Authors:
Francisco J. Galdames
1
and
Fabrice Jaillet
2
Affiliations:
1
Universidad de Chile, Université de Lyon, CNRS, Université Lyon 1 and LIRIS, Chile
;
2
Université de Lyon, IUT Lyon 1, Computer ScienUniversité de Lyon, CNRS, Université Lyon 1 and LIRISce Department, France
Keyword(s):
Simplex Mesh, Triangle Mesh, Optimized Surface Interpolation, Surface Mesh Conversion.
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Geometric Computing
;
Geometry and Modeling
;
Modeling and Algorithms
;
Surface Modeling
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.