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Jianmin Zheng, Yiyu Cai, "Interpolation over Arbitrary Topology Meshes Using a TwoPhase Subdivision Scheme," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 3, pp. 301310, May/June, 2006.  
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@article{ 10.1109/TVCG.2006.49, author = {Jianmin Zheng and Yiyu Cai}, title = {Interpolation over Arbitrary Topology Meshes Using a TwoPhase Subdivision Scheme}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {3}, issn = {10772626}, year = {2006}, pages = {301310}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.49}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Interpolation over Arbitrary Topology Meshes Using a TwoPhase Subdivision Scheme IS  3 SN  10772626 SP301 EP310 EPD  301310 A1  Jianmin Zheng, A1  Yiyu Cai, PY  2006 KW  Computer graphics; computational geometry and object modeling; curve KW  surface KW  solid KW  and object representations; computeraided engineering; computeraided design. VL  12 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—The construction of a smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. This paper presents a twophase process, based on a topological modification of the control mesh and a subsequent CatmullClark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be interpolated. The method has the following features: 1) It is guaranteed to always work and the computation is numerically stable, 2) there is no need to solve a system of linear equations and the whole computation complexity is
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