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Polynomial splines over general T-meshes

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Xin Li, Jiansong Deng & Falai Chen

Authors
  1. Xin Li
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  2. Jiansong Deng
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  3. Falai Chen
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Corresponding author

Correspondence to Xin Li.

Additional information

X. Li is currently a research fellow in School of Computer Engineering, NTU, Singapore.

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Li, X., Deng, J. & Chen, F. Polynomial splines over general T-meshes. Vis Comput 26, 277–286 (2010). https://doi.org/10.1007/s00371-009-0410-9

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  • DOI: https://doi.org/10.1007/s00371-009-0410-9

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