# 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;

## Mathematical and Geometrical Demonstration Models

• 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).

## FEM Models and Sound Analysis

• 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.

## Solid Modeling Utilities

• 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.

## Possible Projects with Part-Design Emphasis

• 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.