Rational Cubic B-Spline Interpolation and Its Applications in Computer Aided Geometric Design

<p>Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights.</p> <p>In utilizing a NURB a designer may desire that it pass through a set of data points {x_i} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the relationship between these assigned weights and the weights of the corresponding interpolating NURB. In this thesis this relationship is explored. Sufficient conditions are developed to produce interpolating NURBS which have positive weights. Applications to the problems of degree reduction and curve fairing are presented. Both theoretical and computational results are presented.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

1994

Author dc:creator

• Wu, Kotien

Contributors dc:contributor

• S. E. Weinstein
• P. Bogacki
• John Swetits
• Wu Li
• J. L. Schwing

• CAD
• B-spline
• Computer-aided design
• Interpolation
• Mathematics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Repository record dc:identifier

https://digitalcommons.odu.edu/mathstat_etds/107

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1109