Piecewise Coons Surfaces Reconstruction over Hierarchical T-Meshes
Received:January 17, 2019  Revised:April 12, 2019
Key Word: Coons surface   PHT-splines   spline space   hierarchical T-mesh   surface reconstruction
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11572081; 11871137) and the Program for Liaoning Innovation Talents in University (Grant No.LCR2018001).
 Author Name Affiliation Pengxiao WANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China Chongjun LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
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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.