Thesis (Ph. D.)--Oregon Health & Science University, Department of Science & Engineering, September 2008. / Includes bibliographical references (leaves 147 - 158).

Thesis (M.A.)--University of Hong Kong, 1966. / Also available in print.

Thesis (M.Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 147-156). Also available in print.

Thesis (M.Phil.)--City University of Hong Kong, 2005. / "Submitted to Department of Computer Engineering and Information Technology in partial fulfillment of the requirements for the degree of Master of Philosophy" Includes bibliographical references (leaves 109-111)

Thesis (Ph. D.)--University of Michigan, 1934. / Lithoprinted. "Reprinted from the Annals of Mathematical Statistics, November, 1933."

Inaug.-diss.-Münster i. W.

The creation of smooth interpolating curves and surfaces is an important aspect of computer graphics. Trigonometric interpolation in the form of the Fourier transform has been a popular technique. For computer graphics, simpler curves and surfaces like the B´ezier curve and B-spline curve have been more popular due to the computational efficiency. Fitting B-spline or B´ezier curves or surfaces to unorganised data points has been more challenging since these curves are not naturally interpolating. Normally a system of equations needs to be solved to obtain the curves or surfaces with the added problem of identifying data points to form piecewise continuous surfaces. We solve the problem of periodic interpolating curves and surfaces using harmonic interpolation [73]. We extend harmonic interpolation to handle an even number of data points. We then show how harmonic interpolation can be applied using geometry images [29] to create smooth interpolating surfaces. We introduce algorithms to manipulate the amount of interpolated points, and the location of the interpolated points. Finally, we show how a smooth interpolating surface created by harmonic interpolation can be converted to a series of B´ezier surfaces. The combination of techniques allows us to quickly create a smooth interpolating surface from a set of unorganised points that have a known spherical structure. Keywords: Interpolation, harmonic interpolation, trigonometric interpolation, B´ezier curves surface fitting, tensor product surfaces. / Prof. W.F. Steeb

In recent years, State Road Route 114 which is located in Montgomery County, Virginia, has gained a bad reputation because of numerous traffic accidents. Most of these accidents resulted in loss of lives and property. Although there are many suggestions and proposals designed to prevent these acidents, to date no actions is taken yet. The focus of this research is to explore a technology-based, low cost solution that will lower or eliminate the risk of accidents on this two-lane rural highway. / Master of Science

No description available.

In the thesis we study the elliptic curves and its use in cryptography. Elliptic curvesencompasses a vast area of mathematics. Elliptic curves have basics in group theory andnumber theory. The points on elliptic curve forms a group under the operation of addition.We study the structure of this group. We describe Hasse’s theorem to estimate the numberof points on the curve. We also discuss that the elliptic curve group may or may not becyclic over finite fields. Elliptic curves have applications in cryptography, we describe theapplication of elliptic curves for discrete logarithm problem and ElGamal cryptosystem.