CAGD - Computer-Aided Geometric Design

I spent a number of years studying CAGD - first in grad school at U. Utah, then in Oslo, and finally at Arizona State (in CS Dept, before transferring to Math). I enjoyed the subject matter very much and was fortunate enough to work with some very talented people. As usual, I got the most satisfaction from implementing algorithms in code, together with some sort of graphical user interface, in order to experiment with parameters and see visual results.

A spline curve: with B-spline & Bezier control polygons, normal vectors, and under tension.

Demonstrating the linear combination of basis functions for a Bezier curve.

Splines (approx and interp) on a sphere.

Random 2D points, Delaunay triangulation, and (dual) Dirichlet tesselation.

F(x,y), Hardy surface interpolant, Shephard surface interpolant.

References

Curves and Surfaces for CAGD