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matrix_3x3.h
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22 
23 #ifndef __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__
24 #define __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__
25 
26 #include <boolean.h>
27 #include <math.h>
28 #include <string.h>
29 
30 #include <retro_common_api.h>
31 #include <retro_inline.h>
32 
33 RETRO_BEGIN_DECLS
34 
35 typedef struct math_matrix_3x3
36 {
37  float data[9];
38 } math_matrix_3x3;
39 
40 #define MAT_ELEM_3X3(mat, r, c) ((mat).data[3 * (r) + (c)])
41 
42 #define matrix_3x3_init(mat, n11, n12, n13, n21, n22, n23, n31, n32, n33) \
43  MAT_ELEM_3X3(mat, 0, 0) = n11; \
44  MAT_ELEM_3X3(mat, 0, 1) = n12; \
45  MAT_ELEM_3X3(mat, 0, 2) = n13; \
46  MAT_ELEM_3X3(mat, 1, 0) = n21; \
47  MAT_ELEM_3X3(mat, 1, 1) = n22; \
48  MAT_ELEM_3X3(mat, 1, 2) = n23; \
49  MAT_ELEM_3X3(mat, 2, 0) = n31; \
50  MAT_ELEM_3X3(mat, 2, 1) = n32; \
51  MAT_ELEM_3X3(mat, 2, 2) = n33
52 
53 #define matrix_3x3_identity(mat) \
54  MAT_ELEM_3X3(mat, 0, 0) = 1.0f; \
55  MAT_ELEM_3X3(mat, 0, 1) = 0; \
56  MAT_ELEM_3X3(mat, 0, 2) = 0; \
57  MAT_ELEM_3X3(mat, 1, 0) = 0; \
58  MAT_ELEM_3X3(mat, 1, 1) = 1.0f; \
59  MAT_ELEM_3X3(mat, 1, 2) = 0; \
60  MAT_ELEM_3X3(mat, 2, 0) = 0; \
61  MAT_ELEM_3X3(mat, 2, 1) = 0; \
62  MAT_ELEM_3X3(mat, 2, 2) = 1.0f
63 
64 #define matrix_3x3_divide_scalar(mat, s) \
65  MAT_ELEM_3X3(mat, 0, 0) /= s; \
66  MAT_ELEM_3X3(mat, 0, 1) /= s; \
67  MAT_ELEM_3X3(mat, 0, 2) /= s; \
68  MAT_ELEM_3X3(mat, 1, 0) /= s; \
69  MAT_ELEM_3X3(mat, 1, 1) /= s; \
70  MAT_ELEM_3X3(mat, 1, 2) /= s; \
71  MAT_ELEM_3X3(mat, 2, 0) /= s; \
72  MAT_ELEM_3X3(mat, 2, 1) /= s; \
73  MAT_ELEM_3X3(mat, 2, 2) /= s
74 
75 #define matrix_3x3_transpose(mat, in) \
76  MAT_ELEM_3X3(mat, 0, 0) = MAT_ELEM_3X3(in, 0, 0); \
77  MAT_ELEM_3X3(mat, 1, 0) = MAT_ELEM_3X3(in, 0, 1); \
78  MAT_ELEM_3X3(mat, 2, 0) = MAT_ELEM_3X3(in, 0, 2); \
79  MAT_ELEM_3X3(mat, 0, 1) = MAT_ELEM_3X3(in, 1, 0); \
80  MAT_ELEM_3X3(mat, 1, 1) = MAT_ELEM_3X3(in, 1, 1); \
81  MAT_ELEM_3X3(mat, 2, 1) = MAT_ELEM_3X3(in, 1, 2); \
82  MAT_ELEM_3X3(mat, 0, 2) = MAT_ELEM_3X3(in, 2, 0); \
83  MAT_ELEM_3X3(mat, 1, 2) = MAT_ELEM_3X3(in, 2, 1); \
84  MAT_ELEM_3X3(mat, 2, 2) = MAT_ELEM_3X3(in, 2, 2)
85 
86 #define matrix_3x3_multiply(out, a, b) \
87  MAT_ELEM_3X3(out, 0, 0) = \
88  MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 0) + \
89  MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 0) + \
90  MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 0); \
91  MAT_ELEM_3X3(out, 0, 1) = \
92  MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 1) + \
93  MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 1) + \
94  MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 1); \
95  MAT_ELEM_3X3(out, 0, 2) = \
96  MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 2) + \
97  MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 2) + \
98  MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 2); \
99  MAT_ELEM_3X3(out, 1, 0) = \
100  MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 0) + \
101  MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 0) + \
102  MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 0); \
103  MAT_ELEM_3X3(out, 1, 1) = \
104  MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 1) + \
105  MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 1) + \
106  MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 1); \
107  MAT_ELEM_3X3(out, 1, 2) = \
108  MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 2) + \
109  MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 2) + \
110  MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 2); \
111  MAT_ELEM_3X3(out, 2, 0) = \
112  MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 0) + \
