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459 lines
12 KiB
459 lines
12 KiB
/* Libart_LGPL - library of basic graphic primitives
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* Copyright (C) 1998 Raph Levien
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Library General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Library General Public License for more details.
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*
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* You should have received a copy of the GNU Library General Public
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* License along with this library; if not, write to the
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* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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* Boston, MA 02111-1307, USA.
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*/
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/* Simple manipulations with affine transformations */
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#include "config.h"
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#include "art_affine.h"
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#include "art_misc.h" /* for M_PI */
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#include <math.h>
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#include <stdio.h> /* for sprintf */
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#include <string.h> /* for strcpy */
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/* According to a strict interpretation of the libart structure, this
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routine should go into its own module, art_point_affine. However,
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it's only two lines of code, and it can be argued that it is one of
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the natural basic functions of an affine transformation.
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*/
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/**
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* art_affine_point: Do an affine transformation of a point.
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* @dst: Where the result point is stored.
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* @src: The original point.
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@ @affine: The affine transformation.
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**/
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void
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art_affine_point (ArtPoint *dst, const ArtPoint *src,
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const double affine[6])
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{
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double x, y;
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x = src->x;
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y = src->y;
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dst->x = x * affine[0] + y * affine[2] + affine[4];
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dst->y = x * affine[1] + y * affine[3] + affine[5];
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}
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/**
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* art_affine_invert: Find the inverse of an affine transformation.
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* @dst: Where the resulting affine is stored.
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* @src: The original affine transformation.
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*
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* All non-degenerate affine transforms are invertible. If the original
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* affine is degenerate or nearly so, expect numerical instability and
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* very likely core dumps on Alpha and other fp-picky architectures.
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* Otherwise, @dst multiplied with @src, or @src multiplied with @dst
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* will be (to within roundoff error) the identity affine.
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**/
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void
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art_affine_invert (double dst[6], const double src[6])
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{
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double r_det;
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r_det = 1.0 / (src[0] * src[3] - src[1] * src[2]);
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dst[0] = src[3] * r_det;
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dst[1] = -src[1] * r_det;
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dst[2] = -src[2] * r_det;
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dst[3] = src[0] * r_det;
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dst[4] = -src[4] * dst[0] - src[5] * dst[2];
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dst[5] = -src[4] * dst[1] - src[5] * dst[3];
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}
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/**
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* art_affine_flip: Flip an affine transformation horizontally and/or vertically.
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* @dst_affine: Where the resulting affine is stored.
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* @src_affine: The original affine transformation.
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* @horiz: Whether or not to flip horizontally.
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* @vert: Whether or not to flip horizontally.
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*
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* Flips the affine transform. FALSE for both @horiz and @vert implements
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* a simple copy operation. TRUE for both @horiz and @vert is a
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* 180 degree rotation. It is ok for @src_affine and @dst_affine to
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* be equal pointers.
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**/
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void
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art_affine_flip (double dst_affine[6], const double src_affine[6], int horz, int vert)
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{
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dst_affine[0] = horz ? - src_affine[0] : src_affine[0];
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dst_affine[1] = horz ? - src_affine[1] : src_affine[1];
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dst_affine[2] = vert ? - src_affine[2] : src_affine[2];
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dst_affine[3] = vert ? - src_affine[3] : src_affine[3];
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dst_affine[4] = horz ? - src_affine[4] : src_affine[4];
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dst_affine[5] = vert ? - src_affine[5] : src_affine[5];
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}
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#define EPSILON 1e-6
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/* It's ridiculous I have to write this myself. This is hardcoded to
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six digits of precision, which is good enough for PostScript.
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The return value is the number of characters (i.e. strlen (str)).
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It is no more than 12. */
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static int
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art_ftoa (char str[80], double x)
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{
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char *p = str;
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int i, j;
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p = str;
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if (fabs (x) < EPSILON / 2)
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{
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strcpy (str, "0");
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return 1;
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}
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if (x < 0)
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{
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*p++ = '-';
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x = -x;
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}
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if ((int)floor ((x + EPSILON / 2) < 1))
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{
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*p++ = '0';
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*p++ = '.';
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i = sprintf (p, "%06d", (int)floor ((x + EPSILON / 2) * 1e6));
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while (i && p[i - 1] == '0')
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i--;
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if (i == 0)
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i--;
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p += i;
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}
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else if (x < 1e6)
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{
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i = sprintf (p, "%d", (int)floor (x + EPSILON / 2));
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p += i;
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if (i < 6)
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{
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int ix;
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*p++ = '.';
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x -= floor (x + EPSILON / 2);
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for (j = i; j < 6; j++)
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x *= 10;
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ix = floor (x + 0.5);
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for (j = 0; j < i; j++)
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ix *= 10;
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/* A cheap hack, this routine can round wrong for fractions
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near one. */
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if (ix == 1000000)
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ix = 999999;
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sprintf (p, "%06d", ix);
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i = 6 - i;
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while (i && p[i - 1] == '0')
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i--;
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if (i == 0)
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i--;
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p += i;
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}
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}
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else
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p += sprintf (p, "%g", x);
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*p = '\0';
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return p - str;
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}
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#include <stdlib.h>
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/**
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* art_affine_to_string: Convert affine transformation to concise PostScript string representation.
