# FROM TRIANGULATION TO SIMPLEX MESH AND VICE-VERSA - A Simple and Efficient Conversion

### Francisco J. Galdames, Fabrice Jaillet

#### Abstract

We propose an accurate method to convert from a triangular mesh model to a simplex mesh and vice-versa. For this, we are taking advantage of the fact that they are topologically duals, turning it into a natural swap between these two models. Unfortunately, they are not geometrically equivalents, leading to loss of information and to geometry deterioration when performing the conversion. Therefore, optimal positions of the vertices in the dual mesh have to be found while avoiding shape degradation. An accurate and effective transformation technique is described in this paper, where we present a direct method to perform an appropriate interpolation of a simplex mesh to obtain its dual, and/or vice-versa. Our method is based on the distance minimization between the local tangent planes of the mesh and vertices of each face.

#### References

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#### Paper Citation

#### in Harvard Style

J. Galdames F. and Jaillet F. (2012). **FROM TRIANGULATION TO SIMPLEX MESH AND VICE-VERSA - A Simple and Efficient Conversion** . In *Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012)* ISBN 978-989-8565-02-0, pages 151-156. DOI: 10.5220/0003851801510156

#### in Bibtex Style

@conference{grapp12,

author={Francisco J. Galdames and Fabrice Jaillet},

title={FROM TRIANGULATION TO SIMPLEX MESH AND VICE-VERSA - A Simple and Efficient Conversion},

booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012)},

year={2012},

pages={151-156},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003851801510156},

isbn={978-989-8565-02-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2012)

TI - FROM TRIANGULATION TO SIMPLEX MESH AND VICE-VERSA - A Simple and Efficient Conversion

SN - 978-989-8565-02-0

AU - J. Galdames F.

AU - Jaillet F.

PY - 2012

SP - 151

EP - 156

DO - 10.5220/0003851801510156