Variational skinning of an ordered set of discrete 2D balls

Greg Slabaugh; Gozde Unal; Tong Fang; Jarek Rossignac; Brian Whited

doi:10.1007/978-3-540-79246-8_34

Variational skinning of an ordered set of discrete 2D balls

Greg Slabaugh^*, Gozde Unal, Tong Fang, Jarek Rossignac, Brian Whited

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

This paper considers the problem of computing an interpolating skin of a ordered set of discrete 2D balls. By construction, the skin is constrained to be C ¹ continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's arc length, curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations.

Original language	English
Title of host publication	Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings
Publisher	Springer Verlag
Pages	450-461
Number of pages	12
ISBN (Print)	3540792457, 9783540792451
DOIs	https://doi.org/10.1007/978-3-540-79246-8_34
Publication status	Published - 2008
Externally published	Yes
Event	5th International Conference on Geometric Modeling and Processing, GMP 2008 - Hangzhou, China Duration: 23 Apr 2008 → 25 Apr 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4975 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Conference on Geometric Modeling and Processing, GMP 2008
Country/Territory	China
City	Hangzhou
Period	23/04/08 → 25/04/08

Access to Document

10.1007/978-3-540-79246-8_34

Cite this

Slabaugh, G., Unal, G., Fang, T., Rossignac, J., & Whited, B. (2008). Variational skinning of an ordered set of discrete 2D balls. In Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings (pp. 450-461). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4975 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-79246-8_34

Slabaugh, Greg ; Unal, Gozde ; Fang, Tong et al. / Variational skinning of an ordered set of discrete 2D balls. Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings. Springer Verlag, 2008. pp. 450-461 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Variational skinning of an ordered set of discrete 2D balls",

abstract = "This paper considers the problem of computing an interpolating skin of a ordered set of discrete 2D balls. By construction, the skin is constrained to be C 1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's arc length, curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations.",

author = "Greg Slabaugh and Gozde Unal and Tong Fang and Jarek Rossignac and Brian Whited",

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Slabaugh, G, Unal, G, Fang, T, Rossignac, J & Whited, B 2008, Variational skinning of an ordered set of discrete 2D balls. in Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4975 LNCS, Springer Verlag, pp. 450-461, 5th International Conference on Geometric Modeling and Processing, GMP 2008, Hangzhou, China, 23/04/08. https://doi.org/10.1007/978-3-540-79246-8_34

Variational skinning of an ordered set of discrete 2D balls. / Slabaugh, Greg; Unal, Gozde; Fang, Tong et al.
Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings. Springer Verlag, 2008. p. 450-461 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4975 LNCS).

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

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N2 - This paper considers the problem of computing an interpolating skin of a ordered set of discrete 2D balls. By construction, the skin is constrained to be C 1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's arc length, curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations.

AB - This paper considers the problem of computing an interpolating skin of a ordered set of discrete 2D balls. By construction, the skin is constrained to be C 1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's arc length, curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations.

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SN - 9783540792451

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Slabaugh G, Unal G, Fang T, Rossignac J, Whited B. Variational skinning of an ordered set of discrete 2D balls. In Advances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings. Springer Verlag. 2008. p. 450-461. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-79246-8_34

Variational skinning of an ordered set of discrete 2D balls

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