зеркало из https://github.com/mozilla/pjs.git
458 строки
12 KiB
C
458 строки
12 KiB
C
/* Libart_LGPL - library of basic graphic primitives
|
|
* Copyright (C) 1998 Raph Levien
|
|
*
|
|
* 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.
|
|
*/
|
|
|
|
/* Simple manipulations with affine transformations */
|
|
|
|
#include <math.h>
|
|
#include <stdio.h> /* for sprintf */
|
|
#include <string.h> /* for strcpy */
|
|
#include "art_misc.h"
|
|
#include "art_point.h"
|
|
#include "art_affine.h"
|
|
|
|
|
|
/* According to a strict interpretation of the libart structure, this
|
|
routine should go into its own module, art_point_affine. However,
|
|
it's only two lines of code, and it can be argued that it is one of
|
|
the natural basic functions of an affine transformation.
|
|
*/
|
|
|
|
/**
|
|
* art_affine_point: Do an affine transformation of a point.
|
|
* @dst: Where the result point is stored.
|
|
* @src: The original point.
|
|
@ @affine: The affine transformation.
|
|
**/
|
|
void
|
|
art_affine_point (ArtPoint *dst, const ArtPoint *src,
|
|
const double affine[6])
|
|
{
|
|
double x, y;
|
|
|
|
x = src->x;
|
|
y = src->y;
|
|
dst->x = x * affine[0] + y * affine[2] + affine[4];
|
|
dst->y = x * affine[1] + y * affine[3] + affine[5];
|
|
}
|
|
|
|
/**
|
|
* art_affine_invert: Find the inverse of an affine transformation.
|
|
* @dst: Where the resulting affine is stored.
|
|
* @src: The original affine transformation.
|
|
*
|
|
* All non-degenerate affine transforms are invertible. If the original
|
|
* affine is degenerate or nearly so, expect numerical instability and
|
|
* very likely core dumps on Alpha and other fp-picky architectures.
|
|
* Otherwise, @dst multiplied with @src, or @src multiplied with @dst
|
|
* will be (to within roundoff error) the identity affine.
|
|
**/
|
|
void
|
|
art_affine_invert (double dst[6], const double src[6])
|
|
{
|
|
double r_det;
|
|
|
|
r_det = 1.0 / (src[0] * src[3] - src[1] * src[2]);
|
|
dst[0] = src[3] * r_det;
|
|
dst[1] = -src[1] * r_det;
|
|
dst[2] = -src[2] * r_det;
|
|
dst[3] = src[0] * r_det;
|
|
dst[4] = -src[4] * dst[0] - src[5] * dst[2];
|
|
dst[5] = -src[4] * dst[1] - src[5] * dst[3];
|
|
}
|
|
|
|
/**
|
|
* art_affine_flip: Flip an affine transformation horizontally and/or vertically.
|
|
* @dst_affine: Where the resulting affine is stored.
|
|
* @src_affine: The original affine transformation.
|
|
* @horiz: Whether or not to flip horizontally.
|
|
* @vert: Whether or not to flip horizontally.
|
|
*
|
|
* Flips the affine transform. FALSE for both @horiz and @vert implements
|
|
* a simple copy operation. TRUE for both @horiz and @vert is a
|
|
* 180 degree rotation. It is ok for @src_affine and @dst_affine to
|
|
* be equal pointers.
|
|
**/
|
|
void
|
|
art_affine_flip (double dst_affine[6], const double src_affine[6], int horz, int vert)
|
|
{
|
|
dst_affine[0] = horz ? - src_affine[0] : src_affine[0];
|
|
dst_affine[1] = horz ? - src_affine[1] : src_affine[1];
|
|
dst_affine[2] = vert ? - src_affine[2] : src_affine[2];
|
|
dst_affine[3] = vert ? - src_affine[3] : src_affine[3];
|
|
dst_affine[4] = horz ? - src_affine[4] : src_affine[4];
|
|
dst_affine[5] = vert ? - src_affine[5] : src_affine[5];
|
|
}
|
|
|
|
#define EPSILON 1e-6
|
|
|
|
/* It's ridiculous I have to write this myself. This is hardcoded to
|
|
six digits of precision, which is good enough for PostScript.
|
|
|
|
The return value is the number of characters (i.e. strlen (str)).
