This is my first attempt at creating a POV-Ray macro for use by the world at
large rather than just for myself. I have endeavored to amend (most) of my bad
programming habits, such as lack of documentation and unnecessary recalculation
of values.  I may have gone a bit overboard, but where's the fun in moderation?

After I worked out the basic geometry for the endpoints, it occurred to me that
the only thing needed to make a 3D beveled version was to shift the center point
a bit out of the z-plane. I went on to decide that 3D stars that looked hollow
from the back were of limited usefulness, so I added in options for a flat back
surface or two-way beveling. Since the macro calls for the user to set a value
for how much the points will "Taper" and people will probably not want to hunt
for the taper value that produces a "regular" star shape, I also built in a
feature that automatically converts a zero value for "Taper" to the most
commonly desired value.

Since it's really short, I've decided to post it both as text here in the body
(for easy perusal) and as a zip file (for easy download). I'll be uploading a
demo image as well.

I had fun writing it and hope that it will prove to be fun and/or useful to a
few folks.

Best Regards,
Mike C.

/*
CREATES A STAR OF RADIUS 1 AT THE ORIGIN IN THE x,y PLANE
If the star has a 3D height (beveled), the "front" protrudes in the -z direction
================================================================================

USAGE:
object{ MakeStar([StarPts],[StarHt],[Taper],[StarDbl]) [Object Modifiers...] }

================================================================================

StarPts: The number of points in the star, a whole number 2 or greater


StarHt:  The height (distance the center of the star extends in the -z
         direction).  0 (zero) creates a flat 2D Star. Remember that the
         unscaled star has a radius of 1. Values greater than 1 are allowed,
         but will make an object that looks more like a pyramid or a spike
         than a star.

Taper:   Value between 0 and 1, Higher values create narrower points.
         (Specifically, it's the proportion of the overall radius of the star
         by which the inner endpoints are drawn in toward the origin.)
         For stars of 5 through 10 points, a special feature has been built in
         such that a Taper of 0 (zero) will result in a "regular" star shape...
         (shaped like a pentacle for 5, "Star of David" for 6, etc. For all
         other numbers of points, a zero Taper is automatically reset to .5.

StarDbl: Whether or not to create a "double star" with a beveled height in both
         the -z and +z directions: 0 (zero) is "no", any other value is "yes".
         If the star has a non-zero height and StarDbl=0, a flat "back"
         surface is created in the x,y plane. This value is ignored when
         StarHt=0.
*/

#macro MakeStar(StarPts,StarHt,Taper,StarDbl)



//Filter inappropiate values (NOT 100% fool proof, but helpful).
#local StarPts=int(abs(StarPts));
#if (StarPts<2) #local StarPts=2; #end
#local StarHt=abs(StarHt);
#local Taper = abs(Taper);
#if (Taper >1)  #local Taper=1;   #end


//Set Taper values when the special zero Taper value is used
#if(Taper=0)
  #if (StarPts<5)  #local Taper=.500; #end
  #if (StarPts=5)  #local Taper=.620; #end
  #if (StarPts=6)  #local Taper=.425; #end
  #if (StarPts=7)  #local Taper=.305; #end
  #if (StarPts=8)  #local Taper=.234; #end
  #if (StarPts=9)  #local Taper=.180; #end
  #if (StarPts=10) #local Taper=.150; #end
  #if (StarPts>10) #local Taper=.500; #end
#end


//Count off the points
union{
#local PtNum =0; #while(PtNum<StarPts)


//Generate and store values reused for locating endpoints
#local PPV   = PtNum*pi*2/StarPts;      #local PSV   = pi/StarPts;
#local LrgX  = sin(PPV);                #local LrgY  = cos(PPV);
#local SmlXa = (1-Taper)*sin(PPV+PSV);  #local SmlYa = (1-Taper)*cos(PPV+PSV);
#local SmlXb = (1-Taper)*sin(PPV-PSV);  #local SmlYb = (1-Taper)*cos(PPV-PSV);

//These two triangles make the "front" of a star point (the whole star if 2D)
triangle {<0,0,-StarHt>,<LrgX,LrgY,0>,<SmlXa,SmlYa,0>}
triangle {<0,0,-StarHt>,<LrgX,LrgY,0>,<SmlXb,SmlYb,0>}

   #if (StarHt != 0)
      #if (StarDbl!= 0)
      //These two triangles make the back side of a "double" 3D star point.
      triangle {<0,0,StarHt>,<LrgX,LrgY,0>,<SmlXa,SmlYa,0>}
      triangle {<0,0,StarHt>,<LrgX,LrgY,0>,<SmlXb,SmlYb,0>}

      #else
      //These two triangles make the flat back of a "single" 3D star point.
      triangle {<0,0,0>,<LrgX,LrgY,0>,<SmlXa,SmlYa,0>}
      triangle {<0,0,0>,<LrgX,LrgY,0>,<SmlXb,SmlYb,0>}
      #end
   #end

#local PtNum=PtNum+1;

#end // end point count off
}    // close union
#end // end the macro

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