--- /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 "config.h"
+#include "art_affine.h"
+#include "art_misc.h" /* for M_PI */
+
+#include <math.h>
+#include <stdio.h> /* for sprintf */
+#include <string.h> /* for strcpy */
+
+
+/* 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);
+}
git.asbjorn.biz / swftools.git / blobdiff