We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.
%0 Conference Paper
%1 klotzl2022reduced
%A Klötzl, Daniel
%A Krake, Tim
%A Zhou, Youjia
%A Stober, Jonathan
%A Schulte, Kathrin
%A Hotz, Ingrid
%A Wang, Bei
%A Weiskopf, Daniel
%B 2022 Topological Data Analysis and Visualization (TopoInVis)
%D 2022
%I IEEE
%K 2022 dropit myown visus visus:kloetzdl visus:kraketm visus:weiskopf
%P 39-48
%R 10.1109/TopoInVis57755.2022.00011
%T Reduced Connectivity for Local Bilinear Jacobi Sets
%U https://doi.org/10.1109/TopoInVis57755.2022.00011
%X We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.
%@ 978-1-6654-9354-3
@inproceedings{klotzl2022reduced,
abstract = {We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.},
added-at = {2023-01-16T13:58:36.000+0100},
author = {Klötzl, Daniel and Krake, Tim and Zhou, Youjia and Stober, Jonathan and Schulte, Kathrin and Hotz, Ingrid and Wang, Bei and Weiskopf, Daniel},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2b7a70399d3649f2a067cbb283f9ca182/kloetzdl},
booktitle = {2022 Topological Data Analysis and Visualization (TopoInVis)},
doi = {10.1109/TopoInVis57755.2022.00011},
eventdate = {17 Oct. 2022},
interhash = {dff036a42ce45a510efb6fccadcc4716},
intrahash = {b7a70399d3649f2a067cbb283f9ca182},
isbn = {978-1-6654-9354-3},
keywords = {2022 dropit myown visus visus:kloetzdl visus:kraketm visus:weiskopf},
pages = {39-48},
publisher = {IEEE},
timestamp = {2023-08-03T12:30:32.000+0200},
title = {Reduced Connectivity for Local Bilinear Jacobi Sets},
url = {https://doi.org/10.1109/TopoInVis57755.2022.00011},
venue = {Oklahoma City, OK, USA},
year = 2022
}
