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.
28 #define MAT3_DET0 -1 /* Indicates singular mat */
29 #define MAT3_EPSILON 1e-12 /* Close enough to zero */
34 # define MAT3_PI 3.14159265358979323846
38 #define USE_XTRA_MAT3_INLINES
40 /* ------------------------------ Types --------------------------------- */
42 typedef double MAT3mat[4][4]; /* 4x4 matrix */
43 typedef double MAT3vec[3]; /* Vector */
44 typedef double MAT3hvec[4]; /* Vector with homogeneous coord */
46 /* ------------------------------ Macros -------------------------------- */
48 /* Tests if a number is within EPSILON of zero */
49 #define MAT3_IS_ZERO(N) ((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)
51 /* Sets a vector to the three given values */
52 #define MAT3_SET_VEC(V,X,Y,Z) ((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))
54 /* Tests a vector for all components close to zero */
55 #define MAT3_IS_ZERO_VEC(V) (MAT3_IS_ZERO((V)[0]) && \
56 MAT3_IS_ZERO((V)[1]) && \
59 /* Dot product of two vectors */
60 #define MAT3_DOT_PRODUCT(V1,V2) \
61 ((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])
63 /* Copy one vector to other */
64 #define MAT3_COPY_VEC(TO,FROM) ((TO)[0] = (FROM)[0], \
65 (TO)[1] = (FROM)[1], \
68 /* Normalize vector to unit length, using TEMP as temporary variable.
69 * TEMP will be zero if vector has zero length */
70 #define MAT3_NORMALIZE_VEC(V,TEMP) \
71 if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
73 MAT3_SCALE_VEC(V,V,TEMP); \
76 /* Scale vector by given factor, storing result vector in RESULT_V */
77 #define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
78 MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))
80 /* Adds vectors V1 and V2, storing result in RESULT_V */
81 #define MAT3_ADD_VEC(RESULT_V,V1,V2) \
82 MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
85 /* Subtracts vector V2 from V1, storing result in RESULT_V */
86 #define MAT3_SUB_VEC(RESULT_V,V1,V2) \
87 MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
90 /* Multiplies vectors V1 and V2, storing result in RESULT_V */
91 #define MAT3_MULT_VEC(RESULT_V,V1,V2) \
92 MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
95 /* Sets RESULT_V to the linear combination of V1 and V2, scaled by
96 * SCALE1 and SCALE2, respectively */
97 #define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
98 MAT3_SET_VEC(RESULT_V, (SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
99 (SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
100 (SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])
102 /* Several of the vector macros are useful for homogeneous-coord vectors */
103 #define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
104 (V)[2]=(Z), (V)[3]=(W))
106 #define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
107 (TO)[1] = (FROM)[1], \
108 (TO)[2] = (FROM)[2], \
111 #define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
112 MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
113 (V)[2]*(SCALE), (V)[3]*(SCALE))
115 #define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
116 MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
117 (V1)[2]+(V2)[2], (V1)[3]+(V2)[3])
119 #define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
120 MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
121 (V1)[2]-(V2)[2], (V1)[3]-(V2)[3])
123 #define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
124 MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
125 (V1)[2]*(V2)[2], (V1)[3]*(V2)[3])
127 /* ------------------------------ Entries ------------------------------- */
131 void MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
132 int MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
133 void MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
134 void MAT3translate (MAT3mat result_mat, MAT3vec trans);
135 void MAT3scale (MAT3mat result_mat, MAT3vec scale);
136 void MAT3shear(MAT3mat result_mat, double xshear, double yshear);
138 #if defined( USE_XTRA_MAT3_INLINES )
140 #define MAT3mult_vec( result_vec, vec, mat) { \
142 tempvec[0]=vec[0]*mat[0][0]+vec[1]*mat[1][0]+vec[2]*mat[2][0]+mat[3][0]; \
143 tempvec[1]=vec[0]*mat[0][1]+vec[1]*mat[1][1]+vec[2]*mat[2][1]+mat[3][1]; \
144 tempvec[2]=vec[0]*mat[0][2]+vec[1]*mat[1][2]+vec[2]*mat[2][2]+mat[3][2]; \
145 result_vec[0] = tempvec[0]; \
146 result_vec[1] = tempvec[1]; \
147 result_vec[2] = tempvec[2]; \
150 #define MAT3cross_product(result_vec, vec1, vec2) { \
152 tempvec[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1]; \
153 tempvec[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2]; \
154 tempvec[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0]; \
155 result_vec[0] = tempvec[0]; \
156 result_vec[1] = tempvec[1]; \
157 result_vec[2] = tempvec[2]; \
160 #if defined( USE_MEM ) || defined( WIN32 )
161 #define MAT3copy( to, from) memcpy(to, from, sizeof(MAT3mat))
162 #define MAT3zero(mat) memset(mat,0x00, sizeof(MAT3mat))
163 #define MAT3mult( result_mat, mat1, mat2) { \
166 for (i = 0; i < 4; i++) \
167 for (j = 0; j < 4; j++) \
168 tmp_mat[i][j] = (mat1[i][0] * mat2[0][j] + mat1[i][1] * mat2[1][j] \
169 + mat1[i][2] * mat2[2][j] + mat1[i][3] * mat2[3][j]); \
170 memcpy(result_mat, tmp_mat, sizeof(MAT3mat)); \
172 #define MAT3identity(mat) { \
174 memset(mat, 0x00, sizeof(MAT3mat)); \
175 for (i = 0; i < 4; i++) mat[i][i] = 1.0; \
178 #else !defined( USE_MEM ) || !defined( WIN32 )
180 #define MAT3copy( to, from) bcopy(from, to, sizeof(MAT3mat))
181 #define MAT3zero(mat) bzero (mat, sizeof(MAT3mat))
182 #define MAT3mult( result_mat, mat1, mat2) { \
185 for (i = 0; i < 4; i++) \
186 for (j = 0; j < 4; j++) \
187 tmp_mat[i][j] = (mat1[i][0] * mat2[0][j] + mat1[i][1] * mat2[1][j] \
188 + mat1[i][2] * mat2[2][j] + mat1[i][3] * mat2[3][j]); \
189 bcopy(tmp_mat, result_mat, sizeof(MAT3mat)); \
191 #define MAT3identity(mat) { \
193 bzero(mat, sizeof(MAT3mat)); \
194 for(i = 0; i < 4; i++) mat[i][i] = 1.0; \
198 #else // !defined( USE_XTRA_MAT3_INLINES )
201 void MAT3identity(MAT3mat);
202 void MAT3zero(MAT3mat);
204 void MAT3copy (MAT3mat to, MAT3mat from);
205 void MAT3mult (MAT3mat result, MAT3mat, MAT3mat);
207 #endif // defined( USE_XTRA_MAT3_INLINES )
209 void MAT3transpose (MAT3mat result, MAT3mat);
210 int MAT3invert (MAT3mat result, MAT3mat);
211 void MAT3print (MAT3mat, FILE *fp);
212 void MAT3print_formatted (MAT3mat, FILE *fp,
213 char *title, char *head, char *format, char *tail);
214 int MAT3equal( void );
215 double MAT3trace( void );
216 int MAT3power( void );
217 int MAT3column_reduce( void );
218 int MAT3kernel_basis( void );
221 int MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
222 void MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);
223 #if !defined( USE_XTRA_MAT3_INLINES )
224 void MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
225 void MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);
226 #endif // !defined( USE_XTRA_MAT3_INLINES )
234 #endif /* MAT3_HAS_BEEN_INCLUDED */