Permalink
Cannot retrieve contributors at this time
Name already in use
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
cairo/src/cairo-matrix.c
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
440 lines (357 sloc)
10.2 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
/* 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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@isi.edu> | |
*/ | |
#include <stdlib.h> | |
#include <math.h> | |
#include "cairoint.h" | |
static cairo_matrix_t const CAIRO_MATRIX_IDENTITY = { | |
{ | |
{1, 0}, | |
{0, 1}, | |
{0, 0} | |
} | |
}; | |
static void | |
_cairo_matrix_scalar_multiply (cairo_matrix_t *matrix, double scalar); | |
static void | |
_cairo_matrix_compute_adjoint (cairo_matrix_t *matrix); | |
cairo_matrix_t * | |
cairo_matrix_create (void) | |
{ | |
cairo_matrix_t *matrix; | |
matrix = malloc (sizeof (cairo_matrix_t)); | |
if (matrix == NULL) | |
return NULL; | |
_cairo_matrix_init (matrix); | |
return matrix; | |
} | |
void | |
_cairo_matrix_init (cairo_matrix_t *matrix) | |
{ | |
cairo_matrix_set_identity (matrix); | |
} | |
void | |
_cairo_matrix_fini (cairo_matrix_t *matrix) | |
{ | |
/* nothing to do here */ | |
} | |
void | |
cairo_matrix_destroy (cairo_matrix_t *matrix) | |
{ | |
_cairo_matrix_fini (matrix); | |
free (matrix); | |
} | |
cairo_status_t | |
cairo_matrix_copy (cairo_matrix_t *matrix, const cairo_matrix_t *other) | |
{ | |
*matrix = *other; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_copy); | |
cairo_status_t | |
cairo_matrix_set_identity (cairo_matrix_t *matrix) | |
{ | |
*matrix = CAIRO_MATRIX_IDENTITY; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_set_identity); | |
cairo_status_t | |
cairo_matrix_set_affine (cairo_matrix_t *matrix, | |
double a, double b, | |
double c, double d, | |
double tx, double ty) | |
{ | |
matrix->m[0][0] = a; matrix->m[0][1] = b; | |
matrix->m[1][0] = c; matrix->m[1][1] = d; | |
matrix->m[2][0] = tx; matrix->m[2][1] = ty; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_set_affine); | |
cairo_status_t | |
cairo_matrix_get_affine (cairo_matrix_t *matrix, | |
double *a, double *b, | |
double *c, double *d, | |
double *tx, double *ty) | |
{ | |
*a = matrix->m[0][0]; *b = matrix->m[0][1]; | |
*c = matrix->m[1][0]; *d = matrix->m[1][1]; | |
*tx = matrix->m[2][0]; *ty = matrix->m[2][1]; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
cairo_status_t | |
_cairo_matrix_set_translate (cairo_matrix_t *matrix, | |
double tx, double ty) | |
{ | |
return cairo_matrix_set_affine (matrix, | |
1, 0, | |
0, 1, | |
tx, ty); | |
} | |
cairo_status_t | |
cairo_matrix_translate (cairo_matrix_t *matrix, double tx, double ty) | |
{ | |
cairo_matrix_t tmp; | |
_cairo_matrix_set_translate (&tmp, tx, ty); | |
return cairo_matrix_multiply (matrix, &tmp, matrix); | |
} | |
cairo_status_t | |
_cairo_matrix_set_scale (cairo_matrix_t *matrix, | |
double sx, double sy) | |
{ | |
return cairo_matrix_set_affine (matrix, | |
sx, 0, | |
0, sy, | |
0, 0); | |
} | |
cairo_status_t | |
cairo_matrix_scale (cairo_matrix_t *matrix, double sx, double sy) | |
{ | |
cairo_matrix_t tmp; | |
_cairo_matrix_set_scale (&tmp, sx, sy); | |
