Title :
Polyhedra operators for mesh refinement
Author :
Ivrissimtzis, Ioannis ; Seidel, Hans-Peter
Author_Institution :
Max-Planck-Inst. fur Inf., Saarbrucken, Germany
Abstract :
We study the factorization of mesh refinement rules in terms of the polyhedra operator´s duality, stellation, and truncation. Using this factorization, we show that the √3-refinement and leapfrog transformation, known from its applications in discrete mathematical chemistry, differ by a conjugation by the duality operator. As an example of this relation we use a variational √3-scheme to draw the mesh of the fullerene molecule C60. We also find the relation between the simplest-scheme refinement and binary refinement of the Catmull-Clark scheme.
Keywords :
chemistry computing; computational geometry; computer graphics; mathematical operators; mesh generation; √3-refinement; C60; Catmull-Clark scheme; binary refinement; discrete mathematical chemistry; factorization; fullerene molecule; leapfrog transformation; mesh refinement rules; polyhedra operator duality; polyhedra operator stellation; polyhedra operator truncation; simplest-scheme refinement; variational √3-scheme; Application software; Chemicals; Chemistry; Computer graphics; Computer science; Solid modeling; Spectral analysis;
Conference_Titel :
Geometric Modeling and Processing, 2002. Proceedings
Print_ISBN :
0-7695-1674-2
DOI :
10.1109/GMAP.2002.1027504
