makeCircles.c

///////////////////////////////////////////
// build table chordVec[d] of circle 1/2 widths at distances d from center
// Code adapted from RobG's EduKit
// Uses Bresenham's circle algorithm
// Modified from RobG's EduKit by Eric Freudenthal and David Pruitt 2016
///////////////////////////////////////////
void computeChordVec(unsigned char chordVec[], unsigned char radius) 
{
  int col = radius, row = 0;	/* first coordinate (radius, 0) */
  
  // key insight: (col+1)**2 - col**2 = 2col+1
  
  int dColSquared = 2 * col - 1;  // change in col**2 for a unit decrease in col
  int dRowSquared = 1;	    // change in row**2 for a unit increase in row

  int radiusSqErr = 0;		/* (radius, 0) is on the circle  */
  int colPrev = 0;		/* initially bogus value  to force first entry*/
  while (col >= row) {		/* only sweep first octant */
    chordVec[row] = col;      /* row always changes in first octant */

    /* mirror into 2nd octant */
    if (colPrev != col)		/* col sometimes repeats in first octant */
      chordVec[col] = row;	/* only save first (max) col for row */
    colPrev = col;

    row++;			/* move vertically (slope <= -1 for first octant) */
    radiusSqErr += dRowSquared;	/* current radiusSqErr */
    dRowSquared += 2; 		/* next dRowSquared */
    if ((2 * radiusSqErr) > dColSquared) { /* only update col if error reduced */
      col--;			/* move horizontally */
      radiusSqErr -= dColSquared;	/* current radiusSqErr */
      dColSquared -= 2;	      /* next dColSquared */
    }
  }
}

#include "stdio.h"
#include "assert.h"


// Generate circles as source files
// (c) Eric Freudenthal, 2016
int main()
{
  int radius;
  char chordVec[151];
  FILE *circleIncludeFile = fopen("abCircle_decls.h", "w");
  FILE *chordIncludeFile = fopen("chordVec.h", "w");
  assert(chordIncludeFile); assert(circleIncludeFile);

  fprintf(circleIncludeFile, "// Automatically generated by makeCircles.  (c) Eric Freudenthal, 2016\n");
  fprintf(circleIncludeFile, "#ifndef abCircle_decls_included\n#define abCircle_decls_included\n\n");

  fprintf(chordIncludeFile, "// Automatically generated by makeCircles.  (c) Eric Freudenthal, 2016\n");
  fprintf(chordIncludeFile, "#ifndef chordVec_included\n#define chordVec_included\n\n");

  for (radius = 2; radius <= 150; radius++) {
    char filename[100];
    unsigned char chordIndex;
    
    computeChordVec(chordVec, radius);

    {				/* chordVecN.c */
      sprintf(filename, "circles/chordVec%d.c", radius);
      FILE *fp = fopen(filename, "w");
      assert(fp);
      fprintf(fp, "// Automatically generated by makeCircles.  (c) Eric Freudenthal, 2016\n");
      fprintf(fp, "#include \"chordVec.h\"\n\n");
      fprintf(fp, "const unsigned char chordVec%d[%d] = {\n", radius, radius+1);
      for (chordIndex = 0; chordIndex <= radius; chordIndex ++) 
	fprintf(fp, "    %d, // dist along axis = %d\n", chordVec[chordIndex], chordIndex);
      fprintf(fp, "};\n\n");
      fclose(fp);
    } {				/* abCircleN.c */
      sprintf(filename, "circles/abCircle%d.c", radius);
      FILE *fp = fopen(filename, "w");
      assert(fp);
      fprintf(fp, "// Automatically generated by makeCircles.  (c) Eric Freudenthal, 2016\n");
      fprintf(fp, "#include \"abCircle.h\"\n\n");
      fprintf(fp, "#include \"chordVec.h\"\n\n");
      fprintf(fp, "const AbCircle circle%d = {" , radius);
      fprintf(fp, "  abCircleGetBounds, abCircleCheck, chordVec%d, %d", radius, radius);
      fprintf(fp, "};\n");
      fclose(fp);
    }
    				/* includes */
    fprintf(chordIncludeFile, "extern const unsigned char chordVec%d[%d];\n", radius, radius+1);
    fprintf(circleIncludeFile, "extern const AbCircle circle%d;\n" , radius);
  }

  fprintf(circleIncludeFile, "\n#endif // included \n");
  fprintf(chordIncludeFile, "\n#endif // included \n");
  fclose(chordIncludeFile);
  fclose(circleIncludeFile);
}