Adding upstream version 2.10.36.upstream/2.10.36

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1487 insertions, 0 deletions

diff --git a/plug-ins/flame/libifs.c b/plug-ins/flame/libifs.c
new file mode 100644
index 0000000..461ac5c
--- /dev/null
+++ b/plug-ins/flame/libifs.c
@@ -0,0 +1,1487 @@
+/*
+   flame - cosmic recursive fractal flames
+   Copyright (C) 1992  Scott Draves <spot@cs.cmu.edu>
+
+   This program is free software: you can redistribute it and/or modify
+   it under the terms of the GNU General Public License as published by
+   the Free Software Foundation; either version 3 of the License, or
+   (at your option) any later version.
+
+   This program 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 General Public License for more details.
+
+   You should have received a copy of the GNU General Public License
+   along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+#include "config.h"
+
+#include <stdlib.h>
+#include <string.h> /* strcmp */
+
+#include "libgimp/gimp.h"
+
+#include "libifs.h"
+
+#define CHOOSE_XFORM_GRAIN 100
+
+static int    flam3_random_bit (void);
+static double flam3_random01   (void);
+
+/*
+ * run the function system described by CP forward N generations.
+ * store the n resulting 3 vectors in POINTS.  the initial point is passed
+ * in POINTS[0].  ignore the first FUSE iterations.
+ */
+
+void
+iterate (control_point *cp,
+         int            n,
+         int            fuse,
+         point         *points)
+{
+  int    i, j, count_large = 0, count_nan = 0;
+  int    xform_distrib[CHOOSE_XFORM_GRAIN];
+  double p[3], t, r, dr;
+  p[0] = points[0][0];
+  p[1] = points[0][1];
+  p[2] = points[0][2];
+
+  /*
+   * first, set up xform, which is an array that converts a uniform random
+   * variable into one with the distribution dictated by the density
+   * fields
+   */
+  dr = 0.0;
+  for (i = 0; i < NXFORMS; i++)
+    dr += cp->xform[i].density;
+  dr = dr / CHOOSE_XFORM_GRAIN;
+
+  j = 0;
+  t = cp->xform[0].density;
+  r = 0.0;
+  for (i = 0; i < CHOOSE_XFORM_GRAIN; i++)
+    {
+      while (r >= t)
+        {
+          j++;
+          t += cp->xform[j].density;
+        }
+      xform_distrib[i] = j;
+      r += dr;
+    }
+
+  for (i = -fuse; i < n; i++)
+    {
+      /* FIXME: the following is supported only by gcc and c99 */
+      int fn = xform_distrib[g_random_int_range (0, CHOOSE_XFORM_GRAIN)];
+      double tx, ty, v;
+
+      if (p[0] > 100.0 || p[0] < -100.0 ||
+        p[1] > 100.0 || p[1] < -100.0)
+      count_large++;
+      if (p[0] != p[0])
+        count_nan++;
+
+#define coef   cp->xform[fn].c
+#define vari   cp->xform[fn].var
+
+      /* first compute the color coord */
+      p[2] = (p[2] + cp->xform[fn].color) / 2.0;
+
+      /* then apply the affine part of the function */
+      tx = coef[0][0] * p[0] + coef[1][0] * p[1] + coef[2][0];
+      ty = coef[0][1] * p[0] + coef[1][1] * p[1] + coef[2][1];
+
+      p[0] = p[1] = 0.0;
+      /* then add in proportional amounts of each of the variations */
+      v = vari[0];
+      if (v > 0.0)
+        {
+          /* linear */
+          double nx, ny;
+          nx = tx;
+          ny = ty;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[1];
+      if (v > 0.0)
+        {
+          /* sinusoidal */
+          double nx, ny;
+          nx = sin (tx);
+          ny = sin (ty);
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[2];
+      if (v > 0.0)
+        {
+          /* spherical */
+          double nx, ny;
+          double r2 = tx * tx + ty * ty + 1e-6;
+          nx = tx / r2;
+          ny = ty / r2;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[3];
+      if (v > 0.0)
+        {
+          /* swirl */
+          double r2 = tx * tx + ty * ty;  /* /k here is fun */
+          double c1 = sin (r2);
+          double c2 = cos (r2);
+          double nx = c1 * tx - c2 * ty;
+          double ny = c2 * tx + c1 * ty;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[4];
+      if (v > 0.0)
+        {
+          /* horseshoe */
+          double a, c1, c2, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            a = atan2(tx, ty);  /* times k here is fun */
+          else
+            a = 0.0;
+          c1 = sin (a);
+          c2 = cos (a);
+          nx = c1 * tx - c2 * ty;
