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// Copyright (c) 2018-2026 Jean-Philippe Bruyère <jp_bruyere@hotmail.com>
//
// This code is licensed under the MIT license (MIT) (http://opensource.org/licenses/MIT)
// most of the matrix logic is grabbed from cairo, so here is the
// licence:
/* cairo - a vector graphics library with display and print output
*
* Copyright © 2002 University of Southern California
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*
* The Original Code is the cairo graphics library.
*
* The Initial Developer of the Original Code is University of Southern
* California.
*
* Contributor(s):
* Carl D. Worth <cworth@cworth.org>
*/
#include "vkvg_matrix.h"
#define ISFINITE(x) ((x) * (x) >= 0.) /* check for NaNs */
// matrix computations mainly taken from http://cairographics.org
static void _vkvg_matrix_scalar_multiply(vkvg_matrix_t* matrix, float scalar) {
matrix->xx *= scalar;
matrix->yx *= scalar;
matrix->xy *= scalar;
matrix->yy *= scalar;
matrix->x0 *= scalar;
matrix->y0 *= scalar;
}
void _vkvg_matrix_get_affine(const vkvg_matrix_t* matrix, float* xx, float* yx, float* xy, float* yy, float* x0,
float* y0) {
*xx = matrix->xx;
*yx = matrix->yx;
*xy = matrix->xy;
*yy = matrix->yy;
if (x0)
*x0 = matrix->x0;
if (y0)
*y0 = matrix->y0;
}
static void _vkvg_matrix_compute_adjoint(vkvg_matrix_t* matrix) {
/* adj (A) = transpose (C:cofactor (A,i,j)) */
float a, b, c, d, tx, ty;
_vkvg_matrix_get_affine(matrix, &a, &b, &c, &d, &tx, &ty);
vkvg_matrix_init(matrix, d, -b, -c, a, c * ty - d * tx, b * tx - a * ty);
}
float _vkvg_matrix_compute_determinant(const vkvg_matrix_t* matrix) {
float a, b, c, d;
a = matrix->xx;
b = matrix->yx;
c = matrix->xy;
d = matrix->yy;
return a * d - b * c;
}
vkvg_status_t vkvg_matrix_invert(vkvg_matrix_t* matrix) {
float det;
/* Simple scaling|translation matrices are quite common... */
if (matrix->xy == 0. && matrix->yx == 0.) {
matrix->x0 = -matrix->x0;
matrix->y0 = -matrix->y0;
if (matrix->xx != 1.f) {
if (matrix->xx == 0.)
return VKVG_STATUS_INVALID_MATRIX;
matrix->xx = 1.f / matrix->xx;
matrix->x0 *= matrix->xx;
}
if (matrix->yy != 1.f) {
if (matrix->yy == 0.)
return VKVG_STATUS_INVALID_MATRIX;
matrix->yy = 1.f / matrix->yy;
matrix->y0 *= matrix->yy;
}
return VKVG_STATUS_SUCCESS;
}
/* inv (A) = 1/det (A) * adj (A) */
det = _vkvg_matrix_compute_determinant(matrix);
if (!ISFINITE(det))
return VKVG_STATUS_INVALID_MATRIX;
if (det == 0)
return VKVG_STATUS_INVALID_MATRIX;
_vkvg_matrix_compute_adjoint(matrix);
_vkvg_matrix_scalar_multiply(matrix, 1 / det);
return VKVG_STATUS_SUCCESS;
}
void vkvg_matrix_init_identity(vkvg_matrix_t* matrix) { vkvg_matrix_init(matrix, 1, 0, 0, 1, 0, 0); }
void vkvg_matrix_init(vkvg_matrix_t* matrix, float xx, float yx, float xy, float yy, float x0, float y0) {
matrix->xx = xx;
matrix->yx = yx;
matrix->xy = xy;
matrix->yy = yy;
matrix->x0 = x0;
matrix->y0 = y0;
}
void vkvg_matrix_init_translate(vkvg_matrix_t* matrix, float tx, float ty) {
vkvg_matrix_init(matrix, 1, 0, 0, 1, tx, ty);
}
void vkvg_matrix_init_scale(vkvg_matrix_t* matrix, float sx, float sy) { vkvg_matrix_init(matrix, sx, 0, 0, sy, 0, 0); }
void vkvg_matrix_init_rotate(vkvg_matrix_t* matrix, float radians) {
float s;
float c;
s = sinf(radians);
c = cosf(radians);
vkvg_matrix_init(matrix, c, s, -s, c, 0, 0);
}
void vkvg_matrix_translate(vkvg_matrix_t* matrix, float tx, float ty) {
vkvg_matrix_t tmp;
vkvg_matrix_init_translate(&tmp, tx, ty);
vkvg_matrix_multiply(matrix, &tmp, matrix);
}
void vkvg_matrix_scale(vkvg_matrix_t* matrix, float sx, float sy) {
vkvg_matrix_t tmp;
vkvg_matrix_init_scale(&tmp, sx, sy);
vkvg_matrix_multiply(matrix, &tmp, matrix);
}
void vkvg_matrix_rotate(vkvg_matrix_t* matrix, float radians) {
vkvg_matrix_t tmp;
vkvg_matrix_init_rotate(&tmp, radians);
vkvg_matrix_multiply(matrix, &tmp, matrix);
}
void vkvg_matrix_multiply(vkvg_matrix_t* result, const vkvg_matrix_t *const a, const vkvg_matrix_t *const b) {
vkvg_matrix_t r;
r.xx = a->xx * b->xx + a->yx * b->xy;
r.yx = a->xx * b->yx + a->yx * b->yy;
r.xy = a->xy * b->xx + a->yy * b->xy;
r.yy = a->xy * b->yx + a->yy * b->yy;
r.x0 = a->x0 * b->xx + a->y0 * b->xy + b->x0;
r.y0 = a->x0 * b->yx + a->y0 * b->yy + b->y0;
*result = r;
}
void vkvg_matrix_transform_distance(const vkvg_matrix_t* matrix, float* dx, float* dy) {
float new_x, new_y;
new_x = (matrix->xx * *dx + matrix->xy * *dy);
new_y = (matrix->yx * *dx + matrix->yy * *dy);
*dx = new_x;
*dy = new_y;
}
void vkvg_matrix_transform_point(const vkvg_matrix_t* matrix, float* x, float* y) {
vkvg_matrix_transform_distance(matrix, x, y);
*x += matrix->x0;
*y += matrix->y0;
}
void vkvg_matrix_get_scale(const vkvg_matrix_t* matrix, float* sx, float* sy) {
*sx = sqrt(matrix->xx * matrix->xx + matrix->xy * matrix->xy);
/*if (matrix->xx < 0)
*sx = -*sx;*/
*sy = sqrt(matrix->yx * matrix->yx + matrix->yy * matrix->yy);
/*if (matrix->yy < 0)
*sy = -*sy;*/
}
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