Piecewise Coons surface reconstruction over arbitrary hierarchical T-meshes
Received:January 17, 2019  Revised:April 03, 2019
Key Word: Coons surface   PHT-splines   Spline space   Hierarchical T-meshes   Surface reconstruction.  
Fund ProjectL:National Natural Science Foundation of China (Nos. 11471066, 11572081,11871137)
Author NameAffiliationE-mail
崇君 李 School of Mathematical Sciences, Dalian University of Technology, chongjun@dlut.edu.cn 
鹏霄 王 School of Mathematical Sciences, Dalian University of Technology,  
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      In this paper, we present a new surface reconstruction algorithm of polynomial spline surface of S(3; 3; 1; 1; T ) over arbitrary hierarchical T-meshes. This surface algorithm is piecewise constructed by interpolation of the 16 parameters of four vertices on each rectangular cell of hierarchical T-meshes. For a given hierarchical T-mesh T and geometric information(the function value, the two first order partial derivatives and the mixed partial derivative) 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; T ), but our algorithm avoids the complexity of PHT-spline basis functions. With this new surface algorithm, surface model can be simplified on its expression than that of polynomial spline surface of S(3; 3; 1; 1; T ) over the same hierarchical T-mesh. Moreover, we give an adaptive subdivision surface algorithm for fitting scattered data points based on piecewise Coons surface construction. The experimental results show that the proposed adaptive algorithm is efficient in fitting scattered data points.
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