+          ny = c2 * tx + c1 * ty;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[5];
+      if (v > 0.0)
+        {
+          /* polar */
+          double nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            nx = atan2 (tx, ty) / G_PI;
+          else
+            nx = 0.0;
+
+          ny = sqrt (tx * tx + ty * ty) - 1.0;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[6];
+      if (v > 0.0)
+        {
+          /* bent */
+          double nx, ny;
+          nx = tx;
+          ny = ty;
+          if (nx < 0.0) nx = nx * 2.0;
+          if (ny < 0.0) ny = ny / 2.0;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[7];
+      if (v > 0.0)
+        {
+          /* folded handkerchief */
+          double theta, r2, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2( tx, ty );
+          else
+            theta = 0.0;
+          r2 = sqrt (tx * tx + ty * ty);
+          nx = sin (theta + r2) * r2;
+          ny = cos (theta - r2) * r2;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[8];
+      if (v > 0.0)
+        {
+          /* heart */
+          double theta, r2, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2( tx, ty );
+          else
+            theta = 0.0;
+          r2 = sqrt (tx * tx + ty * ty);
+          theta *= r2;
+          nx = sin (theta) * r2;
+          ny = cos (theta) * -r2;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[9];
+      if (v > 0.0)
+        {
+          /* disc */
+          double theta, r2, nx, ny;
+          if ( tx < -EPS || tx > EPS ||
+               ty < - EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          nx = tx * G_PI;
+          ny = ty * G_PI;
+          r2 = sqrt (nx * nx * ny * ny);
+          p[0] += v * sin(r2) * theta / G_PI;
+          p[1] += v * cos(r2) * theta / G_PI;
+        }
+
+      v = vari[10];
+      if (v > 0.0)
+        {
+          /* spiral */
+          double theta, r2;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2( tx, ty );
+          else
+            theta = 0.0;
+          r2 = sqrt (tx * tx + ty * ty) + 1e-6;
+          p[0] += v * (cos (theta) + sin (r2)) / r2;
+          p[1] += v * (cos (theta) + cos (r2)) / r2;
+        }
+
+      v = vari[11];
+      if (v > 0.0)
+        {
+          /* hyperbolic */
+          double theta, r2;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          r2 = sqrt (tx * tx + ty * ty) + 1e-6;
+          p[0] += v * sin (theta) / r2;
+          p[1] += v * cos (theta) * r2;
+        }
+
+      v = vari[12];
+      if (v > 0.0 )
+        {
+          double theta, r2;
+          /* diamond */
+          if ( tx < -EPS || tx > EPS ||
+               ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          r2 = sqrt( tx * tx + ty * ty );
+          p[0] += v * sin (theta) * cos (r2);
+          p[1] += v * cos (theta) * sin (r2);
+        }
+
+      v = vari[13];
+      if (v > 0.0)
+        {
+          /* ex */
+          double theta, r2, n0, n1, m0, m1;
+          if ( tx < -EPS || tx > EPS ||
+               ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          r2 = sqrt( tx * tx + ty * ty );
+          n0 = sin(theta + r2);
+          n1 = cos(theta - r2);
+          m0 = n0 * n0 * n0 * r2;
+          m1 = n1 * n1 * n1 * r2;
+          p[0] += v * (m0 + m1);
+          p[1] += v * (m0 - m1);
+        }
+
+      v = vari[14];
+      if ( v > 0.0)
+        {
+          double theta, r2, nx, ny;
+          /* julia */
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          if (flam3_random_bit ())
+            theta += G_PI;
+          r2 = pow (tx * tx + ty * ty, 0.25);
+          nx = r2 * cos (theta);
+          ny = r2 * sin (theta);
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[15];
+      if (v > 0.0)
+        {
+          /* waves */
+          double dx, dy, nx, ny;
+          dx = coef[2][0];
+          dy = coef[2][1];
+          nx = tx + coef[1][0] * sin (ty / ((dx * dx) + EPS));
+          ny = ty + coef[1][1] * sin (tx / ((dy * dy) + EPS));
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[16];
+      if (v > 0.0)
+        {
+          /* fisheye */
+          double theta, r2, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          r2 = sqrt (tx * tx + ty * ty);
+          r2 = 2 * r2 / (r2 + 1);
+          nx = r2 * cos (theta);
+          ny = r2 * sin (theta);
