# On the Link between Mesh Size Adaptation and Irregular Vertices

### Daniel Zint, Roberto Grosso

#### Abstract

In numerical simulations and computer graphics meshes are often required to have varying element sizes. High resolution, i.e. small elements, should be only used where necessary. The transition between element sizes requires introducing irregular vertices. In this work, we examine the occurance of irregular vertices in transition regions by setting up an advancing front triangulation that generates optimal transitions. We establish a relation between the appearance of irregular vertices and the properties of the size function and show that a linear transition between different element sizes can be achieved without any singularities on the interior of the transition. Therefore, we can optimize triangulations by setting transition fronts accordingly. These results are used to estimate properties of block-structured grids, e.g. how many blocks are required to represent a given domain correctly.

Download#### Paper Citation

#### in Harvard Style

Zint D. and Grosso R. (2021). **On the Link between Mesh Size Adaptation and Irregular Vertices**.In *Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,* ISBN 978-989-758-488-6, pages 67-74. DOI: 10.5220/0010259200670074

#### in Bibtex Style

@conference{grapp21,

author={Daniel Zint and Roberto Grosso},

title={On the Link between Mesh Size Adaptation and Irregular Vertices},

booktitle={Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,},

year={2021},

pages={67-74},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010259200670074},

isbn={978-989-758-488-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,

TI - On the Link between Mesh Size Adaptation and Irregular Vertices

SN - 978-989-758-488-6

AU - Zint D.

AU - Grosso R.

PY - 2021

SP - 67

EP - 74

DO - 10.5220/0010259200670074