Term of Award

Fall 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)


Department of Mathematical Sciences

Committee Chair

Yingkang Hu

Committee Member 1

Scott Kersey

Committee Member 2

Xiezhang Li

Committee Member 3

Jiehua Zhu

Committee Member 3 Email



Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.