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[17];
+      if (v > 0.0)
+        {
+          /* popcorn */
+          double dx, dy, nx, ny;
+          dx = tan (3 * ty);
+          dy = tan (3 * tx);
+          nx = tx + coef[2][0] * sin (dx);
+          ny = ty + coef[2][1] * sin (dy);
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[18];
+      if (v > 0.0)
+        {
+          /* exponential */
+          double dx, dy, nx, ny;
+          dx = exp (tx - 1.0);
+          dy = G_PI * ty;
+          nx = cos (dy) * dx;
+          ny = sin (dy) * dx;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[19];
+      if (v > 0.0)
+        {
+          /* power */
+          double theta, r2, tsin, tcos, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          tsin = sin (theta);
+          tcos = cos (theta);
+          r2 = sqrt (tx * tx + ty * ty);
+          r2 = pow (r2, tsin);
+          nx = r2 * tcos;
+          ny = r2 * tsin;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[20];
+      if (v > 0.0)
+        {
+          /* cosine */
+          double nx, ny;
+          nx =  cos (tx * G_PI) * cosh (ty);
+          ny = -sin (tx * G_PI) * sinh (ty);
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[21];
+      if (v > 0.0)
+        {
+          /* rings */
+          double theta, r2, dx, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0;
+          dx = coef[2][0];
+          dx = dx * dx + EPS;
+          r2 = sqrt (tx * tx + ty * ty);
+          r2 = fmod (r2 + dx, 2 * dx) - dx + r2 * (1 - dx);
+          nx = cos (theta) * r2;
+          ny = sin (theta) * r2;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[22];
+      if (v > 0.0)
+        {
+          /* fan */
+          double theta, r2, dx, dy, dx2, nx, ny;
+          if (tx < -EPS || tx > EPS ||
+              ty < -EPS || ty > EPS)
+            theta = atan2 (tx, ty);
+          else
+            theta = 0.0;
+          dx = coef[2][0];
+          dy = coef[2][1];
+          dx = G_PI * (dx * dx + EPS);
+          dx2 = dx / 2;
+          r2 = sqrt (tx * tx + ty * ty );
+          theta += (fmod (theta + dy, dx) > dx2) ? -dx2: dx2;
+          nx = cos (theta) * r2;
+          ny = sin (theta) * r2;
+          p[0] += v * nx;
+          p[1] += v * ny;
+        }
+
+      v = vari[23];
+      if (v > 0.0)
+        {
+          /* eyefish */
+          double r2;
+          r2 = 2.0 * v / (sqrt(tx * tx + ty * ty) + 1.0);
+          p[0] += r2 * tx;
+          p[1] += r2 * ty;
+        }
+
+      v = vari[24];
+      if (v > 0.0)
+        {
+          /* bubble */
+          double r2;
+          r2 = v / ((tx * tx + ty * ty) / 4 + 1);
+          p[0] += r2 * tx;
+          p[1] += r2 * ty;
+        }
+
+      v = vari[25];
+      if (v > 0.0)
+        {
+          /* cylinder */
+          double nx;
+          nx = sin (tx);
+          p[0] += v * nx;
+          p[1] += v * ty;
+        }
+
+      v = vari[26];
+      if (v > 0.0)
+        {
+          /* noise */
+          double rx, sinr, cosr, nois;
+          rx = flam3_random01 () * 2 * G_PI;
+          sinr = sin (rx);
+          cosr = cos (rx);
+          nois = flam3_random01 ();
+          p[0] += v * nois * tx * cosr;
+          p[1] += v * nois * ty * sinr;
+        }
+
+      v = vari[27];
+      if (v > 0.0)
+        {
+          /* blur */
+          double rx, sinr, cosr, nois;
+          rx = flam3_random01 () * 2 * G_PI;
+          sinr = sin (rx);
+          cosr = cos (rx);
+          nois = flam3_random01 ();
+          p[0] += v * nois * cosr;
+          p[1] += v * nois * sinr;
+        }
+
+      v = vari[28];
+      if (v > 0.0)
+        {
+          /* gaussian */
+          double ang, sina, cosa, r2;
+          ang = flam3_random01 () * 2 * G_PI;
+          sina = sin (ang);
+          cosa = cos (ang);
+          r2 = v * (flam3_random01 () + flam3_random01 () + flam3_random01 () +
+                    flam3_random01 () - 2.0);
+          p[0] += r2 * cosa;
+          p[1] += r2 * sina;
+        }
+
+      /* if fuse over, store it */
+      if (i >= 0)
+        {
+          points[i][0] = p[0];
+          points[i][1] = p[1];
+          points[i][2] = p[2];
+        }
+    }
+}
+
+/* args must be non-overlapping */
+void
+mult_matrix (double s1[2][2],
+             double s2[2][2],
+             double d[2][2])