113  MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 0) + \
114  MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 0); \
115  MAT_ELEM_3X3(out, 2, 1) = \
116  MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 1) + \
117  MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 1) + \
118  MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 1); \
119  MAT_ELEM_3X3(out, 2, 2) = \
120  MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 2) + \
121  MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 2) + \
122  MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 2)
123 
124 #define matrix_3x3_determinant(mat) (MAT_ELEM_3X3(mat, 0, 0) * (MAT_ELEM_3X3(mat, 1, 1) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 1, 2) * MAT_ELEM_3X3(mat, 2, 1)) - MAT_ELEM_3X3(mat, 0, 1) * (MAT_ELEM_3X3(mat, 1, 0) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 1, 2) * MAT_ELEM_3X3(mat, 2, 0)) + MAT_ELEM_3X3(mat, 0, 2) * (MAT_ELEM_3X3(mat, 1, 0) * MAT_ELEM_3X3(mat, 2, 1) - MAT_ELEM_3X3(mat, 1, 1) * MAT_ELEM_3X3(mat, 2, 0)))
125 
126 #define matrix_3x3_adjoint(mat) \
127  MAT_ELEM_3X3(mat, 0, 0) = (MAT_ELEM_3X3(mat, 1, 1) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 1, 2) * MAT_ELEM_3X3(mat, 2, 1)); \
128  MAT_ELEM_3X3(mat, 0, 1) = -(MAT_ELEM_3X3(mat, 0, 1) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 0, 2) * MAT_ELEM_3X3(mat, 2, 1)); \
129  MAT_ELEM_3X3(mat, 0, 2) = (MAT_ELEM_3X3(mat, 0, 1) * MAT_ELEM_3X3(mat, 1, 1) - MAT_ELEM_3X3(mat, 0, 2) * MAT_ELEM_3X3(mat, 1, 1)); \
130  MAT_ELEM_3X3(mat, 1, 0) = -(MAT_ELEM_3X3(mat, 1, 0) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 1, 2) * MAT_ELEM_3X3(mat, 2, 0)); \
131  MAT_ELEM_3X3(mat, 1, 1) = (MAT_ELEM_3X3(mat, 0, 0) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 0, 2) * MAT_ELEM_3X3(mat, 2, 0)); \
132  MAT_ELEM_3X3(mat, 1, 2) = -(MAT_ELEM_3X3(mat, 0, 0) * MAT_ELEM_3X3(mat, 1, 2) - MAT_ELEM_3X3(mat, 0, 2) * MAT_ELEM_3X3(mat, 1, 0)); \
133  MAT_ELEM_3X3(mat, 2, 0) = (MAT_ELEM_3X3(mat, 1, 0) * MAT_ELEM_3X3(mat, 2, 1) - MAT_ELEM_3X3(mat, 1, 1) * MAT_ELEM_3X3(mat, 2, 0)); \
134  MAT_ELEM_3X3(mat, 2, 1) = -(MAT_ELEM_3X3(mat, 0, 0) * MAT_ELEM_3X3(mat, 2, 1) - MAT_ELEM_3X3(mat, 0, 1) * MAT_ELEM_3X3(mat, 2, 0)); \
135  MAT_ELEM_3X3(mat, 2, 2) = (MAT_ELEM_3X3(mat, 0, 0) * MAT_ELEM_3X3(mat, 1, 1) - MAT_ELEM_3X3(mat, 0, 1) * MAT_ELEM_3X3(mat, 1, 0))
136 
137 #define FLOATS_ARE_EQUAL(x, y) (fabs(x - y) <= 0.00001f * ((x) > (y) ? (y) : (x)))
138 #define FLOAT_IS_ZERO(x) (FLOATS_ARE_EQUAL((x) + 1, 1))
139 
140 static INLINE bool matrix_3x3_invert(math_matrix_3x3 *mat)
141 {
142  float det = matrix_3x3_determinant(*mat);
143 
144  if (FLOAT_IS_ZERO(det))
145  return false;
146 
147  matrix_3x3_adjoint(*mat);
148  matrix_3x3_divide_scalar(*mat, det);
149 
150  return true;
151 }
152 
153 static INLINE bool matrix_3x3_square_to_quad(
154  const float dx0, const float dy0,
155  const float dx1, const float dy1,
156  const float dx3, const float dy3,
157  const float dx2, const float dy2,
158  math_matrix_3x3 *mat)
159 {
160  float a, b, d, e;
161  float ax = dx0 - dx1 + dx2 - dx3;
162  float ay = dy0 - dy1 + dy2 - dy3;
163  float c = dx0;
164  float f = dy0;
165  float g = 0;
166  float h = 0;
167 
168  if (FLOAT_IS_ZERO(ax) && FLOAT_IS_ZERO(ay))
169  {
170  /* affine case */
171  a = dx1 - dx0;
172  b = dx2 - dx1;
173  d = dy1 - dy0;
174  e = dy2 - dy1;
175  }
176  else
177  {
178  float ax1 = dx1 - dx2;
179  float ax2 = dx3 - dx2;
180  float ay1 = dy1 - dy2;
181  float ay2 = dy3 - dy2;
182 
183  /* determinants */
184  float gtop = ax * ay2 - ax2 * ay;
185  float htop = ax1 * ay - ax * ay1;
186  float bottom = ax1 * ay2 - ax2 * ay1;
187 
188  if (!bottom)
189  return false;
190 
191  g = gtop / bottom;
192  h = htop / bottom;
193 
