A C1 globally interpolatory spline of arbitrary topology

Ying He; Miao Jin; Xianfeng Gu; Hong Qin

doi:10.1007/11567646_25

A C¹ globally interpolatory spline of arbitrary topology

Ying He
, Miao Jin
, Xianfeng Gu
, Hong Qin

Computer Science

Stony Brook University

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

15 Scopus citations

Abstract

Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics. This paper presents a C¹ manifold interpolatory spline that can exactly pass through all the vertices and interpolate their normals for data input of complicated topological type. Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas, and splines defined over local, open domains to arrive at an elegant, easy-to-use spline solution for complicated datasets. The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.

Original language	English
Title of host publication	Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings
Publisher	Springer Verlag
Pages	295-306
Number of pages	12
ISBN (Print)	3540293485, 9783540293484
DOIs	https://doi.org/10.1007/11567646_25
State	Published - 2005
Event	3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005 - Beijing, China Duration: Oct 16 2005 → Oct 16 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3752 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005
Country/Territory	China
City	Beijing
Period	10/16/05 → 10/16/05

Access to Document

10.1007/11567646_25

Cite this

He, Y., Jin, M., Gu, X., & Qin, H. (2005). A C¹ globally interpolatory spline of arbitrary topology. In Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings (pp. 295-306). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3752 LNCS). Springer Verlag. https://doi.org/10.1007/11567646_25

He, Ying ; Jin, Miao ; Gu, Xianfeng et al. / A C¹ globally interpolatory spline of arbitrary topology. Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings. Springer Verlag, 2005. pp. 295-306 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A C1 globally interpolatory spline of arbitrary topology",

abstract = "Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics. This paper presents a C1 manifold interpolatory spline that can exactly pass through all the vertices and interpolate their normals for data input of complicated topological type. Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas, and splines defined over local, open domains to arrive at an elegant, easy-to-use spline solution for complicated datasets. The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.",

author = "Ying He and Miao Jin and Xianfeng Gu and Hong Qin",

year = "2005",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "295--306",

booktitle = "Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings",

note = "3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005 ; Conference date: 16-10-2005 Through 16-10-2005",

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He, Y, Jin, M, Gu, X & Qin, H 2005, A C¹ globally interpolatory spline of arbitrary topology. in Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3752 LNCS, Springer Verlag, pp. 295-306, 3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005, Beijing, China, 10/16/05. https://doi.org/10.1007/11567646_25

A C¹ globally interpolatory spline of arbitrary topology. / He, Ying; Jin, Miao; Gu, Xianfeng et al.
Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings. Springer Verlag, 2005. p. 295-306 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3752 LNCS).

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

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He Y, Jin M, Gu X , Qin H. A C¹ globally interpolatory spline of arbitrary topology. In Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings. Springer Verlag. 2005. p. 295-306. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11567646_25