Automatic Geometry Construction

Sponsor	Jarek Rossignac jarek@cc.gatech.edu CoC 241
Area	GVU

Problem
The most popular representation of a 3D models used in graphics and animation is a table of vertices and a table of triangles that represent a triangular mesh that approximates a closed surface. Each vertex is represented by 3 coordinates ("geometry"). Each triangle is represented by 3 indices into the vertex table ("incidence"). Given an incidence table, can you guess the geometry? Obviously not, unless you get more information. In this project, you will develop a relaxation process that computes a "natural" geometry (i.e. vertex location) for any given incidence table. The relaxation will iteratively move vertices so as to make all edges have approximately the same length. This technology has inportant application for 3D model compression, computer animation, and finteractive design of ree-form shapes. A follow-up project will involve adding constraints (fixing the position of some vertices).

Deliverables

Source code that reads an incidence table from file, displays the 3D model as it evolves, and outputs a file with the resulting geometry.
The incidence files for a few test cases with zero, one, and two handles and a varying number of triangles.
A short report explaining how you have designed the relaxation process and how it performs.

Evaluation
The quality of the solution that can be achieved in reasonable time; the simplicity, readability, and compactness of the code: and the clarity of the report will be considered.