cairo-matrix.c

按照官方的说法：Cairo is a vector graphics library with cross-device output support. 翻译过来

/* 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 <[e-mail]>
 */

#define _GNU_SOURCE
#include <stdlib.h>

#include "cairoint.h"

static void
_cairo_matrix_scalar_multiply (cairo_matrix_t *matrix, double scalar);

static void
_cairo_matrix_compute_adjoint (cairo_matrix_t *matrix);

/**
 * cairo_matrix_init_identity:
 * @matrix: a #cairo_matrix_t
 *
 * Modifies @matrix to be an identity transformation.
 **/
void
cairo_matrix_init_identity (cairo_matrix_t *matrix)
{
    cairo_matrix_init (matrix,
		       1, 0,
		       0, 1,
		       0, 0);
}
slim_hidden_def(cairo_matrix_init_identity);

/**
 * cairo_matrix_init:
 * @matrix: a cairo_matrix_t
 * @xx: xx component of the affine transformation
 * @yx: yx component of the affine transformation
 * @xy: xy component of the affine transformation
 * @yy: yy component of the affine transformation
 * @x0: X translation component of the affine transformation
 * @y0: Y translation component of the affine transformation
 *
 * Sets @matrix to be the affine transformation given by
 * @xx, @yx, @xy, @yy, @x0, @y0. The transformation is given
 * by:
 * <programlisting>
 *  x_new = xx * x + xy * y + x0;
 *  y_new = yx * x + yy * y + y0;
 * </programlisting>
 **/
void
cairo_matrix_init (cairo_matrix_t *matrix,
		   double xx, double yx,

		   double xy, double yy,
		   double x0, double y0)
{
    matrix->xx = xx; matrix->yx = yx;
    matrix->xy = xy; matrix->yy = yy;
    matrix->x0 = x0; matrix->y0 = y0;
}
slim_hidden_def(cairo_matrix_init);

/**
 * _cairo_matrix_get_affine:
 * @matrix: a @cairo_matrix_t
 * @xx: location to store xx component of matrix
 * @yx: location to store yx component of matrix
 * @xy: location to store xy component of matrix
 * @yy: location to store yy component of matrix
 * @x0: location to store x0 (X-translation component) of matrix, or %NULL
 * @y0: location to store y0 (Y-translation component) of matrix, or %NULL
 *
 * Gets the matrix values for the affine tranformation that @matrix represents.
 * See cairo_matrix_init().
 *
 *
 * This function is a leftover from the old public API, but is still
 * mildly useful as an internal means for getting at the matrix
 * members in a positional way. For example, when reassigning to some
 * external matrix type, or when renaming members to more meaningful
 * names (such as a,b,c,d,e,f) for particular manipulations.
 **/
void
_cairo_matrix_get_affine (const cairo_matrix_t *matrix,
			  double *xx, double *yx,
			  double *xy, double *yy,
			  double *x0, double *y0)
{
    *xx  = matrix->xx;
    *yx  = matrix->yx;

    *xy  = matrix->xy;
    *yy  = matrix->yy;

    if (x0)
	*x0 = matrix->x0;
    if (y0)
	*y0 = matrix->y0;
}

/**
 * cairo_matrix_init_translate:
 * @matrix: a cairo_matrix_t
 * @tx: amount to translate in the X direction
 * @ty: amount to translate in the Y direction
 *
 * Initializes @matrix to a transformation that translates by @tx and
 * @ty in the X and Y dimensions, respectively.
 **/
void
cairo_matrix_init_translate (cairo_matrix_t *matrix,
			     double tx, double ty)
{
    cairo_matrix_init (matrix,
		       1, 0,
		       0, 1,
		       tx, ty);
}
slim_hidden_def(cairo_matrix_init_translate);

/**
 * cairo_matrix_translate:
 * @matrix: a cairo_matrix_t
 * @tx: amount to translate in the X direction
 * @ty: amount to translate in the Y direction
 *
 * Applies a translation by @tx, @ty to the transformation in
 * @matrix. The effect of the new transformation is to first translate
 * the coordinates by @tx and @ty, then apply the original transformation
 * to the coordinates.
 **/
void
cairo_matrix_translate (cairo_matrix_t *matrix, double tx, double ty)
{
    cairo_matrix_t tmp;

    cairo_matrix_init_translate (&tmp, tx, ty);

    cairo_matrix_multiply (matrix, &tmp, matrix);
}

/**
 * cairo_matrix_init_scale:
 * @matrix: a cairo_matrix_t
 * @sx: scale factor in the X direction
 * @sy: scale factor in the Y direction
 *
 * Initializes @matrix to a transformation that scales by @sx and @sy
 * in the X and Y dimensions, respectively.
 **/
void
cairo_matrix_init_scale (cairo_matrix_t *matrix,
			 double sx, double sy)
{
    cairo_matrix_init (matrix,
		       sx,  0,
		       0, sy,
		       0, 0);
}
slim_hidden_def(cairo_matrix_init_scale);

