article

A framework for geometric warps and deformations

Authors:

Robert J. Jensen,

Adam FinkelsteinAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 21, Issue 1

Pages 20 - 51

https://doi.org/10.1145/504789.504791

Published: 01 January 2002 Publication History

Abstract

We present a framework for geometric warps and deformations. The framework provides a conceptual and mathematical foundation for analyzing known warps and for developing new warps, and serves as a common base for many warps and deformations. Our framework is composed of two components: a generic modular algorithm for warps and deformations; and a concise, geometrically meaningful formula that describes how warps are evaluated. Together, these two elements comprise a complete framework useful for analyzing, evaluating, designing, and implementing deformation algorithms. While the framework is independent of user-interfaces and geometric model representations and is formally capable of describing any warping algorithm, its design is geared toward the most prevalent class of user-controlled deformations: those computed using geometric operations. To demonstrate the expressive power of the framework, we cast several well-known warps in terms of the framework. To illustrate the framework's usefulness for analyzing and modifying existing warps, we present variations of these warps that provide additional functionality or improved behavior. To show the utility of the framework for developing new warps, we design a novel 3-D warping algorithm: a mesh warp---useful as a modeling and animation tool---that allows users to deform a detailed surface by manipulating a low-resolution mesh of similar shape. Finally, to demonstrate the mathematical utility of the framework, we use the framework to develop guarantees of several mathematical properties such as commutativity and continuity for large classes of deformations.

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Cited By

Zhou DChen XZhang CGuo SAshim KLin J(2022)Research on Topological Deformation of 3D Human Image Based on Laplace Optimization2022 International Conference on High Performance Big Data and Intelligent Systems (HDIS)10.1109/HDIS56859.2022.9991706(329-332)Online publication date: 10-Dec-2022
https://doi.org/10.1109/HDIS56859.2022.9991706
Wang JSilva DKosinka JTelea AHashimoto RRoerdink J(2022)Interactive image manipulation using morphological trees and spline-based skeletonsComputers & Graphics10.1016/j.cag.2022.09.002108(61-73)Online publication date: Nov-2022
https://doi.org/10.1016/j.cag.2022.09.002
Yang GBelongie SHariharan BKoltun VRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Geometry processing with neural fieldsProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541983(22483-22497)Online publication date: 6-Dec-2021
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Index Terms

A framework for geometric warps and deformations
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
    2. Rendering

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 21, Issue 1

January 2002

86 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/504789

Issue’s Table of Contents

Copyright © 2002 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 2002

Published in TOG Volume 21, Issue 1

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Cited By

Zhou DChen XZhang CGuo SAshim KLin J(2022)Research on Topological Deformation of 3D Human Image Based on Laplace Optimization2022 International Conference on High Performance Big Data and Intelligent Systems (HDIS)10.1109/HDIS56859.2022.9991706(329-332)Online publication date: 10-Dec-2022
https://doi.org/10.1109/HDIS56859.2022.9991706
Wang JSilva DKosinka JTelea AHashimoto RRoerdink J(2022)Interactive image manipulation using morphological trees and spline-based skeletonsComputers & Graphics10.1016/j.cag.2022.09.002108(61-73)Online publication date: Nov-2022
https://doi.org/10.1016/j.cag.2022.09.002
Yang GBelongie SHariharan BKoltun VRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Geometry processing with neural fieldsProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541983(22483-22497)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3541983
Yan ZSchaefer S(2019)A Family of Barycentric Coordinates for Co‐Dimension 1 Manifolds with Simplicial FacetsComputer Graphics Forum10.1111/cgf.1379038:5(75-83)Online publication date: 12-Aug-2019
https://doi.org/10.1111/cgf.13790
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Favorskaya MBuryachenko V(2017)Warping Techniques in Video StabilizationComputer Vision in Control Systems-310.1007/978-3-319-67516-9_7(177-215)Online publication date: 27-Oct-2017
https://doi.org/10.1007/978-3-319-67516-9_7
Ciccone LGuay MSumner R(2016)Flow CurvesComputer Graphics Forum10.5555/3151666.315169235:7(247-256)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.5555/3151666.3151692
Wu J(2016)Image Deformation by User-Defined Force FieldsJournal of Signal and Information Processing10.4236/jsip.2016.7100407:01(27-33)Online publication date: 2016
https://doi.org/10.4236/jsip.2016.71004
Ciccone LGuay MSumner R(2016)Flow Curves: an Intuitive Interface for Coherent Scene DeformationComputer Graphics Forum10.1111/cgf.1302235:7(247-256)Online publication date: 27-Oct-2016
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He XChoi K(2015)Using analytical force model for efficient deformation simulation and haptic rendering of soft objectsMultimedia Tools and Applications10.1007/s11042-013-1720-574:6(1823-1844)Online publication date: 1-Mar-2015
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