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Quasi-Developable Mesh Surface Interpolation via Mesh Deformation
May/June 2009 (vol. 15 no. 3)
pp. 518-528
ASCII Text
x 
 
Kai Tang, Ming Chen, "Quasi-Developable Mesh Surface Interpolation via Mesh Deformation," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 3, pp. 518-528, May/June, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2008.192,
author = {Kai Tang and Ming Chen},
title = {Quasi-Developable Mesh Surface Interpolation via Mesh Deformation},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {15},
number = {3},
issn = {1077-2626},
year = {2009},
pages = {518-528},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.192},
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 - Quasi-Developable Mesh Surface Interpolation via Mesh Deformation
IS - 3
SN - 1077-2626
SP518
EP528
EPD - 518-528
A1 - Kai Tang,
A1 - Ming Chen,
PY - 2009
KW - Least squares methods
KW - Computer-aided design
KW - Surface fitting
KW - Developable surface
VL - 15
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Kai Tang, Hong Kong University of Science and Technology, Hong Kong
Ming Chen, Hong Kong University of Science and Technology, Hong Kong
We present a new algorithm for finding a most "developable" smooth mesh surface to interpolate a given set of arbitrary points or space curves. Inspired by the recent progress in mesh editing that employs the concepts of preserving the Laplacian coordinates and handle-based shape editing, we formulate the interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, such as a planar figure, to a final mesh surface that interpolates the given points and/or curves. During the deformation, the developability of the intermediate mesh is maintained by means of preserving the zero-valued Gaussian curvature on the mesh. To treat the high nonlinearity of the geometric constrains owing to the preservation of Gaussian curvature, we linearize those nonlinear constraints using Taylor expansion and eventually construct a sparse and over-determined linear system which is subsequently solved by a robust least-squares solution. By iteratively performing this procedure, the initial mesh is gradually and smoothly "dragged" to the given points and/or curves. The initial experimental data has shown some promising aspects of the proposed algorithm as a general quasi-developable surface interpolation tool.

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Index Terms:
Least squares methods, Computer-aided design, Surface fitting, Developable surface
Citation:
Kai Tang, Ming Chen, "Quasi-Developable Mesh Surface Interpolation via Mesh Deformation," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 3, pp. 518-528, May-June 2009, doi:10.1109/TVCG.2008.192
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