+{
+  d[0][0] = s1[0][0] * s2[0][0] + s1[1][0] * s2[0][1];
+  d[1][0] = s1[0][0] * s2[1][0] + s1[1][0] * s2[1][1];
+  d[0][1] = s1[0][1] * s2[0][0] + s1[1][1] * s2[0][1];
+  d[1][1] = s1[0][1] * s2[1][0] + s1[1][1] * s2[1][1];
+}
+
+static
+double det_matrix (double s[2][2])
+{
+  return s[0][0] * s[1][1] - s[0][1] * s[1][0];
+}
+
+static void
+interpolate_angle (double  t,
+                   double  s,
+                   double *v1,
+                   double *v2,
+                   double *v3,
+                   int     tie,
+                   int     cross)
+{
+  double x = *v1;
+  double y = *v2;
+  double d;
+  static double lastx, lasty;
+
+  /* take the shorter way around the circle... */
+  if (x > y)
+    {
+      d = x - y;
+      if (d > G_PI + EPS ||
+          (d > G_PI - EPS && tie))
+        y += 2 * G_PI;
+    }
+  else
+    {
+      d = y - x;
+      if (d > G_PI + EPS ||
+          (d > G_PI - EPS && tie))
+        x += 2 * G_PI;
+    }
+  /* unless we are supposed to avoid crossing */
+  if (cross)
+    {
+      if (lastx > x)
+        {
+          if (lasty < y)
+            y -= 2 * G_PI;
+        }
+      else
+        {
+          if (lasty > y)
+            y += 2 * G_PI;
+        }
+    }
+  else
+    {
+      lastx = x;
+      lasty = y;
+    }
+
+  *v3 = s * x + t * y;
+}
+
+static void
+interpolate_complex (double  t,
+                     double  s,
+                     double *r1,
+                     double *r2,
+                     double *r3,
+                     int     flip,
+                     int     tie,
+                     int     cross)
+{
+  double c1[2], c2[2], c3[2];
+  double a1, a2, a3, d1, d2, d3;
+
+  c1[0] = r1[0];
+  c1[1] = r1[1];
+  c2[0] = r2[0];
+  c2[1] = r2[1];
+  if (flip)
+    {
+      double t = c1[0];
+      c1[0] = c1[1];
+      c1[1] = t;
+      t = c2[0];
+      c2[0] = c2[1];
+      c2[1] = t;
+    }
+
+  /* convert to log space */
+  a1 = atan2 (c1[1], c1[0]);
+  a2 = atan2 (c2[1], c2[0]);
+  d1 = 0.5 * log (c1[0] * c1[0] + c1[1] * c1[1]);
+  d2 = 0.5 * log (c2[0] * c2[0] + c2[1] * c2[1]);
+
+  /* interpolate linearly */
+  interpolate_angle (t, s, &a1, &a2, &a3, tie, cross);
+  d3 = s * d1 + t * d2;
+
+  /* convert back */
+  d3 = exp (d3);
+  c3[0] = cos (a3) * d3;
+  c3[1] = sin (a3) * d3;
+
+  if (flip)
+    {
+      r3[1] = c3[0];
+      r3[0] = c3[1];
+    }
+  else
+    {
+      r3[0] = c3[0];
+      r3[1] = c3[1];
+    }
+}
+
+static void
+interpolate_matrix (double t,
+                    double m1[3][2],
+                    double m2[3][2],
+                    double m3[3][2])
+{
+  double s = 1.0 - t;
+
+  interpolate_complex (t, s, &m1[0][0], &m2[0][0], &m3[0][0], 0, 0, 0);
+  interpolate_complex (t, s, &m1[1][0], &m2[1][0], &m3[1][0], 1, 1, 0);
+
+  /* handle the translation part of the xform linearly */
+  m3[2][0] = s * m1[2][0] + t * m2[2][0];
+  m3[2][1] = s * m1[2][1] + t * m2[2][1];
+}
+
+#define INTERP(x)  result->x = c0 * cps[i1].x + c1 * cps[i2].x
+
+/*
+ * create a control point that interpolates between the control points
+ * passed in CPS.  for now just do linear.  in the future, add control
+ * point types and other things to the cps.  CPS must be sorted by time.
+ */
+void
+interpolate (control_point  cps[],
+             int            ncps,
+             double         time,
+             control_point *result)
+{
+  int i, j, i1, i2;
+  double c0, c1, t;
+
+  g_return_if_fail (ncps > 0);
+
+  if (ncps == 1)
+    {
+      *result = cps[0];
+      return;
+    }
+  if (cps[0].time >= time)
+    {
+      i1 = 0;
+      i2 = 1;
+    }
+  else if (cps[ncps - 1].time <= time)
+    {
+      i1 = ncps - 2;
+      i2 = ncps - 1;
+    }
+  else
+    {
+      i1 = 0;
+      while (i1 < ncps && cps[i1].time < time)
+        i1++;
+      i1--;
+      i2 = i1 + 1;
+
+      if (i2 == ncps ||
+          (time - cps[i1].time > -1e-7 &&
+           time - cps[i1].time < 1e-7))
+        {
+          *result = cps[i1];
+          return;
+        }
+    }
+
+  c0 = (cps[i2].time - time) / (cps[i2].time - cps[i1].time);
+  c1 = 1.0 - c0;
+
+  result->time = time;
+
+  if (cps[i1].cmap_inter)
+    {
+      for (i = 0; i < 256; i++)
+        {
+          double spread = 0.15;
+          double d0, d1, e0, e1, c = 2 * G_PI * i / 256.0;
+          c = cos(c * cps[i1].cmap_inter) + 4.0 * c1 - 2.0;
