Thesis
Star-flower subdivision
Washington State University
Master of Science (MS), Washington State University
2002
Handle:
https://hdl.handle.net/2376/80
Abstract
A subdivision algorithm is a simple way to generate smooth surfaces for geometric modeling. In this thesis, we present a new subdivision scheme called “star-flower subdivision”. Like other well-known subdivision schemes, such as Catmull-Clark (based on quadrilaterals) and √ 3-subdivision (based on triangular meshes), it also generates smooth objects after a few iterations. This scheme has advantages over previous schemes, however, due to a slower increase in polygon complexity. It subdivides quadrilateral meshes by a factor of 3, not 4, at each iteration. Having the number of facets increase more gradually allows designers to have greater control over the resolution of a refined mesh. We call star-flower subdivision “semi-stationary” because different subdivision rules occur on alternating levels of refinement. In order to apply the scheme to both closed and opened meshes, we also present a strategy to handle boundaries when applying the odd iterations of the scheme. Finally, the proofs of C 2 -continuity everywhere generated by the new scheme, except for extraordinary vertices where they are C 1 -continuous, are shown by numerical analysis. In addition, we also show the results for several common objects, including Stanford Bunny, after applying a limited iterations of star-flower subdivision.
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Details
- Title
- Star-flower subdivision
- Creators
- Cheng-Chih Fan-Chiang
- Contributors
- Robert R. Lewis (Degree Supervisor)
- Awarding Institution
- Washington State University
- Academic Unit
- Electrical Engineering and Computer Science, School of
- Theses and Dissertations
- Master of Science (MS), Washington State University
- Publisher
- Washington State University; Pullman, Wash. :
- Identifiers
- 99900525140901842
- Language
- English
- Resource Type
- Thesis