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Sweeping is a powerful and versatile method of designing objects. Boundary of volumes (henceforth envelope) obtained by sweeping solids have been extensively investigated in the past, though, obtaining an accurate parametrization of the…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
Random sequential adsorption algorithm is a popular tool for modelling structure of monolayers built in irreversible adsorption experiments. However, this algorithm becomes very inefficient when the density of molecules in a layer rises.…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Simulation schemes that allow to change molecular representation in a subvolume of the simulation box while preserving the equilibrium with the surrounding introduce conceptual problems of thermodynamic consistency. In this work we present…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…
Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
The Discretizable Molecular Distance Geometry Problem (DMDGP) aims to determine the three-dimensional protein structure using distance information from nuclear magnetic resonance experiments. The DMDGP has a finite number of candidate…
In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…
Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case where truly subquadratic-time algorithms were given for simple objects such as unit-disks and…
Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision and computer graphics, such as surface registration, segmentation, remeshing, and texture map compression. While various conformal and…
In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…