product of two vectors */
51 #define MAT3_DOT_PRODUCT(V1,V2) \
52 ((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])
54 /* Copy one vector to other */
55 #define MAT3_COPY_VEC(TO,FROM) ((TO)[0] = (FROM)[0], \
56 (TO)[1] = (FROM)[1], \
59 /* Normalize vector to unit length, using TEMP as temporary variable.
60 * TEMP will be zero if vector has zero length */
61 #define MAT3_NORMALIZE_VEC(V,TEMP) \
62 if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
64 MAT3_SCALE_VEC(V,V,TEMP); \
67 /* Scale vector by given factor, storing result vector in RESULT_V */
68 #define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
69 MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))
71 /* Adds vectors V1 and V2, storing result in RESULT_V */
72 #define MAT3_ADD_VEC(RESULT_V,V1,V2) \
73 MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
76 /* Subtracts vector V2 from V1, storing result in RESULT_V */
77 #define MAT3_SUB_VEC(RESULT_V,V1,V2) \
78 MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
81 /* Multiplies vectors V1 and V2, storing result in RESULT_V */
82 #define MAT3_MULT_VEC(RESULT_V,V1,V2) \
83 MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
86 /* Sets RESULT_V to the linear combination of V1 and V2, scaled by
87 * SCALE1 and SCALE2, respectively */
88 #define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
89 MAT3_SET_VEC(RESULT_V, (SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
90 (SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
91 (SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])
93 /* Several of the vector macros are useful for homogeneous-coord vectors */
94 #define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
95 (V)[2]=(Z), (V)[3]=(W))
97 #define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
98 (TO)[1] = (FROM)[1], \
99 (TO)[2] = (FROM)[2], \
102 #define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
103 MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
104 (V)[2]*(SCALE), (V)[3]*(SCALE))
106 #define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
107 MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
108 (V1)[2]+(V2)[2], (V1)[3]+(V2)[3])
110 #define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
111 MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
112 (V1)[2]-(V2)[2], (V1)[3]-(V2)[3])
114 #define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
115 MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
116 (V1)[2]*(V2)[2], (V1)[3]*(V2)[3])
118 /* ------------------------------ Entries ------------------------------- */
122 void MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
123 int MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
124 void MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
125 void MAT3translate (MAT3mat result_mat, MAT3vec trans);
126 void MAT3scale (MAT3mat result_mat, MAT3vec scale);
127 void MAT3shear(MAT3mat result_mat, double xshear, double yshear);
130 void MAT3identity(MAT3mat);
131 void MAT3zero(MAT3mat);
132 void MAT3copy (MAT3mat to, MAT3mat from);
133 void MAT3mult (MAT3mat result, MAT3mat, MAT3mat);
134 void MAT3transpose (MAT3mat result, MAT3mat);
135 int MAT3invert (MAT3mat result, MAT3mat);
136 void MAT3print (MAT3mat, FILE *fp);
137 void MAT3print_formatted (MAT3mat, FILE *fp,
138 char *title, char *head, char *format, char *tail);
139 extern int MAT3equal( void );
140 extern double MAT3trace( void );
141 extern int MAT3power( void );
142 extern int MAT3column_reduce( void );
143 extern int MAT3kernel_basis( void );
146 void MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
147 int MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
148 void MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);
149 void MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);
157 #endif /* MAT3_HAS_BEEN_INCLUDED */