Polynomial splines over general T-meshes

Authors:
Xin Li;Jiansong Deng;Falai Chen
Affiliations:
University of Science and Technology of China, Department of Mathematics, 230026, Hefei, Anhui, China;University of Science and Technology of China, Department of Mathematics, 230026, Hefei, Anhui, China;University of Science and Technology of China, Department of Mathematics, 230026, Hefei, Anhui, China
Venue:
The Visual Computer: International Journal of Computer Graphics - Special Issue: CAD/Graphics 2009
Year:
2010

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Abstract

The present authors have introduced polynomial splines over T-meshes (PHT-splines) and provided theories and applications for PHT-splines over hierarchical T-meshes. This paper generalizes PHT-splines to arbitrary topology over general T-meshes with any structures (GPT-splines). GPT-spline surfaces can be constructed through a unified scheme to interpolate the local geometric information at the basis vertices of the T-mesh. We also discuss general edge insertion and removal algorithms for GPT-splines. As applications, we present algorithms to construct a GPT-spline surface from a quadrilateral mesh and to simplify a tensor-product B-spline surface into a GPT-spline surface with superfluous edges removal.