2006 Student Research Conference:

19th Annual Student Research Conference

19th Annual Student Research Conference

**Fitting Bézier Surfaces To Parameterized Data Points**

Theodore M. Elkow

Dr. Todd Palumbo, Faculty Mentor

Current technology allows doctors to create three dimensional images of anatomical objects, which may be represented on a computer as a set of points in three dimensional space. However, using such a representation becomes impractical as the number of points increases. One solution to this problem is to create a two dimensional surface that covers the exterior of whatever object is being modeled. Bézier surfaces are the two dimensional analog of Bézier curves, which may be familiar from illustration or CAD software. Bézier surfaces use a small number of control points to define the shape of a surface, and hence they are a good way to model a complex object. We have developed a method to fit a triangular Bézier surface to a set of points. I will describe this method and explain the mathematics behind it, show examples of surfaces it has generated, and examine its practical applications.

**Keywords:** Bézier Surface

**Topic(s):**Mathematics

**Presentation Type:** Oral Paper

**Session:** 39-3

**Location:** OP 2111

**Time:** 1:45