Computation of Shortest Paths on Free-Form Parametric Surfaces-Reference-Cited by-同舟云学术

Computation of Shortest Paths on Free-Form Parametric Surfaces

Published:1996-12-01 Issue:4 Volume:118 Page:499-508
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Maekawa T.¹

Affiliation:

1. Department of Ocean Engineering, Massachusetts Institute of Technology, Design Laboratory, Cambridge, MA 02139-4307

Abstract

Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/118/4/499/5666706/499_1.pdf

Reference16 articles.

1. Beck J. M. , FaroukiR. T., and HindsJ. K., “Surface Analysis Methods,” IEEE Computer Graphics and Applications, Vol. 6, No. 12, pp. 18–36, December 1986.

2. Bliss G. A. , “The Geodesic Lines on the Anchor Ring,” Annals of Mathematics, Vol. 4, pp. 1–21, October 1902.

3. Dahlquist, G., and Bjo¨rck, A., Numerical Methods, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974.

4. do Carmo, P. M., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.

5. Ferziger, J. H., Numerical Methods for Engineering Applications, Wiley, 1981.

Cited by 35 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Generation of Tow Paths on a Curved Shell in Three-Dimensional Space for Fiber Steering;Journal of Aircraft;2024-07

2. Geometric modeling of phase ordering for the isotropic–smectic A phase transition;Frontiers in Soft Matter;2024-05-21

3. Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution;Soft Matter;2023

4. Approximation of doubly curved surfaces by analysis-suitable piecewise surfaces with high developability;The Visual Computer;2022-12-01

5. A discrete mechanics approach for musculoskeletal simulations with muscle wrapping;Multibody System Dynamics;2022-10-11