guanaco, a real time implicit surface (cross platform) tracer
A Whitney Umbrella

Actual version: guanaco 0.3.7

No, guanaco is not really a CAD software. What is guanaco? guanaco is a cross-platform software to visualize implicit surface; it is not a cad/csg software, a tool to visualize mesh, or 3d-model. It is not too precise but it is still really young. Its status is in development.
(C) J. Milnor :-) What does it wish to be? guanaco aims to display implicit surface in R^3 defined by a single equation i.e. {(x,y,z) in R^3 : f(x,y,z)=0} ; f does not need to be an algebraic function, nor 0 a regular value of f. It plans to permit moving dynamically the surface within the defined cube of research. Also, it would like to be a cross-platform Linux/OSX/Windows application.
Look at topological type change. How does it work? Well, pretty simple. Just enter your function f, in the right dialog box (with respect to a standard syntax), choose some resolution level, and give it a try. That s it. You may save a screen shot from your creation.
Research of singularities is a heavy computing task. What does it need? With linux, it needs g++3+ because it uses some STL stuff and aims to be as conform as possible to ISO c++; it adopts Glui (a glut c++ based interface) as a GUI . Unfortunately, it needs a fast computer.

But, how does it look like?

It looks like Windows (crosscap is sweet, no?) 1280x1024@32. with windows, like Linux 1280x1024@32. with Linux, and a recent screen shot MacOS X from an early port to MacOS X, thanks to my department colleague, Pr. T. Lachand-Robert.

Some other screenshots:
  1. First classroom -1. First classroom 0. First classroom 1. First classroom 2. First classroom 3. First classroom 4. First classroom 5.
  2. A torus. Yes, it is a topological torus. Topological genus 2 surface. Not singular, but I find it beautiful. Classical test surface. Test surface 2.
  3. First classroom 6. A cubic. Singularities arise in a natural way from caustics. Where are singularities here? ;-) Simple, but important. Hyperbolic umbilic.
  4. Whitney umbrella. Closed Whitney umbrella. Frontier condition but (a) fault. Is it Whitney (a)-regular along the small stratum? (a) but (b)-fault.
  5. Bierstone-Milman surface. Kurdyka surface. Paunescu surface.
  6. Strange? No? A singular foliation? Arrangement of hyperplanes. No comment. A candy?

Some links: