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Stefanie Hahmann, GeorgesPierre Bonneau, "Polynomial Surfaces Interpolating Arbitrary Triangulations," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 1, pp. 99109, JanuaryMarch, 2003.  
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@article{ 10.1109/TVCG.2003.1175100, author = {Stefanie Hahmann and GeorgesPierre Bonneau}, title = {Polynomial Surfaces Interpolating Arbitrary Triangulations}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {9}, number = {1}, issn = {10772626}, year = {2003}, pages = {99109}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2003.1175100}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Polynomial Surfaces Interpolating Arbitrary Triangulations IS  1 SN  10772626 SP99 EP109 EPD  99109 A1  Stefanie Hahmann, A1  GeorgesPierre Bonneau, PY  2003 KW  Triangulation KW  irregular 3D meshes KW  arbitrary topology KW  modeling KW  surfaces KW  triangular patches KW  piecewise polynomial patches KW  interpolation KW  arbitrary tangent vectors KW  reconstruction. VL  9 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—Triangular Bézier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4split method interpolates the vertices of a 2manifold triangle mesh by a set of tangent plane continuous triangular Bézier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular controlpolygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: The tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.
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