cairo/src/cairo-matrix.c

/* 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 under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 * Author: 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;
}