Robust gift wrapping for the three-dimensional convex hull

A conventional gift-wrapping algorithm for constructing the three-dimensional convex hull is revised into a numerically robust one. The proposed algorithm places the highest priority on the topological condition that the boundary of the convex hull should be isomorphic to a sphere, and uses numerical values as lower-prirority information for choosing one among the combinatorially consistent branches. No matter how poor the arithmetic precision may be, the algorithm carries out its task and gives as the output a topologically consistent approximation to the true convex hull

A Geometric Approach to Molecular Docking and Similarity

We present e cient algorithms coupled to geometric data structures for computation of protein-ligand binding sites (docking) and geometric structure similaritychecks for large biopolymers and siloxane based liquid crystals. Our techniques are novel and based on combinatorial geometry computations of regular triangulations,-shapes and embedded sub-graph isomorphism (matching). While there's a lot more than geometry to the solution of molecular docking and similarity computation problems the approach presented in this paper can be used as the geometric kernel of a more complex methodology including biochemical and energetic considerations

MGOS: A library for molecular geometry and its operating system

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)'' as a theoretical framework accompanied by "MG Operating System (MGOS)'' which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. (C) 2019 The Author(s). Published by Elsevier B.V