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Geometric computation software tends to be fragile and fails occasionally. This robustness problem is rooted in the difficulty of making unambiguous decisions about incidence and nonincidence, fundamentally impairing layering the geometry software reliably. Additionally, geometric operations tend to have a large number of special and singular cases, further adding to the difficulty of creating ...

Classification of chromosomes have impct in the recent research. The chromosomes are non-rigid material and they are several times touching each other or they overlap each other in the metaphase images. Now many techniques are required to understand the overlapping chromosomes. This paper presents a novel method for segmenting chromosomes based upon computational geometry. In the proposed appro...

The Cgal project (www.cgal.org) is a collaborative effort of several research institutes in Europe. The mission of the project is to make the most important of the solutions and methods developed in computational geometry available to users in industry and academia.

We improve a number of existing algorithms for determining the location of one or more undesirable facilities amidst a set P of n demand points, under various constraints and distance functions. We assume that the demand points reside within some given bounded region R. Applying concepts and techniques from Computational Geometry, we provide e cient algorithms for the following problems: 1. Bri...

In this paper, a mesh-free approach called smooth particle hydrodynamics (SPH) is proposed to analyze the seepage problem in porous media. In this method, computational domain is discredited by some nodes, and there is no need for background mesh; therefore, it is a truly meshless method. The method was applied to analyze seepage flow through a concrete dam foundation. Using the SPH method, the...

Geometric problems are central in many areas of science and engineering. Computational geometry, the study of combinatorial and algorithmic problems in a geometric setting, and in particular triangulations have tremendous practical applications in areas such as computer graphics, computer vision and imaging, scientific visualization, geographic information systems, astronomy, computational biol...

We present a heuristic search algorithm for the R Manhattan shortest path problem that achieves front-to-front bidirectionality in subquadratic time. In the study of bidirectional search algorithms, front-to-front heuristic computations were thought to be prohibitively expensive (at least quadratic time complexity); our algorithm runs in O(n log n) time and O(n logd−1 n) space, where n is the n...

Discrepancy theory investigates how uniform nonrandom structures can be. For example, given n points in the plane, how should we color them red and blue so as to minimize the difference between the number of red points and the number of blue ones within any disk? Or, how should we place n points in the unit square so that the number of points that lie within any given triangle in the square is ...

Wireless Sensor Networks Due to its potential applications in various situations such as battle eld, emergency relief, environment monitoring, and so on, wireless sensor networks [50, 75, 118, 130] have recently emerged as a premier research topic. Sensor networks consist of a set of sensor nodes which are spread over a geographical area. These nodes are able to perform processing as well as se...