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Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion
Aug. 2012 (vol. 18 no. 8)
pp. 1290-1303
Xin Li, Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
Juan Cao, Sch. of Math. Sci., Xiamen Univ., Xiamen, China
Zhonggui Chen, Dept. of Comput. Sci., Xiamen Univ., Xiamen, China
Hong Qin, Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
This paper develops a novel surface fitting scheme for automatically reconstructing a genus-0 object into a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration B-spline (DCB-spline), a new non-tensor-product spline. In this framework, we efficiently compute Delaunay configurations on sphere by the union of two planar Delaunay configurations. Also, we develop a hierarchical and adaptive method that progressively improves the fitting quality by new knot-insertion strategies guided by surface geometry and fitting error. Within our framework, a genus-0 model can be converted to a single spherical spline representation whose root mean square error is tightly bounded within a user-specified tolerance. The reconstructed continuous representation has many attractive properties such as global smoothness and no auxiliary knots. We conduct several experiments to demonstrate the efficacy of our new approach for reverse engineering and shape modeling.

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Index Terms:
tensors,computational geometry,least mean squares methods,mesh generation,splines (mathematics),surface fitting,hierarchical knot insertion,spherical DCB-spline surfaces,adaptive knot insertion,novel surface fitting scheme,continuous parametric spline surface,Delaunay configuration B-spline,nontensor-product spline,surface geometry,genus-0 model,spherical spline representation,reconstructed continuous representation,reverse engineering,shape modeling,root mean square error,Splines (mathematics),Surface reconstruction,Polynomials,Approximation methods,Surface treatment,Electronic mail,Image reconstruction,non-tensor-product B-splines.,Delaunay configurations,spherical splines,knot placement,knot insertion
Citation:
Xin Li, Juan Cao, Zhonggui Chen, Hong Qin, "Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 8, pp. 1290-1303, Aug. 2012, doi:10.1109/TVCG.2011.156
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