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Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion
Aug. 2012 (vol. 18 no. 8)
pp. 1290-1303
ASCII Text
x 
 
Zhonggui Chen, Xin Li, Juan Cao, 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.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2011.156,
author = { Zhonggui Chen and Xin Li and Juan Cao and Hong Qin},
title = {Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {18},
number = {8},
issn = {1077-2626},
year = {2012},
pages = {1290-1303},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.156},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion
IS - 8
SN - 1077-2626
SP1290
EP1303
EPD - 1290-1303
A1 - Zhonggui Chen,
A1 - Xin Li,
A1 - Juan Cao,
A1 - Hong Qin,
PY - 2012
KW - tensors
KW - computational geometry
KW - least mean squares methods
KW - mesh generation
KW - splines (mathematics)
KW - surface fitting
KW - hierarchical knot insertion
KW - spherical DCB-spline surfaces
KW - adaptive knot insertion
KW - novel surface fitting scheme
KW - continuous parametric spline surface
KW - Delaunay configuration B-spline
KW - nontensor-product spline
KW - surface geometry
KW - genus-0 model
KW - spherical spline representation
KW - reconstructed continuous representation
KW - reverse engineering
KW - shape modeling
KW - root mean square error
KW - Splines (mathematics)
KW - Surface reconstruction
KW - Polynomials
KW - Approximation methods
KW - Surface treatment
KW - Electronic mail
KW - Image reconstruction
KW - non-tensor-product B-splines.
KW - Delaunay configurations
KW - spherical splines
KW - knot placement
KW - knot insertion
VL - 18
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Zhonggui Chen, Dept. of Comput. Sci., Xiamen Univ., Xiamen, China
Xin Li, Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
Juan Cao, Sch. of Math. 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:
Zhonggui Chen, Xin Li, Juan Cao, 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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