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Stationary Subdivision and Multiresolution Surface Representations


Zorin, Denis N. (1998) Stationary Subdivision and Multiresolution Surface Representations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EKMR-0233.


Stationary subdivision is an important tool for generating smooth free-form surfaces used in CAGD and computer graphics. One of the challenges in the construction of subdivision schemes for arbitrary meshes is to guarantee that the surfaces produced by the algorithm are C1-continuous. First results in this direction were obtained only recently. In this thesis we derive necessary and sufficient criteria for Ck-continuity that generalize and extend most known conditions.

We present a new method for analysis of smoothness of subdivision which allows us to analyze subdivision schemes which do not generate surfaces admitting closed-form parameterization on regular meshes, such as the Butterfly scheme and schemes with modified rules for tagged edges.

The theoretical basis for analysis of subdivision that we develop allows us to suggest methods for constructing new subdivision schemes with improved behavior. We present a new interpolating subdivision scheme based on the Butterfly scheme, which generates C1-continuous surfaces from arbitrary meshes.

We describe a multiresolution representation for meshes based on subdivision. Combining subdivision and the smoothing algorithms of Taubin [61] allows us to construct a set of algorithms for interactive multiresolution editing of complex hierarchical meshes of arbitrary topology.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Computer Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Barr, Alan H. (advisor)
  • Schroeder, Peter (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 September 1997
Record Number:CaltechETD:etd-08102005-152703
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3083
Deposited By: Imported from ETD-db
Deposited On:10 Aug 2005
Last Modified:21 Dec 2019 01:49

Thesis Files

PDF (Zorin_dn_1998.pdf) - Final Version
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