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Construction of multiresolution triangular B-Spline surfaces using hexagonal filters
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Date
1999-07-13
Publication Type
Report
ETH Bibliography
yes
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Abstract
We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. Unlike existing methods, the basic idea of our approach is to construct the triangular basis functions from their tensor product relatives in the spirit of box splines by projecting them onto the barycentric plane. The scheme works for splines of any order where the fundamental building blocks of the surface are hierarchies of triangular B-spline scaling functions and wavelets spanning the complement spaces between levels of different resolution. Although our bases functions have been deduced from the corresponding 3D-bases, our decomposition and reconstruction scheme operates directly on the triangular mesh using hexagonal filters. The resulting basis functions are used to approxi mate triangular surfaces and provide many useful properties, such as multiresolution editing, local level of detail, continuity control, surface compression and much more. The performance of our approach is illustrated by various examples including parametric.
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Publication status
published
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Journal / series
Volume
327
Pages / Article No.
Publisher
ETH Zurich, Department of Computer Science
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Triangular B-spline wavelets; Box splines; Multiresolution editing; Hierarchical surface representation; Surface compression; Decomposition; Reconstruction
Organisational unit
02150 - Dep. Informatik / Dep. of Computer Science
Notes
Technical Reports D-INFK.