Article

Poisson shape interpolation

Authors:

Hujun BaoAuthors Info & Claims

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

Pages 267 - 274

https://doi.org/10.1145/1060244.1060274

Published: 13 June 2005 Publication History

Abstract

In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.

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Cited By

Horimoto ASato SSakurai KNakamoto K(2025)A shape control method for soap bubble simulation using external forcesScientific Reports10.1038/s41598-025-90850-215:1Online publication date: 6-Mar-2025
https://doi.org/10.1038/s41598-025-90850-2
Yerimbetova ADaiyrbayeva EMerzlyakova EFionov ABaisholan NTurdalyuly MMukazhanov NTurganbayev A(2023)Creating Digital Watermarks in Bitmap Images Using Lagrange Interpolation and Bezier CurvesJournal of Imaging10.3390/jimaging91002069:10(206)Online publication date: 29-Sep-2023
https://doi.org/10.3390/jimaging9100206
Even MBénard PBarla P(2023)Non‐linear Rough 2D Animation using Transient EmbeddingsComputer Graphics Forum10.1111/cgf.1477142:2(411-425)Online publication date: 23-May-2023
https://doi.org/10.1111/cgf.14771
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Index Terms

Poisson shape interpolation
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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cover image ACM Conferences

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

June 2005

287 pages

ISBN:1595930159

DOI:10.1145/1060244

Program Chairs:
Leif Kobbelt
RWTH Aachen University, Germany
,
Vadim Shapiro
University of Wisconsin--Madison, USA

Copyright © 2005 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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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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New York, NY, United States

Publication History

Published: 13 June 2005

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SPM05

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SPM05: 2005 ACM Symposium on Solid and Physical Modeling

June 13 - 15, 2005

Massachusetts, Cambridge

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Cited By

Horimoto ASato SSakurai KNakamoto K(2025)A shape control method for soap bubble simulation using external forcesScientific Reports10.1038/s41598-025-90850-215:1Online publication date: 6-Mar-2025
https://doi.org/10.1038/s41598-025-90850-2
Yerimbetova ADaiyrbayeva EMerzlyakova EFionov ABaisholan NTurdalyuly MMukazhanov NTurganbayev A(2023)Creating Digital Watermarks in Bitmap Images Using Lagrange Interpolation and Bezier CurvesJournal of Imaging10.3390/jimaging91002069:10(206)Online publication date: 29-Sep-2023
https://doi.org/10.3390/jimaging9100206
Even MBénard PBarla P(2023)Non‐linear Rough 2D Animation using Transient EmbeddingsComputer Graphics Forum10.1111/cgf.1477142:2(411-425)Online publication date: 23-May-2023
https://doi.org/10.1111/cgf.14771
Vyas SChen TMohanty RJiang PKrishnamurthy V(2021)Latent Embedded Graphs for Image and Shape InterpolationComputer-Aided Design10.1016/j.cad.2021.103091140:COnline publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.cad.2021.103091
Sassen JHildebrandt KRumpf M(2020)Nonlinear Deformation Synthesis via Sparse Principal Geodesic AnalysisComputer Graphics Forum10.1111/cgf.1407339:5(119-132)Online publication date: 12-Aug-2020
https://doi.org/10.1111/cgf.14073
Sassen JHeeren BHildebrandt KRumpf M(2020)Geometric optimization using nonlinear rotation-invariant coordinatesComputer Aided Geometric Design10.1016/j.cagd.2020.10182977(101829)Online publication date: Feb-2020
https://doi.org/10.1016/j.cagd.2020.101829
Eisenberger MCremers D(2020)Hamiltonian Dynamics for Real-World Shape InterpolationComputer Vision – ECCV 202010.1007/978-3-030-58548-8_11(179-196)Online publication date: 29-Oct-2020
https://doi.org/10.1007/978-3-030-58548-8_11
Domadiya PShah DMitra S(2019)Guided Deformation TransferProceedings of the 16th ACM SIGGRAPH European Conference on Visual Media Production10.1145/3359998.3369408(1-10)Online publication date: 17-Dec-2019
https://dl.acm.org/doi/10.1145/3359998.3369408
Boukhayma ABoyer E(2019)Surface Motion Capture Animation SynthesisIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2018.283123325:6(2270-2283)Online publication date: 1-Jun-2019
https://doi.org/10.1109/TVCG.2018.2831233
Yang WHua JYao K(2019)CR-Morph: Controllable Rigid Morphing for 2D AnimationJournal of Computer Science and Technology10.1007/s11390-019-1963-334:5(1109-1122)Online publication date: 6-Sep-2019
https://doi.org/10.1007/s11390-019-1963-3
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