1 /* Copyright (C) 2010-2020 The RetroArch team
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23 #ifndef __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__
24 #define __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__
30 #include <retro_common_api.h>
31 #include <retro_inline.h>
35 typedef struct math_matrix_3x3
40 #define MAT_ELEM_3X3(mat, r, c) ((mat).data[3 * (r) + (c)])
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
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
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
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)
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)
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)))
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))
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))
140 static INLINE bool matrix_3x3_invert(math_matrix_3x3 *mat)
142 float det = matrix_3x3_determinant(*mat);
144 if (FLOAT_IS_ZERO(det))
147 matrix_3x3_adjoint(*mat);
148 matrix_3x3_divide_scalar(*mat, det);
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)
161 float ax = dx0 - dx1 + dx2 - dx3;
162 float ay = dy0 - dy1 + dy2 - dy3;
168 if (FLOAT_IS_ZERO(ax) && FLOAT_IS_ZERO(ay))
178 float ax1 = dx1 - dx2;
179 float ax2 = dx3 - dx2;
180 float ay1 = dy1 - dy2;
181 float ay2 = dy3 - dy2;
184 float gtop = ax * ay2 - ax2 * ay;
185 float htop = ax1 * ay - ax * ay1;
186 float bottom = ax1 * ay2 - ax2 * ay1;
194 a = dx1 - dx0 + g * dx1;
195 b = dx3 - dx0 + h * dx3;
196 d = dy1 - dy0 + g * dy1;
197 e = dy3 - dy0 + h * dy3;
200 matrix_3x3_init(*mat,
208 static INLINE bool matrix_3x3_quad_to_square(
209 const float sx0, const float sy0,
210 const float sx1, const float sy1,
211 const float sx2, const float sy2,
212 const float sx3, const float sy3,
213 math_matrix_3x3 *mat)
215 return matrix_3x3_square_to_quad(sx0, sy0, sx1, sy1,
217 mat) ? matrix_3x3_invert(mat) : false;
220 static INLINE bool matrix_3x3_quad_to_quad(
221 const float dx0, const float dy0,
222 const float dx1, const float dy1,
223 const float dx2, const float dy2,
224 const float dx3, const float dy3,
225 const float sx0, const float sy0,
226 const float sx1, const float sy1,
227 const float sx2, const float sy2,
228 const float sx3, const float sy3,
229 math_matrix_3x3 *mat)
231 math_matrix_3x3 square_to_quad;
233 if (matrix_3x3_square_to_quad(dx0, dy0, dx1, dy1,
237 math_matrix_3x3 quad_to_square;
238 if (matrix_3x3_quad_to_square(sx0, sy0, sx1, sy1,
242 matrix_3x3_multiply(*mat, quad_to_square, square_to_quad);