+          if (c >  spread) c =  spread;
+          if (c < -spread) c = -spread;
+          d1 = (c + spread) * 0.5 / spread;
+          d0 = 1.0 - d1;
+          e0 = (d0 < 0.5) ? (d0 * 2) : (d1 * 2);
+          e1 = 1.0 - e0;
+          for (j = 0; j < 3; j++)
+            {
+              result->cmap[i][j] = (d0 * cps[i1].cmap[i][j] +
+                                    d1 * cps[i2].cmap[i][j]);
+#define bright_peak 2.0
+              result->cmap[i][j] = (e1 * result->cmap[i][j] +
+                                    e0 * 1.0);
+            }
+        }
+    }
+  else
+    {
+      for (i = 0; i < 256; i++)
+        {
+          double t[3], s[3];
+          rgb2hsv (cps[i1].cmap[i], s);
+          rgb2hsv (cps[i2].cmap[i], t);
+          for (j = 0; j < 3; j++)
+            t[j] = c0 * s[j] + c1 * t[j];
+          hsv2rgb (t, result->cmap[i]);
+        }
+    }
+
+  result->cmap_index = -1;
+  INTERP(brightness);
+  INTERP(contrast);
+  INTERP(gamma);
+  INTERP(width);
+  INTERP(height);
+  INTERP(spatial_oversample);
+  INTERP(center[0]);
+  INTERP(center[1]);
+  INTERP(pixels_per_unit);
+  INTERP(spatial_filter_radius);
+  INTERP(sample_density);
+  INTERP(zoom);
+  INTERP(nbatches);
+  INTERP(white_level);
+  for (i = 0; i < 2; i++)
+    for (j = 0; j < 2; j++)
+      {
+        INTERP(pulse[i][j]);
+        INTERP(wiggle[i][j]);
+      }
+
+  for (i = 0; i < NXFORMS; i++)
+    {
+      double r;
+      double rh_time;
+
+      INTERP(xform[i].density);
+      if (result->xform[i].density > 0)
+        result->xform[i].density = 1.0;
+      INTERP(xform[i].color);
+      for (j = 0; j < NVARS; j++)
+        INTERP(xform[i].var[j]);
+      t = 0.0;
+      for (j = 0; j < NVARS; j++)
+        t += result->xform[i].var[j];
+      t = 1.0 / t;
+      for (j = 0; j < NVARS; j++)
+        result->xform[i].var[j] *= t;
+
+      interpolate_matrix(c1, cps[i1].xform[i].c, cps[i2].xform[i].c,
+                         result->xform[i].c);
+
+      rh_time = time * 2 * G_PI / (60.0 * 30.0);
+
+      /* apply pulse factor. */
+      r = 1.0;
+      for (j = 0; j < 2; j++)
+        r += result->pulse[j][0] * sin(result->pulse[j][1] * rh_time);
+      for (j = 0; j < 3; j++)
+        {
+          result->xform[i].c[j][0] *= r;
+          result->xform[i].c[j][1] *= r;
+        }
+
+      /* apply wiggle factor */
+      for (j = 0; j < 2; j++)
+        {
+          double tt = result->wiggle[j][1] * rh_time;
+          double m = result->wiggle[j][0];
+          result->xform[i].c[0][0] += m *  cos(tt);
+          result->xform[i].c[1][0] += m * -sin(tt);
+          result->xform[i].c[0][1] += m *  sin(tt);
+          result->xform[i].c[1][1] += m *  cos(tt);
+        }
+    } /* for i */
+}
+
+
+
+/*
+ * split a string passed in ss into tokens on whitespace.
+ * # comments to end of line.  ; terminates the record
+ */
+void
+tokenize (char **ss,
+          char  *argv[],
+          int   *argc)
+{
+  char *s   = *ss;
+  int   i   = 0, state = 0;
+  gint  len = 0;
+
+  len = strlen (s);
+  while (*s != ';' && len > 0)
+    {
+      char c = *s;
+      switch (state)
+        {
+        case 0:
+          if (c == '#')
+            state = 2;
+          else if (!g_ascii_isspace (c))
+            {
+              argv[i] = s;
+              i++;
+              state = 1;
+            }
+          break;
+        case 1:
+          if (g_ascii_isspace (c))
+            {
+              *s = 0;
+              state = 0;
+            }
+          break;
+        case 2:
+          if (c == '\n')
+            state = 0;
+          break;
+        }
+      s++;
+      len--;
+    }
+  *s = 0;
+  *ss = s + 1;
+  *argc = i;
+}
+
+static int
+compare_xforms (const void *va,
+                const void *vb)
+{
+  double aa[2][2];
+  double bb[2][2];
+  double ad, bd;
+  const xform *a = va;
+  const xform *b = vb;
+
+  aa[0][0] = a->c[0][0];
+  aa[0][1] = a->c[0][1];
+  aa[1][0] = a->c[1][0];
+  aa[1][1] = a->c[1][1];
+  bb[0][0] = b->c[0][0];
+  bb[0][1] = b->c[0][1];
+  bb[1][0] = b->c[1][0];
+  bb[1][1] = b->c[1][1];
+  ad = det_matrix (aa);
+  bd = det_matrix (bb);
+  if (ad < bd)
+    return -1;
+  if (ad > bd)
+    return 1;
+  return 0;
+}
+
+#define MAXARGS 1000
+#define streql(x,y) (!strcmp(x,y))
+
+/*
+ * given a pointer to a string SS, fill fields of a control point CP.
