research-article

Interactive Tensor Field Design and Visualization on Surfaces

Authors:

Greg TurkAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 13, Issue 1

Pages 94 - 107

https://doi.org/10.1109/TVCG.2007.16

Published: 01 January 2007 Publication History

Abstract

Designing tensor fields in the plane and on surfaces is a necessary task in many graphics applications, such as painterly rendering, pen-and-ink sketching of smooth surfaces, and anisotropic remeshing. In this article, we present an interactive design system that allows a user to create a wide variety of symmetric tensor fields over 3D surfaces either from scratch or by modifying a meaningful input tensor field such as the curvature tensor. Our system converts each user specification into a basis tensor field and combines them with the input field to make an initial tensor field. However, such a field often contains unwanted degenerate points which cannot always be eliminated due to topological constraints of the underlying surface. To reduce the artifacts caused by these degenerate points, our system allows the user to move a degenerate point or to cancel a pair of degenerate points that have opposite tensor indices. These operations provide control over the number and location of the degenerate points in the field. We observe that a tensor field can be locally converted into a vector field so that there is a one-to-one correspondence between the set of degenerate points in the tensor field and the set of singularities in the vector field. This conversion allows us to effectively perform degenerate point pair cancellation and movement by using similar operations for vector fields. In addition, we adapt the image-based flow visualization technique to tensor fields, therefore allowing interactive display of tensor fields on surfaces. We demonstrate the capabilities of our tensor field design system with painterly rendering, pen-and-ink sketching of surfaces, and anisotropic remeshing.

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Cited By

Hung SZhang YZhang E(2024)Global Topology of 3D Symmetric Tensor FieldsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332693330:1(1282-1291)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326933
Zheng JZhang EZhang Y(2024)Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic OrbifoldsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332692730:1(1292-1301)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326927
Schott HParis AFournier LGuérin EGalin E(2023)Large-scale Terrain Authoring through Interactive Erosion SimulationACM Transactions on Graphics10.1145/359278742:5(1-15)Online publication date: 28-Jul-2023
https://dl.acm.org/doi/10.1145/3592787
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Index Terms

Interactive Tensor Field Design and Visualization on Surfaces
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Image and video acquisition
        3D imaging
  2. Computer graphics

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 13, Issue 1

January 2007

192 pages

ISSN:1077-2626

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Copyright © 2007.

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IEEE Educational Activities Department

United States

Publication History

Published: 01 January 2007

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Cited By

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https://dl.acm.org/doi/10.1109/TVCG.2023.3326933
Zheng JZhang EZhang Y(2024)Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic OrbifoldsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332692730:1(1292-1301)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326927
Schott HParis AFournier LGuérin EGalin E(2023)Large-scale Terrain Authoring through Interactive Erosion SimulationACM Transactions on Graphics10.1145/359278742:5(1-15)Online publication date: 28-Jul-2023
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Wilde TRössl CTheisel H(2020)Flow Map Processing by Space-Time DeformationAdvances in Visual Computing10.1007/978-3-030-64556-4_19(236-247)Online publication date: 5-Oct-2020
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Bessmeltsev MSolomon J(2019)Vectorization of Line Drawings via Polyvector FieldsACM Transactions on Graphics10.1145/320266138:1(1-12)Online publication date: 19-Jan-2019
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Roy LKumar PZhang YZhang E(2019)Robust and Fast Extraction of 3D Symmetric Tensor Field TopologyIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2018.286476825:1(1102-1111)Online publication date: 1-Jan-2019
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