Date of Award

Spring 2018

Document Type

Thesis

Department

Mathematics, Engineering & Computer Science

First Advisor

Ted Wendt

Second Advisor

Eric Sullivan

Third Advisor

Shaun Scott

Abstract

In this paper, we discuss and develop several one-dimensional interpolation techniques. Interpolation is a process for generating functions that pass through specified points in space. In general, given a set of points P = f(x0; y0); (x1; y1); : : : ; (xn; yn)g, interpolation provides a function f(x) such that f(xi) = yi for i = 0; : : : ; n. We start by discussing common techniques used for interpolation, including polynomial, piecewise linear, cubic splines, and B´ezier curves. We also develop two new interpolation techniques: one based on a refinement of quadratic interpolation and the other based on bending properties of physical materials. We examine quantitative and qualitative errors between the existing methods and our new techniques. Finally, we discuss how the new techniques could be generalized and extended into higher dimensions.

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