+ */
+
+void
+parse_control_point (char          **ss,
+                     control_point  *cp)
+{
+  char *argv[MAXARGS];
+  int argc, i, j;
+  gint64  xf_index     = 0;
+  gint    parse_errors = 0;
+  double *slot = NULL, t;
+
+  for (i = 0; i < NXFORMS; i++)
+    {
+      cp->xform[i].density = 0.0;
+      cp->xform[i].color = (i == 0);
+      cp->xform[i].var[0] = 1.0;
+      for (j = 1; j < NVARS; j++)
+        cp->xform[i].var[j] = 0.0;
+      cp->xform[i].c[0][0] = 1.0;
+      cp->xform[i].c[0][1] = 0.0;
+      cp->xform[i].c[1][0] = 0.0;
+      cp->xform[i].c[1][1] = 1.0;
+      cp->xform[i].c[2][0] = 0.0;
+      cp->xform[i].c[2][1] = 0.0;
+    }
+  for (j = 0; j < 2; j++)
+    {
+      cp->pulse[j][0] = 0.0;
+      cp->pulse[j][1] = 60.0;
+      cp->wiggle[j][0] = 0.0;
+      cp->wiggle[j][1] = 60.0;
+    }
+
+  tokenize (ss, argv, &argc);
+
+  i = 0;
+  while (i < argc)
+    {
+      gint itoken;
+
+      itoken = i;
+      if (i < argc)
+        {
+          /* First value belonging to token. */
+          i++;
+        }
+      else
+        {
+          g_printerr ("Not enough parameters. File may be corrupt!\n");
+          parse_errors++;
+          break;
+        }
+
+      if (streql ("xform", argv[itoken]))
+        {
+          if (! g_ascii_string_to_signed (argv[i++], 10, 0, NXFORMS-1, &xf_index, NULL))
+            {
+              g_printerr ("Invalid xform index '%s'\n", argv[i-1]);
+              parse_errors++;
+              xf_index = 0;
+            }
+        }
+      else if (streql ("density", argv[itoken]))
+        {
+          cp->xform[xf_index].density = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("color", argv[itoken]))
+        {
+          cp->xform[xf_index].color = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("coefs", argv[itoken]))
+        {
+          /* We need 6 coef values and we know are at the first */
+          if (i + 5 >= argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          slot = cp->xform[xf_index].c[0];
+          for (j = 0; j < 6; j++)
+            {
+              *slot++ = g_strtod (argv[i++], NULL);
+            }
+          cp->xform[xf_index].density = 1.0;
+        }
+      else if (streql ("var", argv[itoken]))
+        {
+          /* We need NVARS var values and we know are at the first */
+          if (i + NVARS > argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          slot = cp->xform[xf_index].var;
+          for (j = 0; j < NVARS; j++)
+            {
+              *slot++ = g_strtod (argv[i++], NULL);
+            }
+        }
+      else if (streql ("time", argv[itoken]))
+        {
+          cp->time = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("brightness", argv[itoken]))
+        {
+          cp->brightness = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("contrast", argv[itoken]))
+        {
+          cp->contrast = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("gamma", argv[itoken]))
+        {
+          cp->gamma = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("zoom", argv[itoken]))
+        {
+          cp->zoom = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("image_size", argv[itoken]))
+        {
+          gint64 w, h;
+
+          /* We need 2 values and we know are at the first */
+          if (i + 1 >= argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          if (! g_ascii_string_to_signed (argv[i++], 10, 1, GIMP_MAX_IMAGE_SIZE, &w, NULL))
+            {
+              g_printerr ("Ignoring invalid image width '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else if (! g_ascii_string_to_signed (argv[i++], 10, 1, GIMP_MAX_IMAGE_SIZE, &h, NULL))
+            {
+              g_printerr ("Ignoring invalid image_size heigth '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->width  = w;
+              cp->height = h;
+            }
+        }
+      else if (streql ("center", argv[itoken]))
+        {
+          /* We need 2 values and we know are at the first */
+          if (i + 1 >= argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          cp->center[0] = g_strtod (argv[i++], NULL);
+          cp->center[1] = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("pixels_per_unit", argv[itoken]))
+        {
+          cp->pixels_per_unit = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("pulse", argv[itoken]))
+        {
+          /* We need 4 values and we know are at the first */
+          if (i + 3 >= argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          slot = &cp->pulse[0][0];
+          for (j = 0; j < 4; j++)
+            {
+              *slot++ = g_strtod (argv[i++], NULL);
+            }
+        }
+      else if (streql ("wiggle", argv[itoken]))
+        {
+          /* We need 4 values and we know are at the first */
+          if (i + 3 >= argc)
+            {
+              g_printerr ("Not enough parameters. File may be corrupt!\n");
+              parse_errors++;
+              break;
+            }
+          slot = &cp->wiggle[0][0];
+          for (j = 0; j < 4; j++)
+            {
+              *slot++ = g_strtod (argv[i++], NULL);
+            }
+        }
+      else if (streql ("spatial_oversample", argv[itoken]))
+        {
+          gint64 oversample;
+
+          /* Values in the gui seem to be between 1 and 4 */
+          if (! g_ascii_string_to_signed (argv[i++], 10, 1, 4, &oversample, NULL))
+            {
+              g_printerr ("Ignoring invalid spatial oversample value '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->spatial_oversample = oversample;
