Blending surface generation using a fast and accurate analytical solution of a fourth-order PDE with three shape control parameters

This source preferred by Jian Jun Zhang and Lihua You

Authors: You, L.H., Zhang, J.J. and Comninos, P.

http://www.springerlink.com/content/rehdyl0g17r22rjj/fulltext.pdf

Journal: The Visual Computer

Volume: 20

Pages: 199-214

ISSN: 0178-2789

DOI: 10.1007/s00371-004-0241-7

In this paper, we propose to use a fourth-order partial differential equation (PDE) to solve a class of surface-blending problems. This equation has three vector-valued shape control parameters. It incorporates all the previously published forms of fourth-order PDEs for surface blending and can generate a larger class of blending surfaces than existing equations. To apply the proposed PDE to the solution of various blending problems, we have developed a fast and accurate resolution method. Our method modifies Navier’s solution for the elastic bending deformation of thin plates by making it satisfy the boundary conditions exactly. A comparison between our method, the closed-form solution method, and other existing analytical methods indicates that the developed method is able to generate blending surfaces almost as quickly and accurately as the closed-form solution method, far more efficiently and accurately than the numerical methods and other existing analytical methods. Having investigated the effects that the vector-valued shape parameters and the force function of the proposed equation have on the blending surface, we have found that they have a significant influence on its shape. They provide flexible user handles that surface designers can use to adjust the blending surface to acquire the desired shape. The developed method was employed in the investigation of surface-blending problems where the primary surfaces were expressed in parametric, implicit, and explicit forms.

This data was imported from DBLP:

Authors: You, L., Zhang, J.J. and Comninos, P.

Journal: The Visual Computer

Volume: 20

Pages: 199-214

This data was imported from Scopus:

Authors: You, L., Zhang, J.J. and Comninos, P.

Journal: Visual Computer

Volume: 20

Issue: 2-3

Pages: 199-214

ISSN: 0178-2789

DOI: 10.1007/s00371-004-0241-7

In this paper, we propose to use a fourth-order partial differential equation (PDE) to solve a class of surface-blending problems. This equation has three vector-valued shape control parameters. It incorporates all the previously published forms of fourth-order PDEs for surface blending and can generate a larger class of blending surfaces than existing equations. To apply the proposed PDE to the solution of various blending problems, we have developed a fast and accurate resolution method. Our method modifies Navier's solution for the elastic bending deformation of thin plates by making it satisfy the boundary conditions exactly. A comparison between our method, the closed-form solution method, and other existing analytical methods indicates that the developed method is able to generate blending surfaces almost as quickly and accurately as the closed-form solution method, far more efficiently and accurately than the numerical methods and other existing analytical methods. Having investigated the effects that the vector-valued shape parameters and the force function of the proposed equation have on the blending surface, we have found that they have a significant influence on its shape, They provide flexible user handles that surface designers can use to adjust the blending surface to acquire the desired shape. The developed method was employed in the investigation of surface-blending problems where the primary surfaces were expressed in parametric, implicit, and explicit forms.

This data was imported from Web of Science (Lite):

Authors: You, L.H., Zhang, J.J. and Comninos, P.

Journal: VISUAL COMPUTER

Volume: 20

Issue: 2-3

Pages: 199-214

eISSN: 1432-2315

ISSN: 0178-2789

DOI: 10.1007/s00371-004-0241-7

The data on this page was last updated at 05:17 on May 25, 2020.