|
HKUST Institutional Repository >
Mechanical Engineering >
MECH Journal/Magazine Articles >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1783.1/6775
|
| Title: | Quasi-developable mesh surface interpolation via mesh deformation |
| Authors: | Tang, Kai
Chen, Ming |
| Keywords: | Computer-aided design
Developable surface
Least squares methods
Surface fitting |
| Issue Date: | Mar-2009 |
| Citation: | IEEE transactions on visualization and computer graphics, v. 15, no. 3, May-June 2009, p. 518-528 |
| Abstract: | 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. |
| Rights: | © 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. |
| URI: | http://hdl.handle.net/1783.1/6775 |
| Appears in Collections: | MECH Journal/Magazine Articles
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| quasidevelop.pdf | | 2745Kb | Adobe PDF | View/Open |
|
Find published version via |
All items in this Repository are protected by copyright, with all rights reserved.
|
