matrix_3x3.h

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#ifndef __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__
#define __LIBRETRO_SDK_GFX_MATH_MATRIX_3X3_H__

#include <boolean.h>
#include <math.h>
#include <string.h>

#include <retro_common_api.h>
#include <retro_inline.h>

RETRO_BEGIN_DECLS

typedef struct math_matrix_3x3
{
 float data[9];
} math_matrix_3x3;

#define MAT_ELEM_3X3(mat, r, c) ((mat).data[3 * (r) + (c)])

#define matrix_3x3_init(mat, n11, n12, n13, n21, n22, n23, n31, n32, n33) \
 MAT_ELEM_3X3(mat, 0, 0) = n11; \
 MAT_ELEM_3X3(mat, 0, 1) = n12; \
 MAT_ELEM_3X3(mat, 0, 2) = n13; \
 MAT_ELEM_3X3(mat, 1, 0) = n21; \
 MAT_ELEM_3X3(mat, 1, 1) = n22; \
 MAT_ELEM_3X3(mat, 1, 2) = n23; \
 MAT_ELEM_3X3(mat, 2, 0) = n31; \
 MAT_ELEM_3X3(mat, 2, 1) = n32; \
 MAT_ELEM_3X3(mat, 2, 2) = n33

#define matrix_3x3_identity(mat) \
 MAT_ELEM_3X3(mat, 0, 0) = 1.0f; \
 MAT_ELEM_3X3(mat, 0, 1) = 0; \
 MAT_ELEM_3X3(mat, 0, 2) = 0; \
 MAT_ELEM_3X3(mat, 1, 0) = 0; \
 MAT_ELEM_3X3(mat, 1, 1) = 1.0f; \
 MAT_ELEM_3X3(mat, 1, 2) = 0; \
 MAT_ELEM_3X3(mat, 2, 0) = 0; \
 MAT_ELEM_3X3(mat, 2, 1) = 0; \
 MAT_ELEM_3X3(mat, 2, 2) = 1.0f

#define matrix_3x3_divide_scalar(mat, s) \
 MAT_ELEM_3X3(mat, 0, 0) /= s; \
 MAT_ELEM_3X3(mat, 0, 1) /= s; \
 MAT_ELEM_3X3(mat, 0, 2) /= s; \
 MAT_ELEM_3X3(mat, 1, 0) /= s; \
 MAT_ELEM_3X3(mat, 1, 1) /= s; \
 MAT_ELEM_3X3(mat, 1, 2) /= s; \
 MAT_ELEM_3X3(mat, 2, 0) /= s; \
 MAT_ELEM_3X3(mat, 2, 1) /= s; \
 MAT_ELEM_3X3(mat, 2, 2) /= s

#define matrix_3x3_transpose(mat, in) \
 MAT_ELEM_3X3(mat, 0, 0) = MAT_ELEM_3X3(in, 0, 0); \
 MAT_ELEM_3X3(mat, 1, 0) = MAT_ELEM_3X3(in, 0, 1); \
 MAT_ELEM_3X3(mat, 2, 0) = MAT_ELEM_3X3(in, 0, 2); \
 MAT_ELEM_3X3(mat, 0, 1) = MAT_ELEM_3X3(in, 1, 0); \
 MAT_ELEM_3X3(mat, 1, 1) = MAT_ELEM_3X3(in, 1, 1); \
 MAT_ELEM_3X3(mat, 2, 1) = MAT_ELEM_3X3(in, 1, 2); \
 MAT_ELEM_3X3(mat, 0, 2) = MAT_ELEM_3X3(in, 2, 0); \
 MAT_ELEM_3X3(mat, 1, 2) = MAT_ELEM_3X3(in, 2, 1); \
 MAT_ELEM_3X3(mat, 2, 2) = MAT_ELEM_3X3(in, 2, 2)

