Gaussian curvature based tangential redistribution of points on evolving surfaces

Medľa, Matej; Mikula, Karol

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 255-264

Abstract

top
There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.

How to cite

top

Medľa, Matej, and Mikula, Karol. "Gaussian curvature based tangential redistribution of points on evolving surfaces." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 255-264. <http://eudml.org/doc/294907>.

@inProceedings{Medľa2017,
abstract = {There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.},
author = {Medľa, Matej, Mikula, Karol},
booktitle = {Proceedings of Equadiff 14},
keywords = {Surface evolution, point redistribution, finite volume method, mean curvature flow},
location = {Bratislava},
pages = {255-264},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Gaussian curvature based tangential redistribution of points on evolving surfaces},
url = {http://eudml.org/doc/294907},
year = {2017},
}

TY - CLSWK
AU - Medľa, Matej
AU - Mikula, Karol
TI - Gaussian curvature based tangential redistribution of points on evolving surfaces
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 255
EP - 264
AB - There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.
KW - Surface evolution, point redistribution, finite volume method, mean curvature flow
UR - http://eudml.org/doc/294907
ER -

References

top
  1. Freitag, L. A., On combining Laplacian and optimization-based mesh smoothing techniques, , American Society of Mechanical Engineers, Applied Mechanics Division, AMD, (1999). 
  2. Húska, M., Medľa, M., Mikula, K., Morigi, S., Surface quadrangulation, , in preparation. 
  3. Liu, D., Xu, G., Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes, , In Computer-Aided Design, Volume 39, Issue 6, 2007, pp. 506-517, ISSN 0010-4485, https://doi.org/10.1016/j.cad.2007.01.007. 
  4. Mikula, K., Remešíková, M., Sarkoci, P., Ševčovič, D., Manifold evolution with tangential redistribution of points, , SIAM J. Scientific Computing, 36, No. 4 (2014), pp. A1384-A1414. MR3226752
  5. Ševčovič, D., Yazaki, S., Evolution of plane curves with a curvature adjusted tangential velocity, , Japan J. Indust. Appl. Math., 28(3) (2011), 413-442. MR2846183

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.