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Hierarchical B-spline refinement

Authors:

David R. Forsey,

Richard H. BartelsAuthors Info & Claims

ACM SIGGRAPH Computer Graphics, Volume 22, Issue 4

Pages 205 - 212

https://doi.org/10.1145/378456.378512

Published: 01 June 1988 Publication History

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Abstract

Refinement is usually advocated as a means of gaining finer control over a spline curve or surface during editing. For curves, refinement is a local process. It permits the change of control vertices and subsequent editing of the detail in one region of the curve while leaving control vertices in other regions unaffected. For tensor-product surfaces, however, refinement is not local in the sense that it causes control vertices far from a region of interest to change as well as changing the control vertices that influence the region. However, with some care and understanding it is possible to restrict the influence of refinement to the locality at which an editing effect is desired. We present a method of localizing the effect of refinement through the use of overlays, which are hierarchically controlled subdivisions. We also introduce two editing techniques that are effective when using overlays: one is direct surface manipulation through the use of edit points and the other is offset referencing of control vertices.

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Published In

cover image ACM SIGGRAPH Computer Graphics

ACM SIGGRAPH Computer Graphics Volume 22, Issue 4

Aug. 1988

330 pages

ISSN:0097-8930

DOI:10.1145/378456

Editor:
Richard J. Beach
Xerox PARC, Palo Alto, CA

Issue’s Table of Contents

SIGGRAPH '88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques
August 1988
356 pages
ISBN:0897912756
DOI:10.1145/54852
Editor:
Richard J. Beach
Xerox PARC, Palo Alto, CA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1988

Published in SIGGRAPH Volume 22, Issue 4

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https://doi.org/10.1109/TVCG.2023.3271669
Giannelli CImperatore SKreusser LLoayza-Romero EMohammadi FVillamizar N(2024)A general formulation of reweighted least squares fittingMathematics and Computers in Simulation10.1016/j.matcom.2024.04.029Online publication date: May-2024
https://doi.org/10.1016/j.matcom.2024.04.029
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Wang LYu TFang WBui T(2024)Adaptive multi-patch isogeometric analysis with truncated hierarchical B-splines in isotropic/orthotropic mediaComposite Structures10.1016/j.compstruct.2024.118326(118326)Online publication date: Jul-2024
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Chen JHuang TCai ZHuang W(2024)Generalized multilevel B-spline approximation for scattered data interpolation in image processingApplied Mathematical Modelling10.1016/j.apm.2024.05.010134(538-555)Online publication date: Oct-2024
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Beuchler SHiniborch RMorgenstern P(2024)Deal.t: an implementation of multivariate analysis suitable T-splines within the deal.ii frameworkEngineering with Computers10.1007/s00366-024-02002-1Online publication date: 2-Jul-2024
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