This paper describes the plane sweep algorithm for optimal use of tandem replicated data in a document. It is based on an observation that the original plane sweep algorithm is used to search in documents. Plane sweep algorithm does not feature a fast algorithm to find the word that is repeated in tandem in a document. With the help of effective parameters we could make a new technique to creat...

Fáry’s theorem states that every plane graph can be drawn as a straightline drawing. A plane graph is a graph embedded in a plane without edge crossings. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-plane graphs with straight-line edges. A 1-plane graph is a graph embedded in a plane with at most one crossing per edge. We giv...

A new calibration algorithm for multi-camera systems using planar reference patterns is proposed. The algorithm is an extension of Zhang’s flexible calibration technique to the cases with multiple cameras. Rigid displacements between cameras are recovered as well as intrinsic camera parameters only by showing the cameras a model plane with known reference patterns placed at several locations. T...

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Becau...

a disk wang-bézier type generalized ball curve is a wang-bézier type generalized ball curve whose control points are disks in a plane. it can be viewed as a parametric curve with error tolerances. in this paper, we discuss the problem of degree reduction of disk wang-bézier type generalized ball curve, that is, bounding disk wang-bézier type generalized ball curves with lower degree disk wang-b...

A grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on plane grid points and all edges are drawn as straight line segments between their endpoints without any edge-intersection. In this paper we give a very simple algorithm to find a grid drawing of any given 4-connected plane graph G with four or more vertices on the outer face. The algorithm take...

An approach for tracking the motion of a rigid object using parameterized ow models and a compact-structure constraint is proposed. While polynomial parameterized ow models have been shown to be eeective in tracking the rigid motion of planar objects, these models are inappropriate for tracking moving objects that change appearance revealing their 3D structure. We extend these models by adding ...

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