%0 Journal Article
	%A Miloš Šeda
	%D 2007
	%J International Journal of Physical and Mathematical Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 11, 2007
	%T Geometric Data Structures and Their Selected Applications
	%U https://publications.waset.org/pdf/8959
	%V 11
	%X Finding the shortest path between two positions is a
fundamental problem in transportation, routing, and communications
applications. In robot motion planning, the robot should pass around
the obstacles touching none of them, i.e. the goal is to find a
collision-free path from a starting to a target position. This task has
many specific formulations depending on the shape of obstacles,
allowable directions of movements, knowledge of the scene, etc.
Research of path planning has yielded many fundamentally different
approaches to its solution, mainly based on various decomposition
and roadmap methods. In this paper, we show a possible use of
visibility graphs in point-to-point motion planning in the Euclidean
plane and an alternative approach using Voronoi diagrams that
decreases the probability of collisions with obstacles. The second
application area, investigated here, is focused on problems of finding
minimal networks connecting a set of given points in the plane using
either only straight connections between pairs of points (minimum
spanning tree) or allowing the addition of auxiliary points to the set
to obtain shorter spanning networks (minimum Steiner tree).
	%P 551 - 556