Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/80920
Title: Knot optimization for biharmonic B-splines on manifold triangle meshes
Authors: Hou, Fei
He, Ying
Qin, Hong
Hao, Aimin
Keywords: Green's Functions
Biharmonic B-splines
Issue Date: 2016
Source: Hou, F., He, Y., Qin, H., & Hao, A. (2017). Knot optimization for biharmonic B-splines on manifold triangle meshes. IEEE Transactions on Visualization and Computer Graphics, 23(9), 2082-2095.
Series/Report no.: IEEE Transactions on Visualization and Computer Graphics
Abstract: Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.
URI: https://hdl.handle.net/10356/80920
http://hdl.handle.net/10220/45014
ISSN: 1077-2626
DOI: 10.1109/TVCG.2016.2605092
Rights: © 2016 Institute of Electrical and Electronics Engineers (IEEE). This is the author created version of a work that has been peer reviewed and accepted for publication by IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers (IEEE). It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1109/TVCG.2016.2605092].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

Files in This Item:
File Description SizeFormat 
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.pdf9.61 MBAdobe PDFThumbnail
View/Open

SCOPUSTM   
Citations 20

4
checked on Sep 5, 2020

WEB OF SCIENCETM
Citations 20

4
checked on Oct 24, 2020

Page view(s) 20

191
checked on Oct 29, 2020

Download(s) 20

60
checked on Oct 29, 2020

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.