New Results on Path Approximation
Algorithmica
Minimal enclosing parallelepiped in 3D
Computational Geometry: Theory and Applications
Extremal point queries with lines and line segments and related problems
Computational Geometry: Theory and Applications
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We address the problem of stabbing a sequence of indexed balls B= {B1,B2,..., Bn} inR3, where Bi (1 ≤i≤n) has centrepi and radius εi; a solution is anincreasing integer sequence i1,..., im suchthat i1 = 1, im = n and for ij≤ k ≤ ij+1 the line segment PijPij+1 stabs the ball Bk; the goal is tominimise m. The problem finds applications in simplification ofmolecule chains for visualisation, matching and efficient searchingin molecule and protein databases. We implemented the algorithm andcreated a web server where one can input a pdb file and get thesimplified protein chains. We did experiments on thousands ofproteins from the PDB Bank to estimate the simplification ratioachieved.