An efficient algorithm for line clipping by convex polygon

The planar 3-center problem for a set S of points given in the plane asks for three congruent circular disks with the minimum radius, whose union can cover all points of S completely. In this paper, we present an O(n2 log3n) time algorithm for a restricted planar 3-center problem in which the given points are in the convex positions , i.e. The given points are the vertices of a convex polygon exactly.

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REGULAR ENUMERATION OF GRID POINTS IN A CONVEX POLYGON

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195993000191 ◽

1993 ◽

Vol 03 (03) ◽

pp. 305-322

Author(s):

HSUAN-SHIH LEE ◽

RUEI CHUAN CHANG

Keyword(s):

Line Segment ◽

Efficient Algorithm ◽

Convex Polygon ◽

Grid Points

In this paper we present an efficient algorithm for enumerating all the grid points in a convex polygon, where the enumeration is done by scanning the grid points with a set of parallel grid lines. Given a convex n-gon, enumeration can be done in [Formula: see text] time, where K is the number of the grid points reported, l is the diameter of the polygon and w is the length of the shorter sides of the rectangle enclosing the polygon with longer sides parallel to the line segment connecting the diametral pair of the polygon. We also show that the ratio of the number of the scanned grid lines to the minimal is less than some constant.

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Efficient Algorithm for Computing the Triangle Maximizing the Length of Its Smallest Side Inside a Convex Polygon

International Journal of Foundations of Computer Science ◽

10.1142/s0129054120500173 ◽

2020 ◽

Vol 31 (04) ◽

pp. 421-443

Author(s):

Sanjib Sadhu ◽

Sasanka Roy ◽

Soumen Nandi ◽

Subhas C. Nandy ◽

Suchismita Roy

Keyword(s):

Efficient Algorithm ◽

Convex Polygon ◽

Time Algorithm ◽

The Given

Given a convex polygon with [Formula: see text] vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must coincide with a vertex of the polygon. We also propose an [Formula: see text] time algorithm to compute such a triangle inside the given convex polygon.

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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