We present a robust arrangement algorithm for algebraic curves based on floating point arithmetic. The algorithm performs a line sweep, tests the consistency of each sweep update, and modifies the input to prevent inconsistent updates. The output arrangement is realizable by semi-algebraic curves that are close to the input curves. We present a new performance model for robust computational geo...

Traditional power flow analysis techniques such as the Newton-Raphson and the Gauss-Seidel methods are widely used in analyzing power transmission systems. However, they are inefficient and may diverge due to the different network characteristics of power distribution systems such as radial and high R/X ratio. Therefore, other techniques such as the voltage sweep algorithms are developed for po...

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large class of surfaces and curves embedded on...

A new approach to the problem of object segmentation and isosurface detection is introduced. Drawing on the fundamental marching cubes algorithm of Lorensen and Cline, it operates with one space sweep through the voxels (hence it is called the voxel-sweep). It detects all isosurfaces and partitions the objects into connected components on the basis of the continuity of the surfaces. The surface...

A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary step is fixing some rows of the inverse matrix of SLAEs. The second step consists in calculating solutions for all right-hand sides. For reducing the communic...

The sweep-line method is a state space reduction technique for memory-efficient on-the-fly verification of concurrent systems. The method relies on a progress measure capturing inherent progress in the system under verification to store only fragments of the state space in memory at a time and thereby reduce peak memory usage. The sweepline method has been applied to many concurrent systems, bu...

This paper presents fast algorithms for penetration and contact determination between general polyhedral models in dynamic environments. The main contribution is an extension of an earlier expected constant time algorithm between convex polytopes to detect penetrations and contacts. For each pair of non-convex polyhedral models, the algorithm uses the convex hull of each object to determine whi...

A multiphase harmonic load flow algorithm is developed based on backward/forward sweep to examine the effects of various factors on the neutral to earth voltage (NEV), including unsymmetrical system configuration, load unbalance and harmonic injection. The proposed algorithm composes fundamental frequency and harmonic frequencies power flows. The algorithm and the associated models are tested o...