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We study a 1D geometry of a plasma confined between two conducting floating walls with applications to laboratory plasmas. These plasmas are characterized by a quasi-neutral bulk that is joined to the wall by a thin boundary layer called…
This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
Computing the envelope of deforming planar domains is a significant and challenging problem with a wide range of potential applications. We approximate the envelope using circular arc splines, curves that balance geometric flexibility and…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
This paper proposes a novel method for high-quality image segmentation of both objects and scenes. Inspired by the dilation and erosion operations in morphological image processing techniques, the pixel-level image segmentation problems are…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
We investigate the problem of finding inner ap-proximations of positive semidefinite (PSD) cones. We developa novel decomposition framework of the PSD cone by meansof conical combinations of smaller dimensional sub-cones. Weshow that many…
The wetting of solid surfaces by fluids is a problem of great practical importance that has been extensively studied over the years. Most often, the experimental work has involved measurements of the contact angle made by a liquid on the…
We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…
In this paper, we investigate the problem of grasping novel objects in unstructured environments. To address this problem, consideration of the object geometry, reachability and force closure analysis are required. We propose a framework…
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational…
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…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a…