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.
| Original language | English |
|---|---|
| Pages (from-to) | 499-508 |
| Number of pages | 10 |
| Journal | Journal of Mechanical Design, Transactions Of the ASME |
| Volume | 118 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1996 Jan 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
Cite this
Computation of shortest paths on free-form parametric surfaces. / Maekawa, Takashi.
In: Journal of Mechanical Design, Transactions Of the ASME, Vol. 118, No. 4, 01.01.1996, p. 499-508.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Computation of shortest paths on free-form parametric surfaces
AU - Maekawa, Takashi
PY - 1996/1/1
Y1 - 1996/1/1
N2 - 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.
AB - 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.
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U2 - 10.1115/1.2826919
DO - 10.1115/1.2826919
M3 - Article
VL - 118
SP - 499
EP - 508
JO - Journal of Mechanical Design - Transactions of the ASME
JF - Journal of Mechanical Design - Transactions of the ASME
SN - 1050-0472
IS - 4
ER -