Maximum number of degenerate curves in 3D linear tensor Fields

Yue Zhang, Yu Jong Tzeng, Eugene Zhang

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations


3D symmetric tensor fields have a wide range of applications in science and engineering. The topology of a symmetric tensor field, which consists of degenerate curves, can provide critical insights into the behaviors of the tensor fields. Existing methods to extract degenerate curves make some assumptions of the maximum number of degenerate curves in a cell without validating this bound. In this paper, we study the maximum number of degenerate curves in a linear tensor field to contribute to accurate and efficient extraction methods.

Original languageEnglish (US)
Title of host publicationMathematics and Visualization
PublisherSpringer Heidelberg
Number of pages14
ISBN (Electronic)9783319446844
ISBN (Print)9783319446820, 9783319912738, 9783540250326, 9783540250760, 9783540332749, 9783540886051, 9783642150135, 9783642216077, 9783642231742, 9783642273421, 9783642341403, 9783642543005
StatePublished - 2017

Publication series

NameMathematics and Visualization
ISSN (Print)1612-3786
ISSN (Electronic)2197-666X

Bibliographical note

Funding Information:
We wish to thank Christine Escher for valuable discussions concerning Veroness maps. We are also grateful for the constructive comments from our anonymous reviewers. Yue Zhang and Eugene Zhang are partially supported by National Science Foundation Awards IIS 15662236 and 1619383, respectively.

Publisher Copyright:
© 2017, Springer International Publishing AG.


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