Space subdivision to speed-up convex hull construction in E3

• Published in: Advances in engineering software (1992) Vol. 91; pp. 12 - 22
• Main Authors: Skala, Vaclav, Majdisova, Zuzana, Smolik, Michal
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2016
• Subjects: Algorithms; Approximated angle; Computational geometry; Computer programs; Construction; Convex hull; Convexity; Hulls (structures); Initial convex polyhedron; Mathematical analysis; Points distribution; Points reduction; Space subdivision; Subdivisions; Initial convex polyhedron; Convex hull; Points reduction; Space subdivision; Approximated angle; Points distribution
• ISSN: 0965-9978
• DOI: 10.1016/j.advengsoft.2015.09.002

•Algorithm for computing the convex hull of a set of points in E3 we are proposed.•The algorithm is based on spherical space subdivision.•The algorithm eliminates as many input points as possible before the convex hull calculation.•Experimental results show that the proposed algorithm achieves a better time complexity in comparison with other algorithms in E3. Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This algorithm is based on “spherical” space subdivision. The main idea of the S-CH algorithm is to eliminate as many input points as possible before the convex hull construction. The experimental results show that only a very small number of points are used for the final convex hull calculation. Experiments made also proved that the proposed S-CH algorithm achieves a better time complexity in comparison with other algorithms in E3.