#
#  @color=colorlist($ncolor,$mag)
#
#  Returns a list of $ncolor colors which are equally 
#  distinguishable.  These colors all have the smae
#  magnitude (defined as r^2+g^2+b^2) and lie equidistant
#  on a circle in the rgb cube (255x255x255).  This circle
#  forms the bottom of a cone whose apex is either at
#  (0,0,0) or (255,255,255) in rgb space.
#
#
#  @color   list of rgb colors in HTML compatible format rrggbb 
#           where (rr,gg,bb) is 2 digit hex for red,green,blue
#           for example, 00ffa9 is (in decimal) 0 red,
#           255 green, 169 blue.
#  $ncolor  Number of colors returned.
#  $mag     Magnitude of color, magnitude of 0,1 corresponds
#           to rgb 000000 and ffffff.  Intermediate values
#           determine color magnitude defined as r^2+g^+b^2/(3*255^2)
#           Magnitudes ouside the range (0,1) are mapped to (0,1).
#
sub colorlist {
   my ($ncolor,$mag) = @_;
	my ($i,$invert,$pi,$afac,$mfac,$color,$angle,$c,$s,$phase);
	my (@vec);

	return () if $ncolor<1;
	$mag=0 if $mag<0;
	$mag=1 if $mag>1;
	

	@axis=(0.5,0.5,0.5);
	@nor0=(0.25,0.25,-0.5);
	@nor1=(sqrt(3.0)/4.0, -sqrt(3.0)/4.0, 0);

	$pi     = 4*atan2(1,1);
	#  Scaling factor to go from index to angle
	$afac   = 2*$pi/$ncolor;
	$invert = $mag>0.5;
	$mag    = 1-$mag if $invert;
	#  Scaling factor for color components 
	$mfac   = $mag*255*4*sqrt(2)/3.0;
	#  Without phase change color[0] will become complemntary
	#  when inverting
	$phase = $invert ? $pi : 0; 
	#  Find color components for each color on wheel
	for ($color=0;$color<$ncolor;$color++) {
		$angle = $afac*$color+$phase;
		$c = cos($angle);
		$s = sin($angle);

		for ($i=0;$i<3;$i++) {
			$vec[$i] = 
			$mfac*($axis[$i] + $c*$nor0[$i] + $s*$nor1[$i]);
			$vec[$i] = 255-$vec[$i] if $invert;
		}
		#  Convert color to HTML compatible hex string
		$color[$color] = sprintf ("%02x%02x%02x", @vec);
	}
	return @color;
}