An algorithm for rapid computation of Richards's smooth molecular surface is described. The entire surface is computed analytically, triangulated, and displayed at interactive rates. The faster speeds for our program have been achieved by algorithmic improvements, parallelizing the computations, and by taking advantage of the special geometrical properties of such surfaces. Our algorithm is eas...

This supplemental material describes the computation of mass properties of triangulated solids and their derivatives w.r.t. surface vertices. We start by briefly reviewing the volume integrals for mass, center of mass, and moment of inertia. Thereafter, we reduce the volume to surface integrals using the Divergence theorem, resulting in analytical expressions for a volume bounded by a triangula...

ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an polytropic equation of state can be solved analytically for case a working surface, i.e. when initial discontinuity on hydrodynamical quantities form two waves separating from contact discontinuity. The procedure is based extensive use Taub jump conditions relativistic waves, adiabatic, and performing Lorentz trans...

The construction of an information model the processes gear processing hardened large-modular chevron gears is one stages control technological structure and parameters automation design process. Taking into account principles classification, automated process considered as a object, consisting number objects: initial material (input object); environment (process conditions); wheel (output quan...