+            }
+        }
+      else if (streql ("spatial_filter_radius", argv[itoken]))
+        {
+          cp->spatial_filter_radius = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("sample_density", argv[itoken]))
+        {
+          cp->sample_density = g_strtod (argv[i++], NULL);
+        }
+      else if (streql ("nbatches", argv[itoken]))
+        {
+          gint64 nbatches;
+
+          /* Not sure what the maximum should be. It always seems to be set to 1. */
+          if (! g_ascii_string_to_signed (argv[i++], 10, 0, 2, &nbatches, NULL))
+            {
+              g_printerr ("Ignoring invalid nbatches value '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->nbatches = nbatches;
+            }
+        }
+      else if (streql ("white_level", argv[itoken]))
+        {
+          gint64 wl;
+
+          if (! g_ascii_string_to_signed (argv[i++], 10, 0, 255, &wl, NULL))
+            {
+              g_printerr ("Ignoring invalid white level value '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->white_level = wl;
+            }
+        }
+      else if (streql ("cmap", argv[itoken]))
+        {
+          gint64 cmi;
+
+          /* -1 = random */
+          if (! g_ascii_string_to_signed (argv[i++], 10, -1, 255, &cmi, NULL))
+            {
+              g_printerr ("Ignoring invalid color map value '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->cmap_index = cmi;
+            }
+        }
+      else if (streql ("cmap_inter", argv[itoken]))
+        {
+          gint64 cmi;
+
+          /* 0 or 1 */
+          if (! g_ascii_string_to_signed (argv[i++], 10, 0, 1, &cmi, NULL))
+            {
+              g_printerr ("Ignoring invalid color interpolate value '%s'\n", argv[i-1]);
+              parse_errors++;
+            }
+          else
+            {
+              cp->cmap_inter = cmi;
+            }
+        }
+      else
+        {
+          g_printerr ("Invalid token '%s'. File may be corrupt!\n", argv[itoken]);
+          parse_errors++;
+        }
+    }
+
+  if (parse_errors > 0)
+    g_warning ("Input file contains %d errors. File may be corrupt!", parse_errors);
+
+  for (i = 0; i < NXFORMS; i++)
+    {
+      t = 0.0;
+      for (j = 0; j < NVARS; j++)
+        t += cp->xform[i].var[j];
+      t = 1.0 / t;
+      for (j = 0; j < NVARS; j++)
+        cp->xform[i].var[j] *= t;
+    }
+  qsort ((char *) cp->xform, NXFORMS, sizeof(xform), compare_xforms);
+}
+
+void
+print_control_point (FILE          *f,
+                     control_point *cp,
+                     int            quote)
+{
+  int i, j;
+  char *q = quote ? "# " : "";
+  fprintf (f, "%stime %g\n", q, cp->time);
+  if (cp->cmap_index != -1)
+    fprintf (f, "%scmap %d\n", q, cp->cmap_index);
+  fprintf (f, "%simage_size %d %d center %g %g pixels_per_unit %g\n",
+           q, cp->width, cp->height, cp->center[0], cp->center[1],
+           cp->pixels_per_unit);
+  fprintf (f, "%sspatial_oversample %d spatial_filter_radius %g",
+           q, cp->spatial_oversample, cp->spatial_filter_radius);
+  fprintf (f, " sample_density %g\n", cp->sample_density);
+  fprintf (f, "%snbatches %d white_level %d\n",
+           q, cp->nbatches, cp->white_level);
+  fprintf (f, "%sbrightness %g gamma %g cmap_inter %d\n",
+           q, cp->brightness, cp->gamma, cp->cmap_inter);
+
+  for (i = 0; i < NXFORMS; i++)
+    if (cp->xform[i].density > 0.0)
+      {
+        fprintf (f, "%sxform %d density %g color %g\n",
+                 q, i, cp->xform[i].density, cp->xform[i].color);
+        fprintf (f, "%svar", q);
+        for (j = 0; j < NVARS; j++)
+          fprintf (f, " %g", cp->xform[i].var[j]);
+        fprintf (f, "\n%scoefs", q);
+        for (j = 0; j < 3; j++)
+          fprintf (f, " %g %g", cp->xform[i].c[j][0], cp->xform[i].c[j][1]);
+        fprintf (f, "\n");
+      }
+  fprintf (f, "%s;\n", q);
+}
+
+/* returns a uniform variable from 0 to 1 */
+double
+random_uniform01 (void)
+{
+  return g_random_double ();
+}
+
+double random_uniform11 (void)
+{
+  return g_random_double_range (-1, 1);
+}
+
+/* returns a mean 0 variance 1 random variable
+   see numerical recipes p 217 */
+double random_gaussian(void)
+{
+  static int    iset = 0;
+  static double gset;
+  double fac, r, v1, v2;
+
+  if (iset == 0)
+    {
+      do
+        {
+          v1 = random_uniform11 ();
+          v2 = random_uniform11 ();
+          r = v1 * v1 + v2 * v2;
+        }
+      while (r >= 1.0 || r == 0.0);
+      fac = sqrt (-2.0 * log (r) / r);
+      gset = v1 * fac;
+      iset = 1;
+      return v2 * fac;
+    }
+  iset = 0;
+  return gset;
+}
+
+void
+copy_variation (control_point *cp0,
+                control_point *cp1)
+{
+  int i, j;
+  for (i = 0; i < NXFORMS; i++)
+    {
+      for (j = 0; j < NVARS; j++)
+        cp0->xform[i].var[j] = cp1->xform[i].var[j];
+    }
+}
+
+#define random_distrib(v) ((v)[g_random_int_range (0, vlen(v))])
+
+void
+random_control_point (control_point *cp,
+                      int            ivar)
+{
+  int i, nxforms, var;
+  static int xform_distrib[] =
+    {
+      2, 2, 2,
+      3, 3, 3,
+      4, 4,
+      5
+    };
+  static int var_distrib[] =
+    {
+      -1, -1, -1,
+      0, 0, 0, 0,
+      1, 1, 1,
+      2, 2, 2,
+      3, 3,
+      4, 4,
+      5
+    };
+
+  static int mixed_var_distrib[] =
+    {
+      0, 0, 0,
+      1, 1, 1,
+      2, 2, 2,
+      3, 3,
+      4, 4,
+      5, 5
+    };
+
+  get_cmap (cmap_random, cp->cmap, 256);
+  cp->time = 0.0;
+  nxforms = random_distrib (xform_distrib);
+  var = (0 > ivar) ?
