Area-Preserving Hierarchical NURBS Surfaces Computed by the Optimal Freeform Transformation

The equiareality of NURBS surfaces highly affects their rendering and tessellation results. To improve the equiareality of NURBS surfaces, an optimization algorithm using freeform transformations is presented in this paper. The equiareality energy is first formulated and its numerical approximation...

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Bibliographic Details
Published in:Computer aided design 2022-02, Vol.143, p.103134, Article 103134
Main Authors: Li, Xiao-Wei, Yang, Yi-Jun, Zeng, Wei, Bi, Yu-Li, Xu, Jin-Lan, Xu, Gang, Zhang, Xing-Jun
Format: Article
Language:English
Subjects:
Algorithms
Area-preserving parameterization
Least square method
NURBS surfaces
Optimization
Parameterization
Rendering
Tessellation
Transformations
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Summary:The equiareality of NURBS surfaces highly affects their rendering and tessellation results. To improve the equiareality of NURBS surfaces, an optimization algorithm using freeform transformations is presented in this paper. The equiareality energy is first formulated and its numerical approximation is then constructed using the composite Simpson’s rule. By constructing the parameterization of the initial freeform transformation using a low-stretch-mesh-parameterization method, the optimal freeform transformation is obtained by the Levenberg–Marquardt method, which is further interleaved with the freeform refinement procedure to generate a hierarchical NURBS surface with bounded equiareality deviations. Experimental results are given to show the performance of our algorithm for rendering and tessellation applications. •An optimization method is presented to improve the equiareality of NURBS surfaces using the freeform transformation.•The equiareality energy of the hierarchical NURBS surfaces is formulated.•The gradient of the discretized equiareality energy is derived in this paper.
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2021.103134