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Hierarchical and variational geometric modeling with wavelets

Authors:

Steven J. Gortler,

Michael F. CohenAuthors Info & Claims

I3D '95: Proceedings of the 1995 symposium on Interactive 3D graphics

Pages 35 - ff.

https://doi.org/10.1145/199404.199410

Published: 15 April 1995 Publication History

Abstract

This paper discusses how wavelet techniques may be applied to a variety of geometric modeling tools. In particular, wavelet decompositions are shown to be useful for hierarchical control point or least squares editing. In addition, direct curve and surface manipulation methods using an underlying geometric variational principle can be solved more efficiently by using a wavelet basis. Because the wavelet basis is hierarchical, iterative solution methods converge rapidly. Also, since the wavelet coefficients indicate the degree of detail in the solution, the number of basis functions needed to express the variational minimum can be reduced, avoiding unnecessary computation. An implementation of a curve and surface modeler based on these ideas is discussed and experimental results are reported.

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cover image ACM Conferences

I3D '95: Proceedings of the 1995 symposium on Interactive 3D graphics

April 1995

218 pages

ISBN:0897917367

DOI:10.1145/199404

Chairman:
Michael Zyda
Naval Postgraduate School, Monterey, CA

Copyright © 1995 ACM.

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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Published: 15 April 1995

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SI3D95: 1995 Symposium on Interactive 3D Graphics

April 9 - 12, 1995

California, Monterey, USA

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Cited By

Petruzza SSumma BGooch ALaney CGoulden TSchreiner JCallahan SPascucci V(2023)Interactive Visualization and Portable Image Blending of Massive Aerial Image Mosaics2023 IEEE International Conference on Big Data (BigData)10.1109/BigData59044.2023.10386428(3365-3370)Online publication date: 15-Dec-2023
https://doi.org/10.1109/BigData59044.2023.10386428
Zhoutong Zhang Liu YDai Q(2015)Light field from micro-baseline image pair2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR.2015.7299004(3800-3809)Online publication date: Jun-2015
https://doi.org/10.1109/CVPR.2015.7299004
Anderson SDellaert FBarfoot T(2014)A hierarchical wavelet decomposition for continuous-time SLAM2014 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA.2014.6906884(373-380)Online publication date: May-2014
https://doi.org/10.1109/ICRA.2014.6906884
Bornemann PCirak F(2013)A subdivision-based implementation of the hierarchical b-spline finite element methodComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2012.06.023253(584-598)Online publication date: Jan-2013
https://doi.org/10.1016/j.cma.2012.06.023
Jager GKunoth ASchuh W(2013)Approximate continuation of harmonic functions in geodesyJournal of Computational and Applied Mathematics10.1016/j.cam.2012.07.007237:1(62-82)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1016/j.cam.2012.07.007
Krishnan DSzeliski R(2011)Multigrid and multilevel preconditioners for computational photographyACM Transactions on Graphics10.1145/2070781.202421130:6(1-10)Online publication date: 12-Dec-2011
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Krishnan DSzeliski R(2011)Multigrid and multilevel preconditioners for computational photographyProceedings of the 2011 SIGGRAPH Asia Conference10.1145/2024156.2024211(1-10)Online publication date: 12-Dec-2011
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Wang WZhang Y(2010)Wavelets-based NURBS simplification and fairingComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2009.04.003199:5-8(290-300)Online publication date: Jan-2010
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Kazhdan MHoppe H(2008)Streaming multigrid for gradient-domain operations on large imagesACM SIGGRAPH 2008 papers10.1145/1399504.1360620(1-10)Online publication date: 11-Aug-2008
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