mirror of
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252 lines
9.3 KiB
C
252 lines
9.3 KiB
C
/* Copyright (C) 2010-2015 The RetroArch team
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*
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* ---------------------------------------------------------------------------------------
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* The following license statement only applies to this file (matrix_3x3.c).
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* ---------------------------------------------------------------------------------------
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*
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* Permission is hereby granted, free of charge,
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* to any person obtaining a copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software,
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* and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
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* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*/
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#include <gfx/math/matrix_3x3.h>
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#include <math.h>
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#include <string.h>
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#define floats_are_equal(x, y) (fabs(x - y) <= 0.00001f * ((x) > (y) ? (y) : (x)))
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#define float_is_zero(x) (floats_are_equal((x) + 1, 1))
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void matrix_3x3_identity(math_matrix_3x3 *mat)
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{
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unsigned i;
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memset(mat, 0, sizeof(*mat));
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for (i = 0; i < 3; i++)
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MAT_ELEM_3X3(*mat, i, i) = 1.0f;
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}
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void matrix_3x3_inits(math_matrix_3x3 *mat,
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const float n11, const float n12, const float n13,
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const float n21, const float n22, const float n23,
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const float n31, const float n32, const float n33)
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{
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MAT_ELEM_3X3(*mat, 0, 0) = n11;
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MAT_ELEM_3X3(*mat, 0, 1) = n12;
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MAT_ELEM_3X3(*mat, 0, 2) = n13;
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MAT_ELEM_3X3(*mat, 1, 0) = n21;
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MAT_ELEM_3X3(*mat, 1, 1) = n22;
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MAT_ELEM_3X3(*mat, 1, 2) = n23;
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MAT_ELEM_3X3(*mat, 2, 0) = n31;
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MAT_ELEM_3X3(*mat, 2, 1) = n32;
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MAT_ELEM_3X3(*mat, 2, 2) = n33;
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}
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void matrix_3x3_transpose(math_matrix_3x3 *out, const math_matrix_3x3 *in)
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{
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unsigned i, j;
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math_matrix_3x3 mat;
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for (i = 0; i < 3; i++)
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for (j = 0; j < 3; j++)
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MAT_ELEM_3X3(mat, j, i) = MAT_ELEM_3X3(*in, i, j);
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*out = mat;
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}
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void matrix_3x3_multiply(math_matrix_3x3 *out,
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const math_matrix_3x3 *a, const math_matrix_3x3 *b)
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{
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unsigned r, c, k;
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math_matrix_3x3 mat;
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for (r = 0; r < 3; r++)
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{
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for (c = 0; c < 3; c++)
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{
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float dot = 0.0f;
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for (k = 0; k < 3; k++)
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dot += MAT_ELEM_3X3(*a, r, k) * MAT_ELEM_3X3(*b, k, c);
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MAT_ELEM_3X3(mat, r, c) = dot;
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}
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}
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*out = mat;
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}
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void matrix_3x3_divide_scalar(math_matrix_3x3 *mat, const float s)
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{
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unsigned i, j;
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for (i = 0; i < 3; i++)
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for (j = 0; j < 3; j++)
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MAT_ELEM_3X3(*mat, i, j) /= s;
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}
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float matrix_3x3_determinant(const math_matrix_3x3 *mat)
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{
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float det = 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));
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det -= 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));
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det += 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));
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return det;
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}
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void matrix_3x3_adjoint(math_matrix_3x3 *mat)
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{
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math_matrix_3x3 out;
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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MAT_ELEM_3X3(out, 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));
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*mat = out;
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}
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bool matrix_3x3_invert(math_matrix_3x3 *mat)
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{
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float det = matrix_3x3_determinant(mat);
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if (float_is_zero(det))
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return false;
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matrix_3x3_adjoint(mat);
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matrix_3x3_divide_scalar(mat, det);
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return true;
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}
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/**************************************************************************
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*
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* the following code is Copyright 2009 VMware, Inc. All Rights Reserved.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sub license, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice (including the
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* next paragraph) shall be included in all copies or substantial portions
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* of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
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* IN NO EVENT SHALL VMWARE AND/OR ITS SUPPLIERS BE LIABLE FOR
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* ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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**************************************************************************/
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bool matrix_3x3_square_to_quad(const float dx0, const float dy0,
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const float dx1, const float dy1,
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const float dx3, const float dy3,
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const float dx2, const float dy2,
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math_matrix_3x3 *mat)
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{
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float ax = dx0 - dx1 + dx2 - dx3;
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float ay = dy0 - dy1 + dy2 - dy3;
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if (float_is_zero(ax) && float_is_zero(ay))
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{
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/* affine case */
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matrix_3x3_inits(mat,
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dx1 - dx0, dy1 - dy0, 0,
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dx2 - dx1, dy2 - dy1, 0,
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dx0, dy0, 1);
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}
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else
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{
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float a, b, c, d, e, f, g, h;
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float ax1 = dx1 - dx2;
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float ax2 = dx3 - dx2;
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float ay1 = dy1 - dy2;
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float ay2 = dy3 - dy2;
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/* determinants */
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float gtop = ax * ay2 - ax2 * ay;
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float htop = ax1 * ay - ax * ay1;
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float bottom = ax1 * ay2 - ax2 * ay1;
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if (!bottom)
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return false;
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g = gtop / bottom;
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h = htop / bottom;
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a = dx1 - dx0 + g * dx1;
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b = dx3 - dx0 + h * dx3;
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c = dx0;
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d = dy1 - dy0 + g * dy1;
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e = dy3 - dy0 + h * dy3;
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f = dy0;
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matrix_3x3_inits(mat,
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a, d, g,
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b, e, h,
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c, f, 1.f);
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}
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return true;
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}
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bool matrix_3x3_quad_to_square(const float sx0, const float sy0,
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const float sx1, const float sy1,
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const float sx2, const float sy2,
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const float sx3, const float sy3,
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math_matrix_3x3 *mat)
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{
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if (!matrix_3x3_square_to_quad(sx0, sy0, sx1, sy1,
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sx2, sy2, sx3, sy3,
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mat))
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return false;
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return matrix_3x3_invert(mat);
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}
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bool matrix_3x3_quad_to_quad(const float dx0, const float dy0,
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const float dx1, const float dy1,
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const float dx2, const float dy2,
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const float dx3, const float dy3,
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const float sx0, const float sy0,
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const float sx1, const float sy1,
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const float sx2, const float sy2,
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const float sx3, const float sy3,
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math_matrix_3x3 *mat)
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{
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math_matrix_3x3 quad_to_square, square_to_quad;
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if (!matrix_3x3_square_to_quad(dx0, dy0, dx1, dy1,
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dx2, dy2, dx3, dy3,
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&square_to_quad))
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return false;
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if (!matrix_3x3_quad_to_square(sx0, sy0, sx1, sy1,
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sx2, sy2, sx3, sy3,
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&quad_to_square))
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return false;
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matrix_3x3_multiply(mat, &quad_to_square, &square_to_quad);
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return true;
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}
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