[OpenSCAD] Minkowski sum slowness

[Giles Bathgate]

I have been doing some further investigation regarding minkowski sum slowness.

My hypothesis was that openscad spheres have much more facets than neccecery
to prove my hypothesis I created a sphere in terms of simpler
primitives e.g. circle, and
rotate_extrude

   module halfcircle(r) {
     difference() {
       circle(r);
       translate([-r,0])square([r*2,r]);
     }
   }

   module sphere_alternate(r) {
     rotate_extrude()
       rotate([0,0,90])halfcircle(r);
   }

   $fn=20;
   minkowski() {
      cube([20,20,30]);
      sphere_alternate(5);
   }

I then compiled this script:

Parsing design (AST generation)...
Compiling design (CSG Tree generation)...
Compilation finished.
Compiling design (CSG Products generation)...
Processing uncached minkowski statement...
..rendering time: 0 hours, 0 minutes, 59 seconds
Compiling design (CSG Products normalization)...
CSG generation finished.
Total rendering time: 0 hours, 1 minutes, 0 seconds

With comparison to the standard sphere script:

   $fn=20;
   minkowski() {
      cube([20,20,30]);
      sphere(5);
   }

You can see this is about twice as slow:

Parsing design (AST generation)...
Compiling design (CSG Tree generation)...
Compilation finished.
Compiling design (CSG Products generation)...
Processing uncached minkowski statement...
..rendering time: 0 hours, 2 minutes, 26 seconds
Compiling design (CSG Products normalization)...
CSG generation finished.
Total rendering time: 0 hours, 2 minutes, 27 seconds

Looking at the primitives.cc code for the built-in sphere you can see
that the reason for this is that the number of fragments is calculated
on a per ring basis. What it means is that when viewed from above
(with $fn set to 10 for example) you can see that the sphere's
projection (or outermost ring) is a 10 sided circle, however when
viewed from the front the sphere projection has many more sides.

I experimented with setting the number of fragments identical for
every ring in the sphere, and setting the number of rings to half the
number of fragments this gives a "symmetrical sphere", in that it
looks the same when viewed from any direction

I have pushed a patch for this to
http://gitorious.org/openscad/openscad/commits/sphere-cylinder-optimisation

After this patch is applied with the default settings (i.e. $fn not
set) the sphere has a much better appearance imho.

More interestingly the same script as in the original post is about
twice the speed.

$fn=50;

minkowski()
{
 cube([10,10,1]);
 sphere(r=2,h=1);
}

Parsing design (AST generation)...
Compiling design (CSG Tree generation)...
Compilation finished.
Compiling design (CSG Products generation)...
Processing uncached minkowski statement...
..rendering time: 0 hours, 8 minutes, 54 seconds
Compiling design (CSG Products normalization)...
CSG generation finished.
Total rendering time: 0 hours, 8 minutes, 54 seconds