Improving the area-preserving parameterization of rational Bézier surfaces by rational bilinear transformation

To improve the area-preserving parameterization quality of rational Bézier surfaces, an optimization algorithm using bilinear reparameterization is proposed. First, the rational Bézier surface is transformed using a rational bilinear transformation, which provides greater degrees of freedom compared...

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Bibliographic Details
Main Authors: Xiaowei Li, Yingjie Wu, Yaohui Sun, Xin Chen, Yanru Chen, Yi-jun Yang
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Graphical Models
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Online Access:http://www.sciencedirect.com/science/article/pii/S1524070325000256
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Summary:To improve the area-preserving parameterization quality of rational Bézier surfaces, an optimization algorithm using bilinear reparameterization is proposed. First, the rational Bézier surface is transformed using a rational bilinear transformation, which provides greater degrees of freedom compared to Möbius transformations, while preserving the rational Bézier representation. Then, the energy function is discretized using the composite Simpson’s rule, and its gradients are computed for optimization. Finally, the optimal rational bilinear transformation is determined using the L-BFGS method. Experimental results are presented to demonstrate the reparameterization effects through the circle-packing texture map, iso-parametric curve net, and color-coded images of APP energy in the proposed approach.
ISSN:1524-0703