/**
 * cairo_matrix_scale:
 * @matrix: a #cairo_matrix_t
 * @sx: scale factor in the X direction
 * @sy: scale factor in the Y direction
 *
 * Applies scaling by @tx, @ty to the transformation in @matrix. The
 * effect of the new transformation is to first scale the coordinates
 * by @sx and @sy, then apply the original transformation to the coordinates.
 **/
void
cairo_matrix_scale (cairo_matrix_t *matrix, double sx, double sy)
{
    cairo_matrix_t tmp;

    cairo_matrix_init_scale (&tmp, sx, sy);

    cairo_matrix_multiply (matrix, &tmp, matrix);
}
slim_hidden_def(cairo_matrix_scale);

/**
 * cairo_matrix_init_rotate:
 * @matrix: a cairo_matrix_t
 * @radians: angle of rotation, in radians. The direction of rotation
 * is defined such that positive angles rotate in the direction from
 * the positive X axis toward the positive Y axis. With the default
 * axis orientation of cairo, positive angles rotate in a clockwise
 * direction.
 *
 * Initialized @matrix to a transformation that rotates by @radians.
 **/
void
cairo_matrix_init_rotate (cairo_matrix_t *matrix,
			  double radians)
{
    double  s;
    double  c;

    s = sin (radians);
    c = cos (radians);

    cairo_matrix_init (matrix,
		       c, s,
		       -s, c,
		       0, 0);
}
slim_hidden_def(cairo_matrix_init_rotate);

/**
 * cairo_matrix_rotate:
 * @matrix: a @cairo_matrix_t
 * @radians: angle of rotation, in radians. The direction of rotation
 * is defined such that positive angles rotate in the direction from
 * the positive X axis toward the positive Y axis. With the default
 * axis orientation of cairo, positive angles rotate in a clockwise
 * direction.
 *
 * Applies rotation by @radians to the transformation in
 * @matrix. The effect of the new transformation is to first rotate the
 * coordinates by @radians, then apply the original transformation
 * to the coordinates.
 **/
void
cairo_matrix_rotate (cairo_matrix_t *matrix, double radians)
{
    cairo_matrix_t tmp;

    cairo_matrix_init_rotate (&tmp, radians);

    cairo_matrix_multiply (matrix, &tmp, matrix);
}

/**
 * cairo_matrix_multiply:
 * @result: a @cairo_matrix_t in which to store the result
 * @a: a @cairo_matrix_t
 * @b: a @cairo_matrix_t
 *
 * Multiplies the affine transformations in @a and @b together
 * and stores the result in @result. The effect of the resulting
 * transformation is to first apply the transformation in @a to the
 * coordinates and then apply the transformation in @b to the
 * coordinates.
 *
 * It is allowable for @result to be identical to either @a or @b.
 **/
/*
 * XXX: The ordering of the arguments to this function corresponds
 *      to [row_vector]*A*B. If we want to use column vectors instead,
 *      then we need to switch the two arguments and fix up all
 *      uses.
 */
void
cairo_matrix_multiply (cairo_matrix_t *result, const cairo_matrix_t *a, const cairo_matrix_t *b)
{
    cairo_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;
}
slim_hidden_def(cairo_matrix_multiply);

/**
 * cairo_matrix_transform_distance:
 * @matrix: a @cairo_matrix_t
 * @dx: X component of a distance vector. An in/out parameter
 * @dy: Y component of a distance vector. An in/out parameter
 *
 * Transforms the distance vector (@dx,@dy) by @matrix. This is
 * similar to cairo_matrix_transform() except that the translation
 * components of the transformation are ignored. The calculation of
 * the returned vector is as follows:
 *
 * <programlisting>
 * dx2 = dx1 * a + dy1 * c;
 * dy2 = dx1 * b + dy1 * d;
 * </programlisting>
 *
 * Affine transformations are position invariant, so the same vector
 * always transforms to the same vector. If (@x1,@y1) transforms
 * to (@x2,@y2) then (@x1+@dx1,@y1+@dy1) will transform to
 * (@x1+@dx2,@y1+@dy2) for all values of @x1 and @x2.
 **/
void
cairo_matrix_transform_distance (const cairo_matrix_t *matrix, double *dx, double *dy)
{
    double 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;
}
slim_hidden_def(cairo_matrix_transform_distance);

/**
 * cairo_matrix_transform_point:
 * @matrix: a @cairo_matrix_t
 * @x: X position. An in/out parameter
 * @y: Y position. An in/out parameter
 *
 * Transforms the point (@x, @y) by @matrix.
 **/
void
cairo_matrix_transform_point (const cairo_matrix_t *matrix, double *x, double *y)
{
    cairo_matrix_transform_distance (matrix, x, y);

    *x += matrix->x0;
    *y += matrix->y0;
}
slim_hidden_def(cairo_matrix_transform_point);

void
_cairo_matrix_transform_bounding_box (const cairo_matrix_t *matrix,
				      double *x, double *y,
				      double *width, double *height)
{
    int i;
    double quad_x[4], quad_y[4];