王鹏宵,李崇君.基于层次T网格的分片孔斯曲面重构[J].数学研究及应用,2019,39(6):677~699
基于层次T网格的分片孔斯曲面重构
Piecewise Coons Surfaces Reconstruction over Hierarchical T-Meshes
投稿时间:2019-01-17  修订日期:2019-04-12
DOI:10.3770/j.issn:2095-2651.2019.06.012
中文关键词:  孔斯曲面  PHT样条  样条空间  层次T网格  曲面重构
英文关键词:Coons surface  PHT-splines  spline space  hierarchical T-mesh  surface reconstruction
基金项目:国家自然科学基金(Grant Nos.11572081; 11871137),辽宁省高等学校创新人才支持计划(Grant No.LCR2018001).
作者单位
王鹏宵 大连理工大学数学科学学院, 辽宁 大连116024 
李崇君 大连理工大学数学科学学院, 辽宁 大连116024 
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中文摘要:
      本文提出一种基于任意层次T网格的多项式(PHT)样条空间$S(3,3,1,1,T)$的一个新的曲面重构算法.该算法由分片插值于层次T网格上每个小矩形单元对应4个顶点的16个参数的孔斯曲面形式给出.对于一个给定的T网格和相应基点处的几何信息(函数值,两个一阶偏导数和混合导数值),可得到与$S(3,3,1,1,T)$的PHT样条曲面相同的结果,且曲面表达形式更简单,同时,在离散数据点的曲面拟合中,我们给出了自适应的曲面加细算法.数值算例显示,该自适应算法能够有效的拟合离散数据点.
英文摘要:
      In this paper, we present a new surface reconstruction algorithm for polynomial spline surfaces of $S(3,3,1,1,{\cal T})$ over arbitrary hierarchical T-mesh $\cal T$. The surface is piecewisely constructed by Coons surface interpolation of the 16 parameters at four vertices on each rectangular cell of hierarchical T-mesh. For a given hierarchical T-mesh $\cal T$ and geometric information (the function values, the two first order partial derivatives and the mixed partial derivatives) at corresponding basis vertices of the hierarchical T-mesh, the surface is the same as the polynomial spline surface of $S(3,3,1,1,{\cal T})$, but our algorithm avoids the complexity of PHT-spline basis functions. Moreover, we give an adaptively refined surface algorithm for fitting scattered data points based on piecewise Coons surface construction. The numerical results show that the proposed adaptive algorithm is efficient in fitting scattered data points.
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