Computing the link center of a simple polygon

Lenhart, William; Pollack, Richard; Sack, Jörg-Rüdiger; Seidel, Raimund; Sharir, Micha; Suri, Subhash; Toussaint, Godfried T.; Whitesides, Sue; Yap, Chee

doi:10.1007/bf02187913

Cited by 43 publications

(24 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The geodesic center [13] minimizes the maximum geodesic distance to any point in the shape. The link center [10] in a polygonal region minimizes the maximum number of straight line segments in the geodesic path to any point in the shape. The geodesic median [8] minimizes the average geodesic distance in the L 1 norm to any point in the shape.…”

Section: Center Points Of 2d Shapesmentioning

confidence: 99%

Extended grassfire transform on medial axes of 2D shapes

Liu

Chambers

Letscher

et al. 2011

Computer-Aided Design

View full text Add to dashboard Cite

The medial axis is an important shape descriptor first introduced by Blum [2] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a "center point", is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.

show abstract

Section: Center Points Of 2d Shapesmentioning

confidence: 99%

Extended grassfire transform on medial axes of 2D shapes

Liu

Chambers

Letscher

et al. 2011

Computer-Aided Design

View full text Add to dashboard Cite

show abstract

“…Efcient algorithms for link diameter and link center are given in Refs. (10,14,19,17,24) and (23,30). A minimum-link path between two x e d p o i n ts in a multiply connected polygon can be computed e ciently.…”

Section: From O(h Log H) T O O(h)mentioning

confidence: 99%

Optimal Shortest Path and Minimum-Link Path Queries between Two Convex Polygons inside a Simple Polygonal Obstacle

Chiang

Tamassia

1997

Int. J. Comput. Geom. Appl.

View full text Add to dashboard Cite

We present e cient algorithms for shortest-path and minimum-link-path queries between two c o n vex polygons inside a simple polygon P , which acts as an obstacle to be avoided. Let n be the number of vertices of P , and h the total numberof vertices of the query polygons. We s h o w that shortest-path queries can be performed optimally in time O(log h + log n) (plus O(k) time for reporting the k edges of the path) using a data structure with O(n) space and preprocessing time, and that minimum-link-path queries can be performed in optimal time O(log h +log n) ( p l u s O(k) to report the k links), with O(n 3 ) space and preprocessing t i m e . We also extend our results to the dynamic case, and give a uni ed data structure that supports both queries for convex polygons in the same region of a connected planar subdivision S. The update operations consist of insertions and deletions of edges and vertices. Let n be the current n umber of vertices in S. The data structure uses O(n) space, supports updates in O(log 2 n) time, and performs shortest-path and minimumlink-path queries in times O(log h + l o g 2 n) ( p l u s O(k) to report the k edges of the path) and O(log h + k log 2 n), respectively. P erforming shortest-path queries is a variation of the well-studied separation problem, which has not been e ciently solved before in the presence of obstacles. Also, it was not previously known how to perform minimum-linkpath queries in a dynamic environment, even for two-point queries.

show abstract

“…[51] who provided a simple 0(n 2 ) time algorithm to compute LC(P). Note that the link center of P is not necessarily a point as is the case with the geodesic center of P, but the link center may in fact be a geodesically convex region contained in P. Later Djidjev et 11.1.…”

Section: Constrained Link Centermentioning

confidence: 99%

Geometric and computational aspects of manufacturing processes

Bose

1994

Computers & Graphics

View full text Add to dashboard Cite

Computing the link center of a simple polygon

Cited by 43 publications

References 12 publications

Extended grassfire transform on medial axes of 2D shapes

Extended grassfire transform on medial axes of 2D shapes

Optimal Shortest Path and Minimum-Link Path Queries between Two Convex Polygons inside a Simple Polygonal Obstacle

Geometric and computational aspects of manufacturing processes

Contact Info

Product

Resources

About