Some Ideas for Your CS285 Course Project

Develop a Parameterized Procedural Model Generator for:

A simple spanning surface in a knot drawn in a plane (with crossings);
Hyperbolic tessellation of the Poincarre disk (including texture mapping for regular n-gons);
For an intriguing bell shape -- couple to sound analysis (see below);
Some type of puzzle piece;
2.5D or 3D rolling-ball mazes;
Conical, elliptical, or hyperbolical gear wheels;
Artistic sculpture family;

Design and build (SFF) a polyhedral model of the Klein quartic with octahedral symmetry.
Design, analyze, and build (SFF) a convex polyhedral object that is stable only on one of its faces, i.e., it always rolls to that same face.
Build a model of the Projective Plane in the form of the 3-fold symmetrical Boy's Surface. Make the surface thick and "transparent" so that the model can be built with SFF.
Design, analyze, model, and build (cardboard?) a hinged, closed, concave polyhedron that flexes, i.e., can change its shape to some degree. Note, this object will maintain a constant volume during this transformation.
Design, model, and implement a new kind of "Expandagon" model. Let yourself be inspired by Hobermann's structures.
Design, analyze, and model as a kinematic SLIDE file one of the Jitterbug assemblies (show model purchased at Bridges 2001).

Make an intriguing bell shape with a few parameters to change this shape. Analyze and evaluate its sound as a function of these parameters. Try to make this design loop happen at "interactive" speed.
Try to find the inherent (approximate) symmetries in the shape of a scanned in object (perhaps by Eigenanalysis?).
Analyze and compare the sound spectrum of an MEC (standard elastica) and a MVS Miniumum (curvature) Variation Surface of the same geometric shape.

Enhance the surface mesh generator in slide to a 2.5D mesh generator describing the volume of thin plates with 3D tetrahedra, so as to have a quick path to the sound analysis for these parts.
Add (polyhedral) Boolean CSG constructs to the SIF language and expand the viewer to display the result along the line of the paper by Rappaport and Spitz: "Interactive Boolean Operations for Conceptual Design of 3-D Solids," Siggraph'97 Proc., p.269-278. This work need not start from scratch, but can use a C++ library that Jordan Smith has already written.

Make tiles that can snap together into non-2-manifold cellular structures.
In particular, do an injection mold for a 6D hypercube = 30-sided rhombic polyhedron with interior cells (3D Penrose tile).
Design and build prototypes for a modular snap-together part (for eventual implementation with injection molding) to make large smooth mathematical surfaces (like Klein bottles).
Design a new and better "lego" brick with interesting assembly possibilities.
In particular, make the injection mold for the two rhombic Zonohedra bricks that allow aperiodic tiling of 3-space in analogy to the aperiodic tiling of two-space with Penrose tiles. The tile should be somewhat "transparent" so that one can look inside the zonohedra construction.

Construct a "playground" to experiment with wavelet-based Miniumum (curvature) Variation Curves.
Enhance Brakke's surface evolver with a Miniumum (curvature) Variation functional.