+      random_distrib(var_distrib) :
+      ivar;
+  for (i = 0; i < nxforms; i++)
+    {
+      int j, k;
+      cp->xform[i].density = 1.0 / nxforms;
+      cp->xform[i].color = i == 0;
+      for (j = 0; j < 3; j++)
+        for (k = 0; k < 2; k++)
+          cp->xform[i].c[j][k] = random_uniform11();
+      for (j = 0; j < NVARS; j++)
+        cp->xform[i].var[j] = 0.0;
+      if (var >= 0)
+        cp->xform[i].var[var] = 1.0;
+      else
+        cp->xform[i].var[random_distrib(mixed_var_distrib)] = 1.0;
+
+    }
+  for (; i < NXFORMS; i++)
+    cp->xform[i].density = 0.0;
+}
+
+/*
+ * find a 2d bounding box that does not enclose eps of the fractal density
+ * in each compass direction.  works by binary search.
+ * this is stupid, it should just use the find nth smallest algorithm.
+ */
+void
+estimate_bounding_box (control_point *cp,
+                       double         eps,
+                       double        *bmin,
+                       double        *bmax)
+{
+  int    i, j, batch = (eps == 0.0) ? 10000 : 10.0/eps;
+  int    low_target = batch * eps;
+  int    high_target = batch - low_target;
+  point  min, max, delta;
+  point *points = g_malloc0 (sizeof (point) * batch);
+
+  iterate (cp, batch, 20, points);
+
+  min[0] = min[1] =  1e10;
+  max[0] = max[1] = -1e10;
+
+  for (i = 0; i < batch; i++)
+    {
+      if (points[i][0] < min[0]) min[0] = points[i][0];
+      if (points[i][1] < min[1]) min[1] = points[i][1];
+      if (points[i][0] > max[0]) max[0] = points[i][0];
+      if (points[i][1] > max[1]) max[1] = points[i][1];
+    }
+
+  if (low_target == 0)
+    {
+      bmin[0] = min[0];
+      bmin[1] = min[1];
+      bmax[0] = max[0];
+      bmax[1] = max[1];
+      return;
+    }
+
+  delta[0] = (max[0] - min[0]) * 0.25;
+  delta[1] = (max[1] - min[1]) * 0.25;
+
+  bmax[0] = bmin[0] = min[0] + 2.0 * delta[0];
+  bmax[1] = bmin[1] = min[1] + 2.0 * delta[1];
+
+  for (i = 0; i < 14; i++)
+    {
+      int n, s, e, w;
+      n = s = e = w = 0;
+      for (j = 0; j < batch; j++)
+        {
+          if (points[j][0] < bmin[0]) n++;
+          if (points[j][0] > bmax[0]) s++;
+          if (points[j][1] < bmin[1]) w++;
+          if (points[j][1] > bmax[1]) e++;
+        }
+      bmin[0] += (n <  low_target) ? delta[0] : -delta[0];
+      bmax[0] += (s < high_target) ? delta[0] : -delta[0];
+      bmin[1] += (w <  low_target) ? delta[1] : -delta[1];
+      bmax[1] += (e < high_target) ? delta[1] : -delta[1];
+      delta[0] = delta[0] / 2.0;
+      delta[1] = delta[1] / 2.0;
+    }
+  g_free (points);
+}
+
+/* this has serious flaws in it */
+
+double
+standard_metric (control_point *cp1,
+                 control_point *cp2)
+{
+  int    i, j, k;
+  double t;
+  double dist = 0.0;
+
+  for (i = 0; i < NXFORMS; i++)
+    {
+      double var_dist = 0.0;
+      double coef_dist = 0.0;
+      for (j = 0; j < NVARS; j++)
+        {
+          t = cp1->xform[i].var[j] - cp2->xform[i].var[j];
+          var_dist += t * t;
+        }
+      for (j = 0; j < 3; j++)
+        for (k = 0; k < 2; k++)
+          {
+            t = cp1->xform[i].c[j][k] - cp2->xform[i].c[j][k];
+            coef_dist += t *t;
+          }
+      /* weight them equally for now. */
+      dist += var_dist + coef_dist;
+    }
+  return dist;
+}
+
+static int
+flam3_random_bit (void)
+{
+  static int n = 0;
+  static int l;
+  if (n == 0)
+    {
+      l = g_random_int ();
+      n = 20;
+    }
+  else
+    {
+      l = l >> 1;
+      n--;
+    }
+  return l & 1;
+}
+
+static double
+flam3_random01 (void)
+{
+  return (g_random_int () & 0xfffffff) / (double) 0xfffffff;
+}