The Minkowski sum of two simple surfaces generated by slope-monotone closed curves

Joon Kyung Seong; Myung Soo Kim; K. Sugihara

doi:10.1109/GMAP.2002.1027494

The Minkowski sum of two simple surfaces generated by slope-monotone closed curves

Joon Kyung Seong, Myung Soo Kim, K. Sugihara

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

21 Citations (Scopus)

Abstract

We present an algorithm for computing Minkowski sums among surfaces of revolution and surfaces of linear extrusion, generated by slope-monotone closed curves. The special structure of these simple surfaces allows the process of normal matching between two surfaces to be expressed as an explicit equation. Based on this insight, we also present an efficient algorithm for computing the distance between two simple surfaces, even though they may in general be non-convex. Using an experimental implementation, the distance between two surfaces of revolution was computed in less than 0.5 msec on average.

Original language	English
Title of host publication	Proceedings - Geometric Modeling and Processing
Subtitle of host publication	Theory and Applications, GMP 2002
Editors	Hiromasa Suzuki, Ralph Martin
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	33-42
Number of pages	10
ISBN (Electronic)	0769516742, 9780769516745
DOIs	https://doi.org/10.1109/GMAP.2002.1027494
Publication status	Published - 2002
Externally published	Yes
Event	Geometric Modeling and Processing, GMP 2002 - Wako, Saitama, Japan Duration: 2002 Jul 10 → 2002 Jul 12

Publication series

Name	Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002

Other

Other	Geometric Modeling and Processing, GMP 2002
Country/Territory	Japan
City	Wako, Saitama
Period	02/7/10 → 02/7/12

Bibliographical note

Funding Information:
The authors would like to thank the anonymous reviewers for their useful comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [4] developed at the Technion, Israel. This research was supported in part by the Korean Ministry of Information and Communication (MIC) under the program of IT Research Center for CGVR, and in part by the Korean Ministry of Science and Technology (MOST) under the National Research Lab Project.

Publisher Copyright:
© 2002 IEEE.

ASJC Scopus subject areas

Engineering (miscellaneous)
Geometry and Topology
Modelling and Simulation

Access to Document

10.1109/GMAP.2002.1027494

Cite this

Seong, J. K., Kim, M. S., & Sugihara, K. (2002). The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. In H. Suzuki, & R. Martin (Eds.), Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002 (pp. 33-42). Article 1027494 (Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GMAP.2002.1027494

The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. / Seong, Joon Kyung; Kim, Myung Soo; Sugihara, K.
Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002. ed. / Hiromasa Suzuki; Ralph Martin. Institute of Electrical and Electronics Engineers Inc., 2002. p. 33-42 1027494 (Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Seong, JK, Kim, MS & Sugihara, K 2002, The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. in H Suzuki & R Martin (eds), Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002., 1027494, Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002, Institute of Electrical and Electronics Engineers Inc., pp. 33-42, Geometric Modeling and Processing, GMP 2002, Wako, Saitama, Japan, 02/7/10. https://doi.org/10.1109/GMAP.2002.1027494

Seong JK, Kim MS, Sugihara K. The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. In Suzuki H, Martin R, editors, Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002. Institute of Electrical and Electronics Engineers Inc. 2002. p. 33-42. 1027494. (Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002). doi: 10.1109/GMAP.2002.1027494

Seong, Joon Kyung ; Kim, Myung Soo ; Sugihara, K. / The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002. editor / Hiromasa Suzuki ; Ralph Martin. Institute of Electrical and Electronics Engineers Inc., 2002. pp. 33-42 (Proceedings - Geometric Modeling and Processing: Theory and Applications, GMP 2002).

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abstract = "We present an algorithm for computing Minkowski sums among surfaces of revolution and surfaces of linear extrusion, generated by slope-monotone closed curves. The special structure of these simple surfaces allows the process of normal matching between two surfaces to be expressed as an explicit equation. Based on this insight, we also present an efficient algorithm for computing the distance between two simple surfaces, even though they may in general be non-convex. Using an experimental implementation, the distance between two surfaces of revolution was computed in less than 0.5 msec on average.",

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The Minkowski sum of two simple surfaces generated by slope-monotone closed curves

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