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* @str: Where to store the resulting string.
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* @src: The affine transform.
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*
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* Converts an affine transform into a bit of PostScript code that
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* implements the transform. Special cases of scaling, rotation, and
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* translation are detected, and the corresponding PostScript
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* operators used (this greatly aids understanding the output
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* generated). The identity transform is mapped to the null string.
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**/
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void
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art_affine_to_string (char str[128], const double src[6])
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{
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char tmp[80];
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int i, ix;
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#if 0
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for (i = 0; i < 1000; i++)
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{
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double d = rand () * .1 / RAND_MAX;
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art_ftoa (tmp, d);
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printf ("%g %f %s\n", d, d, tmp);
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}
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#endif
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if (fabs (src[4]) < EPSILON && fabs (src[5]) < EPSILON)
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{
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/* could be scale or rotate */
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if (fabs (src[1]) < EPSILON && fabs (src[2]) < EPSILON)
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{
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/* scale */
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if (fabs (src[0] - 1) < EPSILON && fabs (src[3] - 1) < EPSILON)
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{
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/* identity transform */
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str[0] = '\0';
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return;
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}
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else
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{
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ix = 0;
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ix += art_ftoa (str + ix, src[0]);
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str[ix++] = ' ';
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ix += art_ftoa (str + ix, src[3]);
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strcpy (str + ix, " scale");
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return;
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}
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}
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else
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{
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/* could be rotate */
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if (fabs (src[0] - src[3]) < EPSILON &&
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fabs (src[1] + src[2]) < EPSILON &&
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fabs (src[0] * src[0] + src[1] * src[1] - 1) < 2 * EPSILON)
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{
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double theta;
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theta = (180 / M_PI) * atan2 (src[1], src[0]);
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art_ftoa (tmp, theta);
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sprintf (str, "%s rotate", tmp);
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return;
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}
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}
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}
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else
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{
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/* could be translate */
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if (fabs (src[0] - 1) < EPSILON && fabs (src[1]) < EPSILON &&
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fabs (src[2]) < EPSILON && fabs (src[3] - 1) < EPSILON)
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{
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ix = 0;
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ix += art_ftoa (str + ix, src[4]);
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str[ix++] = ' ';
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ix += art_ftoa (str + ix, src[5]);
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strcpy (str + ix, " translate");
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return;
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}
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}
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ix = 0;
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str[ix++] = '[';
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str[ix++] = ' ';
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for (i = 0; i < 6; i++)
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{
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ix += art_ftoa (str + ix, src[i]);
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str[ix++] = ' ';
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}
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strcpy (str + ix, "] concat");
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}
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/**
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* art_affine_multiply: Multiply two affine transformation matrices.
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* @dst: Where to store the result.
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* @src1: The first affine transform to multiply.
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* @src2: The second affine transform to multiply.
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*
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* Multiplies two affine transforms together, i.e. the resulting @dst
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* is equivalent to doing first @src1 then @src2. Note that the
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* PostScript concat operator multiplies on the left, i.e. "M concat"
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* is equivalent to "CTM = multiply (M, CTM)";
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*
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* It is safe to call this function with @dst equal to @src1 or @src2.
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**/
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void
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art_affine_multiply (double dst[6], const double src1[6], const double src2[6])
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{
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double d0, d1, d2, d3, d4, d5;
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d0 = src1[0] * src2[0] + src1[1] * src2[2];
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d1 = src1[0] * src2[1] + src1[1] * src2[3];
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d2 = src1[2] * src2[0] + src1[3] * src2[2];
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d3 = src1[2] * src2[1] + src1[3] * src2[3];
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d4 = src1[4] * src2[0] + src1[5] * src2[2] + src2[4];
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d5 = src1[4] * src2[1] + src1[5] * src2[3] + src2[5];
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dst[0] = d0;
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dst[1] = d1;
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dst[2] = d2;
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dst[3] = d3;
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dst[4] = d4;
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dst[5] = d5;
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}
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/**
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* art_affine_identity: Set up the identity matrix.
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* @dst: Where to store the resulting affine transform.
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*
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* Sets up an identity matrix.
