Fourier transform of a decagon and related images

cmdlines

gcc -o d10fourier d10fourier.c -O6 -Wall -std=c99 -pedantic -Wextra -lm -DTEN=10 -DPIC_WIDTH=1920 -DPIC_HEIGHT=1080 -DFRAME_COUNT=1440
parallel -j 8 ./d10fourier {} ::: $(seq 0 719)
ffmpeg -framerate 24 -i d10fourier-%04d.png -video_size 1920x1080 -c:v libx265 -preset slower -crf 27 -pix_fmt yuv420p d10fourier.mp4

gcc -o d14fourier d10fourier.c -O6 -Wall -std=c99 -pedantic -Wextra -lm -DTEN=14 -DPIC_WIDTH=1920 -DPIC_HEIGHT=1080 -DFRAME_COUNT=1440
parallel -j 8 ./d14fourier {} ::: $(seq 0 719)
ffmpeg -framerate 24 -i d14fourier-%04d.png -video_size 1920x1080 -c:v libx265 -preset slower -crf 27 -pix_fmt yuv420p d14fourier.mp4

d10fourier.c

// d10fourier.c - compute the Fourier transform of a regular decagon
// David A. Madore <http://www.madore.org/~david/>
// Initially written 2018-04-22 (based on an earlier e8fourier program)
// This version 2026-01-10

/* This program is in the Public Domain.  However, I would appreciate
 * being credited if significant parts of it are being used
 * somewhere. */

/* The author of this program disclaims all warranties with regard to
 * this software, including all implied warranties of merchantability
 * and fitness for a particular purpose: in no event shall the author
 * be liable for any damages arising out of or in connection with the
 * use or performance of this software.  If you need this sort of
 * legalese, you are an idiot and you should not use a computer. */

/* Compile with something like
   gcc -o d10fourier d10fourier.c -O6 -Wall -std=c99 -Wextra -lm
 * The "convert" program from ImageMagick is used to convert .ppm to
 * .png (this should be easy to change, search for "convert" in
 * main()).  Various compile-time adjustable parameters are below. */

#ifndef PIC_WIDTH
#define PIC_WIDTH 1920			// Image width
#endif

#ifndef PIC_HEIGHT
#define PIC_HEIGHT 1080			// Image height
#endif

#ifndef PIC_SCALE
#define PIC_SCALE 16			// Pixels per unit distance
#endif

#ifndef FRAME_COUNT
#define FRAME_COUNT 1440		// Frame count for a full cycle
#endif

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>
#include <time.h>
#include <unistd.h>
#include <errno.h>
#include <sys/types.h>
#include <sys/wait.h>

#ifndef TEN
#define TEN 10
#endif
#define DIM 2

#ifndef M_PI
// Stupid <math.h> does not define this by order of the assholes who
// removed this from the C99 standard.
#define M_PI 3.141592653589793238462643383279502884
#endif

double vecs[TEN][DIM];

int
main (int argc, char *argv[])
{
  int frameno = 0;
  char havearg = 0;
  if ( argc >= 2 )
    {
      havearg = 1;
      sscanf (argv[1], "%d", &frameno);
    }
  double phaseshift = (double)frameno / FRAME_COUNT;
  for ( int k=0 ; k<TEN ; k++ )
    {
      vecs[k][0] = cos(M_PI*2*k/TEN);
      vecs[k][1] = sin(M_PI*2*k/TEN);
    }
  char buf[255];
  if ( havearg )
    snprintf (buf, sizeof(buf), "d%02dfourier-%04d.ppm", TEN, frameno);
  else
    snprintf (buf, sizeof(buf), "d%02dfourier.ppm", TEN);
  FILE *ppmf = fopen (buf, "w");
  if ( ! ppmf )
    {
      fprintf (stderr, "Failed to open %s for writing: %s\n",
	       buf, strerror(errno));
      exit (EXIT_FAILURE);
    }
  fprintf (ppmf, "P3\n%d %d 255\n", PIC_WIDTH, PIC_HEIGHT);
  for ( int l=0 ; l<PIC_HEIGHT ; l++ )
    {
      for ( int k=0 ; k<PIC_WIDTH ; k++ )
	{
	  double v[DIM];
	  v[0] = ((k-PIC_WIDTH/2-0.5)/PIC_SCALE);
	  v[1] = ((PIC_HEIGHT/2-0.5-l)/PIC_SCALE);
	  double val = 0;
	  for ( int r=0 ; r<TEN/2 ; r++ )
	    {
	      double dot = 0;
	      for ( int i=0 ; i<DIM ; i++ )
		dot += vecs[r][i] * v[i];
	      dot += ((r%2) ? -2*phaseshift : 2*phaseshift);
	      val += 2*cos(M_PI*dot);
	    }
	  // Fourier transform takes values between -10 and 10.
	  assert (val >= -TEN && val <= TEN);
#if 0 // Color gradient (blue for negative, black for zero, white for positive)
	  if ( val < 0. )
	    {
	      int i = (int)((val+TEN)*255/(TEN+0.));
	      fprintf (ppmf, " %d %d %d", 0, 0, 255-i);
	    }
	  else
	    {
	      int i = (int)((val)*255/(TEN+0.));
	      fprintf (ppmf, " %d %d %d", i, i, i);
	    }
#elif 0 // Black for negative, white for positive
	  if ( val < -0.3 )
	    fprintf (ppmf, " %d %d %d", 0, 0, 0);
	  else if ( val > 0.3 )
	    fprintf (ppmf, " %d %d %d", 255, 255, 255);
	  else
	    {
	      int i = (int)((val+0.3)*425.);
	      assert (i>=0 && i<=255);
	      fprintf (ppmf, " %d %d %d", i, i, i);
	    }
#else // White for [-1,1], black outside of [-1.5,1.5]
	  if ( val >= -1 && val <= 1 )
	    fprintf (ppmf, " %d %d %d", 255, 255, 255);
	  else if ( val > 1.5 || val < -1.5 )
	    fprintf (ppmf, " %d %d %d", 0, 0, 0);
	  else
	    {
	      int i = (int)(255-(fabs(val)-1.)*510.);
	      assert (i>=0 && i<=255);
	      fprintf (ppmf, " %d %d %d", i, i, i);
	    }
#endif
	}
      fprintf (ppmf, "\n");
    }
  fclose (ppmf);
  // Now convert PPM image to PNG.
  pid_t convpid = fork ();
  if ( convpid < 0 )
    {
      fprintf (stderr, "Failed to fork: %s\n", strerror(errno));
      exit (EXIT_FAILURE);
    }
  if ( convpid == 0 )
    {
      char buf2[255];
      if ( havearg )
	snprintf (buf2, sizeof(buf2), "d%02dfourier-%04d.png", TEN, frameno);
      else
	snprintf (buf2, sizeof(buf2), "d%02dfourier.png", TEN);
      execlp ("convert", "convert", buf, buf2, (char *)NULL);
      fprintf (stderr, "Failed to execlp: %s\n", strerror(errno));
      exit (EXIT_FAILURE);
    }
  else
    {
      waitpid (convpid, NULL, 0);
      unlink (buf);
    }
  exit (EXIT_SUCCESS);
}