#define matrix_3x3_multiply(out, a, b) \
 MAT_ELEM_3X3(out, 0, 0) = \
 MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 0) + \
 MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 0) + \
 MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 0); \
 MAT_ELEM_3X3(out, 0, 1) = \
 MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 1) + \
 MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 1) + \
 MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 1); \
 MAT_ELEM_3X3(out, 0, 2) = \
 MAT_ELEM_3X3(a, 0, 0) * MAT_ELEM_3X3(b, 0, 2) + \
 MAT_ELEM_3X3(a, 0, 1) * MAT_ELEM_3X3(b, 1, 2) + \
 MAT_ELEM_3X3(a, 0, 2) * MAT_ELEM_3X3(b, 2, 2); \
 MAT_ELEM_3X3(out, 1, 0) = \
 MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 0) + \
 MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 0) + \
 MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 0); \
 MAT_ELEM_3X3(out, 1, 1) = \
 MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 1) + \
 MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 1) + \
 MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 1); \
 MAT_ELEM_3X3(out, 1, 2) = \
 MAT_ELEM_3X3(a, 1, 0) * MAT_ELEM_3X3(b, 0, 2) + \
 MAT_ELEM_3X3(a, 1, 1) * MAT_ELEM_3X3(b, 1, 2) + \
 MAT_ELEM_3X3(a, 1, 2) * MAT_ELEM_3X3(b, 2, 2); \
 MAT_ELEM_3X3(out, 2, 0) = \
 MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 0) + \
 MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 0) + \
 MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 0); \
 MAT_ELEM_3X3(out, 2, 1) = \
 MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 1) + \
 MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 1) + \
 MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 1); \
 MAT_ELEM_3X3(out, 2, 2) = \
 MAT_ELEM_3X3(a, 2, 0) * MAT_ELEM_3X3(b, 0, 2) + \
 MAT_ELEM_3X3(a, 2, 1) * MAT_ELEM_3X3(b, 1, 2) + \
 MAT_ELEM_3X3(a, 2, 2) * MAT_ELEM_3X3(b, 2, 2)

#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)))

#define matrix_3x3_adjoint(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, 0, 1) * MAT_ELEM_3X3(mat, 2, 2) - MAT_ELEM_3X3(mat, 0, 2) * MAT_ELEM_3X3(mat, 2, 1)); \
 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)); \
 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)); \
 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)); \
 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)); \
 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)); \
 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)); \
 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))

#define FLOATS_ARE_EQUAL(x, y) (fabs(x - y) <= 0.00001f * ((x) > (y) ? (y) : (x)))
#define FLOAT_IS_ZERO(x) (FLOATS_ARE_EQUAL((x) + 1, 1))

static INLINE bool matrix_3x3_invert(math_matrix_3x3 *mat)
{
 float det = matrix_3x3_determinant(*mat);

 if (FLOAT_IS_ZERO(det))
 return false;

 matrix_3x3_adjoint(*mat);
 matrix_3x3_divide_scalar(*mat, det);

 return true;
}

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)
{
 float a, b, d, e;
 float ax = dx0 - dx1 + dx2 - dx3;
 float ay = dy0 - dy1 + dy2 - dy3;
 float c = dx0;
 float f = dy0;
 float g = 0;
 float h = 0;

 if (FLOAT_IS_ZERO(ax) && FLOAT_IS_ZERO(ay))
 {
 /* affine case */
 a = dx1 - dx0;
 b = dx2 - dx1;
 d = dy1 - dy0;
 e = dy2 - dy1;
 }
 else
 {
 float ax1 = dx1 - dx2;
 float ax2 = dx3 - dx2;
 float ay1 = dy1 - dy2;
 float ay2 = dy3 - dy2;

 /* determinants */
 float gtop = ax * ay2 - ax2 * ay;
 float htop = ax1 * ay - ax * ay1;
 float bottom = ax1 * ay2 - ax2 * ay1;

 if (!bottom)
 return false;

 g = gtop / bottom;
 h = htop / bottom;

 a = dx1 - dx0 + g * dx1;
 b = dx3 - dx0 + h * dx3;
 d = dy1 - dy0 + g * dy1;
 e = dy3 - dy0 + h * dy3;
 }


 matrix_3x3_init(*mat,
 a, d, g,
 b, e, h,
 c, f, 1.f);

 return true;
}

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)
{
 return matrix_3x3_square_to_quad(sx0, sy0, sx1, sy1,
 sx2, sy2, sx3, sy3,
 mat) ? matrix_3x3_invert(mat) : false;
}

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)
{
 math_matrix_3x3 square_to_quad;

 if (matrix_3x3_square_to_quad(dx0, dy0, dx1, dy1,
 dx2, dy2, dx3, dy3,
 &square_to_quad))
 {
 math_matrix_3x3 quad_to_square;
 if (matrix_3x3_quad_to_square(sx0, sy0, sx1, sy1,
 sx2, sy2, sx3, sy3,
 &quad_to_square))
 {
 matrix_3x3_multiply(*mat, quad_to_square, square_to_quad);

 return true;
 }
 }

 return false;
}

RETRO_END_DECLS

#endif