Visualization of Affine Invariant Tetrahedrization ( Slice-Based Method for Visualizing the Structure of Tetrahedrization )


The Transactions of the Korea Information Processing Society (1994 ~ 2000), Vol. 3, No. 7, pp. 1894-1905, Dec. 1996
10.3745/KIPSTE.1996.3.7.1894,   PDF Download:

Abstract

Delaunay triangulation which is the dual of dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delaunay tetrahedrization does not have an affine invariant transformation property. In this paper, we present a new type of tetrafedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2-D triangulation extended to three-dimensional tetrahedrization . A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.


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Cite this article
[IEEE Style]
L. Kun, "Visualization of Affine Invariant Tetrahedrization ( Slice-Based Method for Visualizing the Structure of Tetrahedrization )," The Transactions of the Korea Information Processing Society (1994 ~ 2000), vol. 3, no. 7, pp. 1894-1905, 1996. DOI: 10.3745/KIPSTE.1996.3.7.1894.

[ACM Style]
Lee Kun. 1996. Visualization of Affine Invariant Tetrahedrization ( Slice-Based Method for Visualizing the Structure of Tetrahedrization ). The Transactions of the Korea Information Processing Society (1994 ~ 2000), 3, 7, (1996), 1894-1905. DOI: 10.3745/KIPSTE.1996.3.7.1894.