Motion planning for AmigoBot with line-segment-based map and Voronoi diagram

2016 ◽  
Author(s):  
Qing Hui ◽  
Jin Cheng
Keyword(s):  
Motion Planning ◽  
Voronoi Diagram ◽  
Line Segment

BASELINE BOUNDED HALF-PLANE VORONOI DIAGRAM

2013 ◽  
Vol 05 (03) ◽  
pp. 1350021 ◽  
Author(s):  
BING SU ◽  
YINFENG XU ◽  
BINHAI ZHU
Keyword(s):  
Voronoi Diagram ◽  
Half Plane ◽  
Line Segment ◽  
Euclidean Plane ◽  
Voronoi Region ◽  
Point Set ◽  
Set Of Points

Given a set of points P = {p1, p2, …, pn} in the Euclidean plane, with each point piassociated with a given direction vi∈ V. P(pi, vi) defines a half-plane and L(pi, vi) denotes the baseline that is perpendicular to viand passing through pi. Define a region dominated by piand vias a Baseline Bounded Half-Plane Voronoi Region, denoted as V or(pi, vi), if a point x ∈ V or(pi, vi), then (1) x ∈ P(pi, vi); (2) the line segment l(x, pi) does not cross any baseline; (3) if there is a point pj, such that x ∈ P(pj, vj), and the line segment l(x, pj) does not cross any baseline then d(x, pi) ≤ d(x, pj), j ≠ i. The Baseline Bounded Half-Plane Voronoi Diagram, denoted as V or(P, V), is the union of all V or(pi, vi). We show that V or(pi, vi) and V or(P, V) can be computed in O(n log n) and O(n2log n) time, respectively. For the heterogeneous point set, the same problem is also considered.

Topology and context-based pattern extraction using line-segment Voronoi diagram

2015 ◽  
Author(s):  
Sandeep K. Dey ◽  
Panagiotis Cheilaris ◽  
Nathalie Casati ◽  
Maria Gabrani ◽  
Evanthia Papadopoulo
Keyword(s):  
Voronoi Diagram ◽  
Line Segment ◽  
Pattern Extraction

THE ANCHORED VORONOI DIAGRAM: STATIC, DYNAMIC VERSIONS AND APPLICATIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 315-332
Author(s):  
J. M. DÍAZ-BÁÑEZ ◽  
F. GÓMEZ ◽  
I. VENTURA
Keyword(s):  
Fixed Point ◽  
Voronoi Diagram ◽  
Line Segment ◽  
Time Complexity ◽  
Optimization Problems ◽  
Dynamic Version

For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment [Formula: see text] is equidistant to both p and q. We show that those bisectors have nice properties and, therefore, this new structure can be computed in O(n log n) time and O(n) space both for nearest-site and furthest-site versions. Also, we prove that the dynamic version of this diagram can be built in O(n2λ6s+2(n) log n) time complexity, where s is a constant depending on the function that describes the motion of the points. Finally, we show how to use these structures for solving several locational optimization problems.

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