Querying simplexes in quasi-triangulation
Computer-Aided Design
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Given a quasi-triangulation of a molecule, searching the simplexes of a particular bounding state for the spherical probe of a given radius occurs frequently. While such simplexes can be found by linearly scanning all simplexes in the quasi-triangulation, it is desirable to do the search faster. This paper presents an algorithm for searching simplexes quickly using the $kd$-tree data structure. The approach is based on the transformation of the simplex search problem in the $\mathbb{R}^3$ space to the orthogonal range search problem of points in another $\mathbb{R}^3$ space.