+++ /dev/null
-/* 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);
-}
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