Affine-invariant tetrahedrization

Kun Lee

doi:10.1117/12.251808

30 September 1996 Affine-invariant tetrahedrization

Kun Lee

Proceedings Volume 2826, Vision Geometry V; (1996) https://doi.org/10.1117/12.251808
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Delaunay triangulation 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 tetrahedrization 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 2D triangulation extended to 3D tetrahedrization. A new associate norm between two points in 3D space is defined. The visualization of tetrahedrization (i.e. tetrahedral domain, representative data points and transformed data points) can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

Citation Download Citation

Kun Lee "Affine-invariant tetrahedrization", Proc. SPIE 2826, Vision Geometry V, (30 September 1996); https://doi.org/10.1117/12.251808

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