Document Type
Dissertation
Degree
Doctor of Philosophy
Major
Mathematics
Date of Defense
9-30-2009
Graduate Advisor
Wenjie He, PhD.
Committee
Chui, Charles
Jiang, Qingtang
Cai, Haiyan
Abstract
This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs", and such biorthogonal wavelets ``NURBlets". Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout intervals; it fulfills interpolation at boundaries as well.
OCLC Number
599974669
Recommended Citation
Zhu, Weiwei, "The Multilevel Structures of NURBs and NURBlets on Intervals" (2009). Dissertations. 509.
https://irl.umsl.edu/dissertation/509