|
|
It is no more than 12. */
|
|
static int
|
|
art_ftoa (char str[80], double x)
|
|
{
|
|
char *p = str;
|
|
int i, j;
|
|
|
|
p = str;
|
|
if (fabs (x) < EPSILON / 2)
|
|
{
|
|
strcpy (str, "0");
|
|
return 1;
|
|
}
|
|
if (x < 0)
|
|
{
|
|
*p++ = '-';
|
|
x = -x;
|
|
}
|
|
if ((int)floor ((x + EPSILON / 2) < 1))
|
|
{
|
|
*p++ = '0';
|
|
*p++ = '.';
|
|
i = sprintf (p, "%06d", (int)floor ((x + EPSILON / 2) * 1e6));
|
|
while (i && p[i - 1] == '0')
|
|
i--;
|
|
if (i == 0)
|
|
i--;
|
|
p += i;
|
|
}
|
|
else if (x < 1e6)
|
|
{
|
|
i = sprintf (p, "%d", (int)floor (x + EPSILON / 2));
|
|
p += i;
|
|
if (i < 6)
|
|
{
|
|
int ix;
|
|
|
|
*p++ = '.';
|
|
x -= floor (x + EPSILON / 2);
|
|
for (j = i; j < 6; j++)
|
|
x *= 10;
|
|
ix = floor (x + 0.5);
|
|
|
|
for (j = 0; j < i; j++)
|
|
ix *= 10;
|
|
|
|
/* A cheap hack, this routine can round wrong for fractions
|
|
near one. */
|
|
if (ix == 1000000)
|
|
ix = 999999;
|
|
|
|
sprintf (p, "%06d", ix);
|
|
i = 6 - i;
|
|
while (i && p[i - 1] == '0')
|
|
i--;
|
|
if (i == 0)
|
|
i--;
|
|
p += i;
|
|
}
|
|
}
|
|
else
|
|
p += sprintf (p, "%g", x);
|
|
|
|
*p = '\0';
|
|
return p - str;
|
|
}
|
|
|
|
|
|
|
|
#include <stdlib.h>
|
|
/**
|
|
* art_affine_to_string: Convert affine transformation to concise PostScript string representation.
|
|
* @str: Where to store the resulting string.
|
|
* @src: The affine transform.
|
|
*
|
|
* Converts an affine transform into a bit of PostScript code that
|
|
* implements the transform. Special cases of scaling, rotation, and
|
|
* translation are detected, and the corresponding PostScript
|
|
* operators used (this greatly aids understanding the output
|
|
* generated). The identity transform is mapped to the null string.
|
|
**/
|
|
void
|
|
art_affine_to_string (char str[128], const double src[6])
|
|
{
|
|
char tmp[80];
|
|
int i, ix;
|
|
|
|
#if 0
|
|
for (i = 0; i < 1000; i++)
|
|
{
|
|
double d = rand () * .1 / RAND_MAX;
|
|
art_ftoa (tmp, d);
|
|
printf ("%g %f %s\n", d, d, tmp);
|
|
}
|
|
#endif
|
|
if (fabs (src[4]) < EPSILON && fabs (src[5]) < EPSILON)
|
|
{
|
|
/* could be scale or rotate */
|
|
if (fabs (src[1]) < EPSILON && fabs (src[2]) < EPSILON)
|
|
{
|
|
/* scale */
|
|
if (fabs (src[0] - 1) < EPSILON && fabs (src[3] - 1) < EPSILON)
|
|
{
|
|
/* identity transform */
|
|
str[0] = '\0';
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
ix = 0;
|
|
ix += art_ftoa (str + ix, src[0]);
|
|
str[ix++] = ' ';
|
|
ix += art_ftoa (str + ix, src[3]);
|
|
strcpy (str + ix, " scale");
|
|
return;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* could be rotate */
|
|
if (fabs (src[0] - src[3]) < EPSILON &&
|
|
fabs (src[1] + src[2]) < EPSILON &&
|
|
fabs (src[0] * src[0] + src[1] * src[1] - 1) < 2 * EPSILON)
|
|
{
|
|
double theta;
|
|
|
|
theta = (180 / M_PI) * atan2 (src[1], src[0]);
|
|
art_ftoa (tmp, theta);
|
|
sprintf (str, "%s rotate", tmp);
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* could be translate */
|
|
if (fabs (src[0] - 1) < EPSILON && fabs (src[1]) < EPSILON &&
|
|
fabs (src[2]) < EPSILON && fabs (src[3] - 1) < EPSILON)
|
|
{
|
|
ix = 0;
|
|
ix += art_ftoa (str + ix, src[4]);
|
|
str[ix++] = ' ';
|
|
ix += art_ftoa (str + ix, src[5]);
|
|
strcpy (str + ix, " translate");
|
|
return;
|
|
}
|
|
}
|
|
|
|
ix = 0;
|
|
str[ix++] = '[';
|
|
str[ix++] = ' ';
|
|
for (i = 0; i < 6; i++)
|
|
{
|
|
ix += art_ftoa (str + ix, src[i]);
|
|
str[ix++] = ' ';
|
|
}
|
|
strcpy (str + ix, "] concat");
|
|
}
|
|
|
|
/**
|
|
* art_affine_multiply: Multiply two affine transformation matrices.
