Analysis-Suitable T-Spline Fitting for Sculptured Surface Reconstruction
LU Yu 1，2 , WANG Jian 1 , PENG Lihua1 ，XU Long1
( 1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; 2. Wuhan Branch, ZWSOFT Ltd. (Guangzhou), Wuhan 430000, China )
摘要高精度高效率的曲面重构是先进航空制造与测量的重要步骤。B 样条与 NURBS 作为成熟的建模工具，是现在曲面重构的主要方法。然而，B 样条与 NURBS 控制网格的拓扑要求使得其对曲面进行建模时会产生很多的冗余控制顶点。近些年来新提出的 T 样条较好地解决了这个问题，其后发展出的 T 样条的子类适合分析 T 样条（ASTS）进一步优化了该样条的性质。目前，T 样条已被成功应用于曲面重构，而基于 ASTS 的曲面重构算法却亟待开发。提出了一种基于适合分析 T 样条的曲面重构方法。该方法能够通过自适应的初始 T 网格构建与高效的局部细化方法，构建出符合误差要求的 AST 样条模型。试验结果表明，在控制顶点数量相同的情况下，提出的算法能够重构出比 NURBS 更加精确的样条模型；与一般的 T 样条重构算法相比，具有更高的计算效率。
Abstract：Surface reconstruction with high efficiency and accuracy is required in advanced aerospace manufacturing and measurement. As wildly used models, B-spline and NURBS are the main tools for surface reconstruction in existing methods. However, the topological constrains of B-splines and NURBS control meshes make it produce a lot of redundant control points when modeling surfaces. Newly proposed T-splines in recent years have provided a method to solve this problem. Analysis-suitable T-splines (ASTS), a subset of T-splines with certain topological constrains were later developed, which optimized the mathematical properties and localized refinement capability of T-splines. T-splines have been successfully applied to surface reconstruction, while ASTS-based surface reconstruction algorithms are in vacancy at the moment. This paper proposes a surface reconstruction method based on analysis-suitable T-splines. Adaptive construction of an initial AST-mesh and efficient local refinement are performed in the algorithm to generate an ASTS surface within certain tolerance. Our experimental results show that the proposed ASTS fitting can generate spline surface with higher accuracy than NURBS fitting with the same amount of control parameters. The computing efficiency of the proposed algorithm is higher than simple T-spline fitting.
2020, 
