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Stationary Subdivision and Multiresolution Surface Representations

Zorin, Denis N. (1997) Stationary Subdivision and Multiresolution Surface Representations. California Institute of Technology . (Unpublished)

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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 Ck-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 Ck-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:Report or Paper (Technical Report)
Group:Computer Science Technical Reports
Record Number:CaltechCSTR:1997.cs-tr-97-32
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:26830
Deposited By: Imported from CaltechCSTR
Deposited On:30 Apr 2001
Last Modified:26 Dec 2012 14:06

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