194  a = dx1 - dx0 + g * dx1;
195  b = dx3 - dx0 + h * dx3;
196  d = dy1 - dy0 + g * dy1;
197  e = dy3 - dy0 + h * dy3;
198  }
199 
200 
201  matrix_3x3_init(*mat,
202  a, d, g,
203  b, e, h,
204  c, f, 1.f);
205 
206  return true;
207 }
208 
209 static INLINE bool matrix_3x3_quad_to_square(
210  const float sx0, const float sy0,
211  const float sx1, const float sy1,
212  const float sx2, const float sy2,
213  const float sx3, const float sy3,
214  math_matrix_3x3 *mat)
215 {
216  return matrix_3x3_square_to_quad(sx0, sy0, sx1, sy1,
217  sx2, sy2, sx3, sy3,
218  mat) ? matrix_3x3_invert(mat) : false;
219 }
220 
221 static INLINE bool matrix_3x3_quad_to_quad(
222  const float dx0, const float dy0,
223  const float dx1, const float dy1,
224  const float dx2, const float dy2,
225  const float dx3, const float dy3,
226  const float sx0, const float sy0,
227  const float sx1, const float sy1,
228  const float sx2, const float sy2,
229  const float sx3, const float sy3,
230  math_matrix_3x3 *mat)
231 {
232  math_matrix_3x3 square_to_quad;
233 
234  if (matrix_3x3_square_to_quad(dx0, dy0, dx1, dy1,
235  dx2, dy2, dx3, dy3,
236  &square_to_quad))
237  {
238  math_matrix_3x3 quad_to_square;
239  if (matrix_3x3_quad_to_square(sx0, sy0, sx1, sy1,
240  sx2, sy2, sx3, sy3,
241  &quad_to_square))
242  {
243  matrix_3x3_multiply(*mat, quad_to_square, square_to_quad);
244 
245  return true;
246  }
247  }
248 
249  return false;
250 }
251 
252 RETRO_END_DECLS
253 
254 #endif
matrix_3x3_init
#define matrix_3x3_init(mat, n11, n12, n13, n21, n22, n23, n31, n32, n33)
Definition: matrix_3x3.h:42
INLINE
#define INLINE
Definition: retro_inline.h:35
RETRO_BEGIN_DECLS
#define RETRO_BEGIN_DECLS
Definition: retro_common_api.h:41
f
GLfloat f
Definition: glext.h:8207
bottom
GLint GLint bottom
Definition: glext.h:8393
data
Definition: ibxm.h:9
c
const GLubyte * c
Definition: glext.h:9812
b
GLboolean GLboolean GLboolean b
Definition: glext.h:6844
math_matrix_3x3
Definition: matrix_3x3.h:35
FLOAT_IS_ZERO
#define FLOAT_IS_ZERO(x)
Definition: matrix_3x3.h:138
matrix_3x3_invert
static INLINE bool matrix_3x3_invert(math_matrix_3x3 *mat)
Definition: matrix_3x3.h:140
matrix_3x3_determinant
#define matrix_3x3_determinant(mat)
Definition: matrix_3x3.h:124
matrix_3x3_adjoint
#define matrix_3x3_adjoint(mat)
Definition: matrix_3x3.h:126
matrix_3x3_square_to_quad
static INLINE bool matrix_3x3_square_to_quad(const float dx0, const float dy0, const float dx1, const float dy1, const float dx3, const float dy3, const float dx2, const float dy2, math_matrix_3x3 *mat)
Definition: matrix_3x3.h:153
math_matrix_3x3
RETRO_BEGIN_DECLS struct math_matrix_3x3 math_matrix_3x3
RETRO_END_DECLS
#define RETRO_END_DECLS
Definition: retro_common_api.h:42
g
GLboolean GLboolean g
Definition: glext.h:6844
matrix_3x3_multiply
#define matrix_3x3_multiply(out, a, b)
Definition: matrix_3x3.h:86
h
GLfloat GLfloat GLfloat GLfloat h
Definition: glext.h:8390
matrix_3x3_quad_to_square
static INLINE bool matrix_3x3_quad_to_square(const float sx0, const float sy0, const float sx1, const float sy1, const float sx2, const float sy2, const float sx3, const float sy3, math_matrix_3x3 *mat)
Definition: matrix_3x3.h:209
matrix_3x3_quad_to_quad
static INLINE bool matrix_3x3_quad_to_quad(const float dx0, const float dy0, const float dx1, const float dy1, const float dx2, const float dy2, const float dx3, const float dy3, const float sx0, const float sy0, const float sx1, const float sy1, const float sx2, const float sy2, const float sx3, const float sy3, math_matrix_3x3 *mat)
Definition: matrix_3x3.h:221
a
GLboolean GLboolean GLboolean GLboolean a
Definition: glext.h:6844
matrix_3x3_divide_scalar
#define matrix_3x3_divide_scalar(mat, s)
Definition: matrix_3x3.h:64
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