return cairo_matrix_multiply (matrix, &tmp, matrix); | |
} | |
slim_hidden_def(cairo_matrix_scale); | |
cairo_status_t | |
_cairo_matrix_set_rotate (cairo_matrix_t *matrix, | |
double radians) | |
{ | |
return cairo_matrix_set_affine (matrix, | |
cos (radians), sin (radians), | |
-sin (radians), cos (radians), | |
0, 0); | |
} | |
cairo_status_t | |
cairo_matrix_rotate (cairo_matrix_t *matrix, double radians) | |
{ | |
cairo_matrix_t tmp; | |
_cairo_matrix_set_rotate (&tmp, radians); | |
return cairo_matrix_multiply (matrix, &tmp, matrix); | |
} | |
cairo_status_t | |
cairo_matrix_multiply (cairo_matrix_t *result, const cairo_matrix_t *a, const cairo_matrix_t *b) | |
{ | |
cairo_matrix_t r; | |
int row, col, n; | |
double t; | |
for (row = 0; row < 3; row++) { | |
for (col = 0; col < 2; col++) { | |
if (row == 2) | |
t = b->m[2][col]; | |
else | |
t = 0; | |
for (n = 0; n < 2; n++) { | |
t += a->m[row][n] * b->m[n][col]; | |
} | |
r.m[row][col] = t; | |
} | |
} | |
*result = r; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_multiply); | |
cairo_status_t | |
cairo_matrix_transform_distance (cairo_matrix_t *matrix, double *dx, double *dy) | |
{ | |
double new_x, new_y; | |
new_x = (matrix->m[0][0] * *dx | |
+ matrix->m[1][0] * *dy); | |
new_y = (matrix->m[0][1] * *dx | |
+ matrix->m[1][1] * *dy); | |
*dx = new_x; | |
*dy = new_y; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_transform_distance); | |
cairo_status_t | |
cairo_matrix_transform_point (cairo_matrix_t *matrix, double *x, double *y) | |
{ | |
cairo_matrix_transform_distance (matrix, x, y); | |
*x += matrix->m[2][0]; | |
*y += matrix->m[2][1]; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_transform_point); | |
cairo_status_t | |
_cairo_matrix_transform_bounding_box (cairo_matrix_t *matrix, | |
double *x, double *y, | |
double *width, double *height) | |
{ | |
int i; | |
double quad_x[4], quad_y[4]; | |
double dx1, dy1; | |
double dx2, dy2; | |
double min_x, max_x; | |
double min_y, max_y; | |
quad_x[0] = *x; | |
quad_y[0] = *y; | |
cairo_matrix_transform_point (matrix, &quad_x[0], &quad_y[0]); | |
dx1 = *width; | |
dy1 = 0; | |
cairo_matrix_transform_distance (matrix, &dx1, &dy1); | |
quad_x[1] = quad_x[0] + dx1; | |
quad_y[1] = quad_y[0] + dy1; | |
dx2 = 0; | |
dy2 = *height; | |
cairo_matrix_transform_distance (matrix, &dx2, &dy2); | |
quad_x[2] = quad_x[0] + dx2; | |
quad_y[2] = quad_y[0] + dy2; | |
quad_x[3] = quad_x[0] + dx1 + dx2; | |
quad_y[3] = quad_y[0] + dy1 + dy2; | |
min_x = max_x = quad_x[0]; | |
min_y = max_y = quad_y[0]; | |
for (i=1; i < 4; i++) { | |
if (quad_x[i] < min_x) | |
min_x = quad_x[i]; | |
if (quad_x[i] > max_x) | |
max_x = quad_x[i]; | |
if (quad_y[i] < min_y) | |
min_y = quad_y[i]; | |
if (quad_y[i] > max_y) | |
max_y = quad_y[i]; | |
} | |
*x = min_x; | |
*y = min_y; | |
*width = max_x - min_x; | |
*height = max_y - min_y; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
static void | |
_cairo_matrix_scalar_multiply (cairo_matrix_t *matrix, double scalar) | |
{ | |
int row, col; | |
for (row = 0; row < 3; row++) | |
for (col = 0; col < 2; col++) | |
matrix->m[row][col] *= scalar; | |
} | |