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**/
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void
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art_affine_identity (double dst[6])
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{
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dst[0] = 1;
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dst[1] = 0;
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dst[2] = 0;
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dst[3] = 1;
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dst[4] = 0;
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dst[5] = 0;
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}
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/**
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* art_affine_scale: Set up a scaling matrix.
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* @dst: Where to store the resulting affine transform.
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* @sx: X scale factor.
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* @sy: Y scale factor.
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*
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* Sets up a scaling matrix.
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**/
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void
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art_affine_scale (double dst[6], double sx, double sy)
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{
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dst[0] = sx;
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dst[1] = 0;
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dst[2] = 0;
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dst[3] = sy;
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dst[4] = 0;
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dst[5] = 0;
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}
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/**
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* art_affine_rotate: Set up a rotation affine transform.
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* @dst: Where to store the resulting affine transform.
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* @theta: Rotation angle in degrees.
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*
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* Sets up a rotation matrix. In the standard libart coordinate
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* system, in which increasing y moves downward, this is a
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* counterclockwise rotation. In the standard PostScript coordinate
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* system, which is reversed in the y direction, it is a clockwise
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* rotation.
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**/
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void
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art_affine_rotate (double dst[6], double theta)
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{
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double s, c;
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s = sin (theta * M_PI / 180.0);
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c = cos (theta * M_PI / 180.0);
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dst[0] = c;
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dst[1] = s;
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dst[2] = -s;
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dst[3] = c;
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dst[4] = 0;
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dst[5] = 0;
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}
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/**
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* art_affine_shear: Set up a shearing matrix.
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* @dst: Where to store the resulting affine transform.
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* @theta: Shear angle in degrees.
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*
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* Sets up a shearing matrix. In the standard libart coordinate system
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* and a small value for theta, || becomes \\. Horizontal lines remain
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* unchanged.
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**/
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void
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art_affine_shear (double dst[6], double theta)
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{
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double t;
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t = tan (theta * M_PI / 180.0);
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dst[0] = 1;
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dst[1] = 0;
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dst[2] = t;
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dst[3] = 1;
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dst[4] = 0;
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dst[5] = 0;
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}
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/**
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* art_affine_translate: Set up a translation matrix.
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* @dst: Where to store the resulting affine transform.
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* @tx: X translation amount.
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* @tx: Y translation amount.
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*
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* Sets up a translation matrix.
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**/
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void
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art_affine_translate (double dst[6], double tx, double ty)
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{
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dst[0] = 1;
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dst[1] = 0;
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dst[2] = 0;
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dst[3] = 1;
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dst[4] = tx;
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dst[5] = ty;
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}
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/**
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* art_affine_expansion: Find the affine's expansion factor.
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* @src: The affine transformation.
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*
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* Finds the expansion factor, i.e. the square root of the factor
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* by which the affine transform affects area. In an affine transform
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* composed of scaling, rotation, shearing, and translation, returns
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* the amount of scaling.
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*
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* Return value: the expansion factor.
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**/
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double
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art_affine_expansion (const double src[6])
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{
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return sqrt (fabs (src[0] * src[3] - src[1] * src[2]));
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}
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/**
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* art_affine_rectilinear: Determine whether the affine transformation is rectilinear.
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* @src: The original affine transformation.
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*
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* Determines whether @src is rectilinear, i.e. grid-aligned
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* rectangles are transformed to other grid-aligned rectangles. The
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* implementation has epsilon-tolerance for roundoff errors.
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*
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* Return value: TRUE if @src is rectilinear.
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**/
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int
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art_affine_rectilinear (const double src[6])
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{
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return ((fabs (src[1]) < EPSILON && fabs (src[2]) < EPSILON) ||
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(fabs (src[0]) < EPSILON && fabs (src[3]) < EPSILON));
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}
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/**
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* art_affine_equal: Determine whether two affine transformations are equal.
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* @matrix1: An affine transformation.
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* @matrix2: Another affine transformation.
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*
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* Determines whether @matrix1 and @matrix2 are equal, with
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* epsilon-tolerance for roundoff errors.
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*
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* Return value: TRUE if @matrix1 and @matrix2 are equal.
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**/
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int
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art_affine_equal (double matrix1[6], double matrix2[6])
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{
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return (fabs (matrix1[0] - matrix2[0]) < EPSILON &&
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fabs (matrix1[1] - matrix2[1]) < EPSILON &&
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fabs (matrix1[2] - matrix2[2]) < EPSILON &&
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fabs (matrix1[3] - matrix2[3]) < EPSILON &&
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fabs (matrix1[4] - matrix2[4]) < EPSILON &&
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fabs (matrix1[5] - matrix2[5]) < EPSILON);
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}
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