|
|
* @dst: Where to store the result.
|
|
* @src1: The first affine transform to multiply.
|
|
* @src2: The second affine transform to multiply.
|
|
*
|
|
* Multiplies two affine transforms together, i.e. the resulting @dst
|
|
* is equivalent to doing first @src1 then @src2. Note that the
|
|
* PostScript concat operator multiplies on the left, i.e. "M concat"
|
|
* is equivalent to "CTM = multiply (M, CTM)";
|
|
*
|
|
* It is safe to call this function with @dst equal to @src1 or @src2.
|
|
**/
|
|
void
|
|
art_affine_multiply (double dst[6], const double src1[6], const double src2[6])
|
|
{
|
|
double d0, d1, d2, d3, d4, d5;
|
|
|
|
d0 = src1[0] * src2[0] + src1[1] * src2[2];
|
|
d1 = src1[0] * src2[1] + src1[1] * src2[3];
|
|
d2 = src1[2] * src2[0] + src1[3] * src2[2];
|
|
d3 = src1[2] * src2[1] + src1[3] * src2[3];
|
|
d4 = src1[4] * src2[0] + src1[5] * src2[2] + src2[4];
|
|
d5 = src1[4] * src2[1] + src1[5] * src2[3] + src2[5];
|
|
dst[0] = d0;
|
|
dst[1] = d1;
|
|
dst[2] = d2;
|
|
dst[3] = d3;
|
|
dst[4] = d4;
|
|
dst[5] = d5;
|
|
}
|
|
|
|
/**
|
|
* art_affine_identity: Set up the identity matrix.
|
|
* @dst: Where to store the resulting affine transform.
|
|
*
|
|
* Sets up an identity matrix.
|
|
**/
|
|
void
|
|
art_affine_identity (double dst[6])
|
|
{
|
|
dst[0] = 1;
|
|
dst[1] = 0;
|
|
dst[2] = 0;
|
|
dst[3] = 1;
|
|
dst[4] = 0;
|
|
dst[5] = 0;
|
|
}
|
|
|
|
|
|
/**
|
|
* art_affine_scale: Set up a scaling matrix.
|
|
* @dst: Where to store the resulting affine transform.
|
|
* @sx: X scale factor.
|
|
* @sy: Y scale factor.
|
|
*
|
|
* Sets up a scaling matrix.
|
|
**/
|
|
void
|
|
art_affine_scale (double dst[6], double sx, double sy)
|
|
{
|
|
dst[0] = sx;
|
|
dst[1] = 0;
|
|
dst[2] = 0;
|
|
dst[3] = sy;
|
|
dst[4] = 0;
|
|
dst[5] = 0;
|
|
}
|
|
|
|
/**
|
|
* art_affine_rotate: Set up a rotation affine transform.
|
|
* @dst: Where to store the resulting affine transform.
|
|
* @theta: Rotation angle in degrees.
|
|
*
|
|
* Sets up a rotation matrix. In the standard libart coordinate
|
|
* system, in which increasing y moves downward, this is a
|
|
* counterclockwise rotation. In the standard PostScript coordinate
|
|
* system, which is reversed in the y direction, it is a clockwise
|
|
* rotation.
