Partition of Unity Parametrics: A framework for meta-modeling
Adam Runions and Faramarz Samavati
Department of Computer Science, University of Calgary
Abstract
We propose Partition of Unity Parametrics (PUPs), a natural extension
of NURBS that maintains affine invariance. PUPs replace the weighted
basis functions of NURBS with arbitrary weight-functions (WFs). By
choosing appropriate WFs, PUPs yield a comprehensive geometric
modeling framework, accounting for a variety of beneficial properties,
such as local-support, specified smoothness, arbitrary sharp features
and approximating or interpolating curves. Additionally, we consider
interactive specification of WFs to fine-tune the character of curves
and generate non-trivial effects. This serves as a basis for a system
where users model the tools used for modeling, here weight-functions,
in tandem with the model itself, which we dub a meta-modeling
system. PUP curves and surfaces are considered in detail. Curves
illustrate basic concepts that apply directly to surfaces. For
surfaces, the advantages of PUPs are more pronounced; permitting
non-tensor WFs and direct parameter space manipulations. These
features allow us to address two difficult geometric modeling problems
(sketching features onto surfaces and converting planar meshes into
parametric surfaces) in a conceptually and computationally simple way.
Reference
Adam Runions and Faramarz Samavati. Partition of Unity Parametrics: A
framework for meta-modeling. The Visual Computer 27(6-8),
pp. 495-505, 2011.
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