path: root/libart_lgpl/art_affine.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 "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];
}

#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;
}


/**
 * 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_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]));
}