|
|
**/
|
|
void
|
|
art_affine_rotate (double dst[6], double theta)
|
|
{
|
|
double s, c;
|
|
|
|
s = sin (theta * M_PI / 180.0);
|
|
c = cos (theta * M_PI / 180.0);
|
|
dst[0] = c;
|
|
dst[1] = s;
|
|
dst[2] = -s;
|
|
dst[3] = c;
|
|
dst[4] = 0;
|
|
dst[5] = 0;
|
|
}
|
|
|
|
/**
|
|
* art_affine_shear: Set up a shearing matrix.
|
|
* @dst: Where to store the resulting affine transform.
|
|
* @theta: Shear angle in degrees.
|
|
*
|
|
* Sets up a shearing matrix. In the standard libart coordinate system
|
|
* and a small value for theta, || becomes \\. Horizontal lines remain
|
|
* unchanged.
|
|
**/
|
|
void
|
|
art_affine_shear (double dst[6], double theta)
|
|
{
|
|
double t;
|
|
|
|
t = tan (theta * M_PI / 180.0);
|
|
dst[0] = 1;
|
|
dst[1] = 0;
|
|
dst[2] = t;
|
|
dst[3] = 1;
|
|
dst[4] = 0;
|
|
dst[5] = 0;
|
|
}
|
|
|
|
/**
|
|
* art_affine_translate: Set up a translation matrix.
|
|
* @dst: Where to store the resulting affine transform.
|
|
* @tx: X translation amount.
|
|
* @tx: Y translation amount.
|
|
*
|
|
* Sets up a translation matrix.
|
|
**/
|
|
void
|
|
art_affine_translate (double dst[6], double tx, double ty)
|
|
{
|
|
dst[0] = 1;
|
|
dst[1] = 0;
|
|
dst[2] = 0;
|
|
dst[3] = 1;
|
|
dst[4] = tx;
|
|
dst[5] = ty;
|
|
}
|
|
|
|
/**
|
|
* art_affine_expansion: Find the affine's expansion factor.
|
|
* @src: The affine transformation.
|
|
*
|
|
* Finds the expansion factor, i.e. the square root of the factor
|
|
* by which the affine transform affects area. In an affine transform
|
|
* composed of scaling, rotation, shearing, and translation, returns
|
|
* the amount of scaling.
|
|
*
|
|
* Return value: the expansion factor.
|
|
**/
|
|
double
|
|
art_affine_expansion (const double src[6])
|
|
{
|
|
return sqrt (fabs (src[0] * src[3] - src[1] * src[2]));
|
|
}
|
|
|
|
/**
|
|
* art_affine_rectilinear: Determine whether the affine transformation is rectilinear.
|
|
* @src: The original affine transformation.
|
|
*
|
|
* Determines whether @src is rectilinear, i.e. grid-aligned
|
|
* rectangles are transformed to other grid-aligned rectangles. The
|
|
* implementation has epsilon-tolerance for roundoff errors.
|
|
*
|
|
* Return value: TRUE if @src is rectilinear.
|
|
**/
|
|
int
|
|
art_affine_rectilinear (const double src[6])
|
|
{
|
|
return ((fabs (src[1]) < EPSILON && fabs (src[2]) < EPSILON) ||
|
|
(fabs (src[0]) < EPSILON && fabs (src[3]) < EPSILON));
|
|
}
|
|
|
|
/**
|
|
* art_affine_equal: Determine whether two affine transformations are equal.
|
|
* @matrix1: An affine transformation.
|
|
* @matrix2: Another affine transformation.
|
|
*
|
|
* Determines whether @matrix1 and @matrix2 are equal, with
|
|
* epsilon-tolerance for roundoff errors.
|
|
*
|
|
* Return value: TRUE if @matrix1 and @matrix2 are equal.
|
|
**/
|
|
int
|
|
art_affine_equal (double matrix1[6], double matrix2[6])
|
|
{
|
|
return (fabs (matrix1[0] - matrix2[0]) < EPSILON &&
|
|
fabs (matrix1[1] - matrix2[1]) < EPSILON &&
|
|
fabs (matrix1[2] - matrix2[2]) < EPSILON &&
|
|
fabs (matrix1[3] - matrix2[3]) < EPSILON &&
|
|
fabs (matrix1[4] - matrix2[4]) < EPSILON &&
|
|
fabs (matrix1[5] - matrix2[5]) < EPSILON);
|
|
}
|