Journal•ISSN: 0218-1959

# International Journal of Computational Geometry and Applications

World Scientific

About: International Journal of Computational Geometry and Applications is an academic journal published by World Scientific. The journal publishes majorly in the area(s): Computational geometry & Simple polygon. It has an ISSN identifier of 0218-1959. Over the lifetime, 803 publications have been published receiving 17771 citations. The journal is also known as: International journal of computational geometry & applications.

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TL;DR: As a measure for the resemblance of curves in arbitrary dimensions the authors consider the so-called Frechet-distance, which is compatible with parametrizations of the curves, and for polygonal chains P and Q consisting of p and q edges an algorithm of runtime O(pq log( pq))) measuring the Frechet Distance.

Abstract: As a measure for the resemblance of curves in arbitrary dimensions we consider the so-called Frechet-distance, which is compatible with parametrizations of the curves. For polygonal chains P and Q consisting of p and q edges an algorithm of runtime O(pq log(pq)) measuring the Frechet-distance between P and Q is developed. Then some important variants are considered, namely the Frechet-distance for closed curves, the nonmonotone Frechet-distance and a distance function derived from the Frechet-distance measuring whether P resembles some part of the curve Q.

1,008 citations

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TL;DR: The analysis of expansive configuration spaces has inspired a new randomized planning algorithm that tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space.

Abstract: We introduce the notion of expansiveness to characterize a family of robot configuration spaces whose connectivity can be effectively captured by a roadmap of randomly-sampled milestones. The analysis of expansive configuration spaces has inspired us to develop a new randomized planning algorithm. This new algorithm tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space. Thus, it is well-suited for problems where only a single query is submitted for a given environment. The algorithm has been implemented and successfully applied to complex assembly maintainability problems from the automotive industry.

441 citations

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TL;DR: A method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise is described and analyzed.

Abstract: In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2 or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.

400 citations

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TL;DR: This work gives a similar algorithm, simplifying the computation and the proof of the geometric guarantee, and guarantees that the output surface is homeomorphic to the original surface; to the knowledge this is the first such topological guarantee for this problem.

Abstract: The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm1 using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming that the sample was sufficiently dense. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the first such topological guarantee for this problem.

337 citations

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TL;DR: This paper defines the models, main related notions and properties as cells, boundaries, duality, orientability, Euler characteristic, and shows the correspondence between the combinatorial models and combinatorially cellular quasi-manifolds, here defined as combinatorials simplicial quasi- manifolds to which a structure into cells is added.

Abstract: The scope of this work is Geometric Modeling. We study the representation and the construction of subdivisions of quasi-manifolds, using a topology-based approach. Quasi-manifolds are here defined as a subset of pseudo-manifolds, which are well-known objects in Algebraic Topology. N-dimensional generalized maps (resp. n-dimensional maps) are combinatorial models defined for representing the topology of subdivisions of orientable or non-orientable quasi-manifolds with or without boundaries (resp. orientable quasi-manifolds without boundaries). In this paper, we define the models, main related notions and properties as cells, boundaries, duality, orientability, Euler characteristic. Basic operations are proposed for handling the models. We also show the correspondence between the combinatorial models and combinatorial cellular quasi-manifolds, here defined as combinatorial simplicial quasi-manifolds to which a structure into cells is added. This correspondence establishes that the models are rigorous and un...

299 citations