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A butterfly subdivision scheme for surface interpolation with tension control

Editor: John C. Beatty Authors:

Nira Dyn,

David Levine,

John A. GregoryAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 9, Issue 2

Pages 160 - 169

https://doi.org/10.1145/78956.78958

Published: 01 April 1990 Publication History

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Abstract

A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C¹ for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.

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A butterfly subdivision scheme for surface interpolation with tension control

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Reviews

Reviewer: Heinrich W. Guggenheimer

The authors have previously studied the convergence of linear interpolatory subdivision schemes for B-spline curves [1]. The schemes investigated generally do not yield smooth (C 2 ) curves. This paper reports on an implementation of a linear interpolatory subdivision scheme for triangulated surfaces (constructing a new subdivision point out of eight neighbors). This scheme depends on a scalar or tensor parameter for which a formal regularity analysis of the limit surface is not available, but it seems to work well (within the narrow limits on the parameters imposed by geometry) on piecewise C 1 surfaces. The usefulness of such a scheme in design experimentation obviously depends on the speed of computation, which in turn depends much more on the internal data structures of the program than on the mathematics of the algorithm. The entire field of CAD would be in much better shape if researchers made their programs available or indicated enough of the crucial technicalities. The bibliography gives a nice survey of the work done in this field.

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 9, Issue 2

April 1990

86 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/78956

Editor:
John C. Beatty

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1990

Published in TOG Volume 9, Issue 2

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https://doi.org/10.1186/s12938-024-01251-x
Edavamadathil Sivaram VLi TRamamoorthi R(2024)Neural Geometry Fields For MeshesACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657399(1-11)Online publication date: 13-Jul-2024
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Ghaffar AMustafa GAbdul Karim S(2024)A 3-point point quinary approximating subdivision schemes and its application in geometric modeling and computer graphicsITM Web of Conferences10.1051/itmconf/2024630101863(01018)Online publication date: 13-Feb-2024
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Abstract

References

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Index Terms

Recommendations

A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control

A generalized curve subdivision scheme of arbitrary order with a tension parameter

A generalized surface subdivision scheme of arbitrary order with a tension parameter

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