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

IF 2.2 4区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Graphical Models Pub Date : 2025-07-03 DOI:10.1016/j.gmod.2025.101278

Xiaowei Li , Yingjie Wu , Yaohui Sun , Xin Chen , Yanru Chen , Yi-jun Yang

引用次数: 0

Abstract

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.

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利用有理双线性变换改进有理bsamzier曲面的保面积参数化

为了提高有理bsamzier曲面的保面积参数化质量，提出了一种双线性再参数化优化算法。首先，使用一个有理双线性变换变换有理b逍遥曲面，与Möbius变换相比，它提供了更大的自由度，同时保留了有理b逍遥表示。然后，利用复合辛普森规则对能量函数进行离散化，并计算其梯度进行优化。最后，利用L-BFGS方法确定了最优有理双线性变换。实验结果通过圆填充纹理图、等参数曲线网和APP能量彩色编码图像验证了该方法的再参数化效果。

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来源期刊

Graphical Models 工程技术-计算机：软件工程

CiteScore

3.60

自引率

5.90%

发文量

审稿时长

47 days

期刊介绍： Graphical Models is recognized internationally as a highly rated, top tier journal and is focused on the creation, geometric processing, animation, and visualization of graphical models and on their applications in engineering, science, culture, and entertainment. GMOD provides its readers with thoroughly reviewed and carefully selected papers that disseminate exciting innovations, that teach rigorous theoretical foundations, that propose robust and efficient solutions, or that describe ambitious systems or applications in a variety of topics. We invite papers in five categories: research (contributions of novel theoretical or practical approaches or solutions), survey (opinionated views of the state-of-the-art and challenges in a specific topic), system (the architecture and implementation details of an innovative architecture for a complete system that supports model/animation design, acquisition, analysis, visualization?), application (description of a novel application of know techniques and evaluation of its impact), or lecture (an elegant and inspiring perspective on previously published results that clarifies them and teaches them in a new way). GMOD offers its authors an accelerated review, feedback from experts in the field, immediate online publication of accepted papers, no restriction on color and length (when justified by the content) in the online version, and a broad promotion of published papers. A prestigious group of editors selected from among the premier international researchers in their fields oversees the review process.