X-Git-Url: http://git.asbjorn.biz/?a=blobdiff_plain;f=lib%2Fart%2Fart_affine.c;fp=lib%2Fart%2Fart_affine.c;h=9f332a35201680baea9e1ee254d7ba203cfdc8ef;hb=418ef05b5d0b74e6f19200ffa40bcc3afccb5029;hp=0000000000000000000000000000000000000000;hpb=c1f4a906117e98e2f4ba59abc1ce153e8129bc19;p=swftools.git diff --git a/lib/art/art_affine.c b/lib/art/art_affine.c new file mode 100644 index 0000000..9f332a3 --- /dev/null +++ b/lib/art/art_affine.c @@ -0,0 +1,458 @@ +/* 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 +#include /* for sprintf */ +#include /* 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 +/** + * 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); +}