/* This function isn't a correct adjoint in that the implicit 1 in the | |
homogeneous result should actually be ad-bc instead. But, since this | |
adjoint is only used in the computation of the inverse, which | |
divides by det (A)=ad-bc anyway, everything works out in the end. */ | |
static void | |
_cairo_matrix_compute_adjoint (cairo_matrix_t *matrix) | |
{ | |
/* adj (A) = transpose (C:cofactor (A,i,j)) */ | |
double a, b, c, d, tx, ty; | |
a = matrix->m[0][0]; b = matrix->m[0][1]; | |
c = matrix->m[1][0]; d = matrix->m[1][1]; | |
tx = matrix->m[2][0]; ty = matrix->m[2][1]; | |
cairo_matrix_set_affine (matrix, | |
d, -b, | |
-c, a, | |
c*ty - d*tx, b*tx - a*ty); | |
} | |
cairo_status_t | |
cairo_matrix_invert (cairo_matrix_t *matrix) | |
{ | |
/* inv (A) = 1/det (A) * adj (A) */ | |
double det; | |
_cairo_matrix_compute_determinant (matrix, &det); | |
if (det == 0) | |
return CAIRO_STATUS_INVALID_MATRIX; | |
_cairo_matrix_compute_adjoint (matrix); | |
_cairo_matrix_scalar_multiply (matrix, 1 / det); | |
return CAIRO_STATUS_SUCCESS; | |
} | |
slim_hidden_def(cairo_matrix_invert); | |
cairo_status_t | |
_cairo_matrix_compute_determinant (cairo_matrix_t *matrix, double *det) | |
{ | |
double a, b, c, d; | |
a = matrix->m[0][0]; b = matrix->m[0][1]; | |
c = matrix->m[1][0]; d = matrix->m[1][1]; | |
*det = a*d - b*c; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
cairo_status_t | |
_cairo_matrix_compute_eigen_values (cairo_matrix_t *matrix, double *lambda1, double *lambda2) | |
{ | |
/* The eigenvalues of an NxN matrix M are found by solving the polynomial: | |
det (M - lI) = 0 | |
The zeros in our homogeneous 3x3 matrix make this equation equal | |
to that formed by the sub-matrix: | |
M = a b | |
c d | |
by which: | |
l^2 - (a+d)l + (ad - bc) = 0 | |
l = (a+d +/- sqrt (a^2 + 2ad + d^2 - 4 (ad-bc))) / 2; | |
*/ | |
double a, b, c, d, rad; | |
a = matrix->m[0][0]; | |
b = matrix->m[0][1]; | |
c = matrix->m[1][0]; | |
d = matrix->m[1][1]; | |
rad = sqrt (a*a + 2*a*d + d*d - 4*(a*d - b*c)); | |
*lambda1 = (a + d + rad) / 2.0; | |
*lambda2 = (a + d - rad) / 2.0; | |
return CAIRO_STATUS_SUCCESS; | |
} | |
/* Compute the amount that each basis vector is scaled by. */ | |
cairo_status_t | |
_cairo_matrix_compute_scale_factors (cairo_matrix_t *matrix, double *sx, double *sy) | |
{ | |
double x, y; | |
x = 1.0; | |
y = 0.0; | |
cairo_matrix_transform_distance (matrix, &x, &y); | |
*sx = sqrt(x*x + y*y); | |
x = 0.0; | |
y = 1.0; | |
cairo_matrix_transform_distance (matrix, &x, &y); | |
*sy = sqrt(x*x + y*y); | |
return CAIRO_STATUS_SUCCESS; | |
} | |
int | |
_cairo_matrix_is_integer_translation(cairo_matrix_t *mat, | |
int *itx, int *ity) | |
{ | |
double a, b, c, d, tx, ty; | |
int ttx, tty; | |
int ok = 0; | |
cairo_matrix_get_affine (mat, &a, &b, &c, &d, &tx, &ty); | |
ttx = _cairo_fixed_from_double (tx); | |
tty = _cairo_fixed_from_double (ty); | |
ok = ((a == 1.0) | |
&& (b == 0.0) | |
&& (c == 0.0) | |
&& (d == 1.0) | |
&& (_cairo_fixed_is_integer(ttx)) | |
&& (_cairo_fixed_is_integer(tty))); | |
if (ok) { | |
*itx = _cairo_fixed_integer_part(ttx); | |
*ity = _cairo_fixed_integer_part(tty); | |
return 1; | |
} | |
return 0; | |
} |