. "[C909BBA10E2E]" . . . "Z(MSM0021630518)" . "RIV/00216305:26210/06:PU55815" . . "2006-02-24+01:00"^^ . "Geometric Data Structures and Their Selected Applications" . "477004" . "26210" . . . "RIV/00216305:26210/06:PU55815!RIV07-MSM-26210___" . "Geometrick\u00E9 datov\u00E9 struktury a jejich aplikace"@cs . . "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 connectio" . "6"^^ . . "\u0160eda, Milo\u0161" . . . "Geometrick\u00E9 datov\u00E9 struktury a jejich aplikace"@cs . "975-00803-0-0" . "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 connectio"@en . "61-66" . . "Geometric Data Structures and Their Selected Applications" . . . . "1"^^ . "Hled\u00E1n\u00ED nejkrat\u0161\u00EDch cest z ur\u010Den\u00E9 po\u010D\u00E1te\u010Dn\u00ED do koncov\u00E9 pozice je z\u00E1kladn\u00ED \u00FAlohou v doprav\u011B, okru\u017En\u00EDch probl\u00E9mech i komunika\u010Dn\u00EDch aplikac\u00EDch. V \u00FAloze pl\u00E1nov\u00E1n\u00ED pohybu robotu m\u00E1 robot proj\u00EDt z po\u010D\u00E1te\u010Dn\u00ED do koncov\u00E9 pozice ve sc\u00E9n\u011B s p\u0159ek\u00E1\u017Ekami tak, aby nedo\u0161lo ke kolizi s n\u011Bkterou z p\u0159ek\u00E1\u017Eek. ve sc\u00E9n\u011B s p\u0159ek\u00E1\u017Ekami tak, aby nedo\u0161lo ke kolizi s n\u011Bkterou z p\u0159ek\u00E1\u017Eek. Tato \u00FAloha m\u00E1 \u0159adu specifick\u00FDch formulac\u00ED, kter\u00E9 z\u00E1vis\u00ED na tvaru p\u0159ek\u00E1\u017Eek, povolen\u00E9mu zp\u016Fsobu pohybu, znalosti sc\u00E9ny atd. V\u00FDzkum t\u00E9to problematiky p\u0159inesl n\u011Bkolik odli\u0161n\u00FDch p\u0159\u00EDstup\u016F \u0159e\u0161en\u00ED v\u011Bt\u0161inou zalo\u017Een\u00FDch na r\u016Fzn\u00FDch dekompozic\u00EDch sc\u00E9ny a metod\u00E1ch silni\u010Dn\u00ED mapy. V p\u0159\u00EDsp\u011Bvku zkoum\u00E1me mo\u017En\u00E9 vyu\u017Eit\u00ED graf\u016F viditelnosti v pl\u00E1nov\u00E1n\u00ED trasy robotu mezi dv\u011Bma pozicemi v euklidovsk\u00E9 rovin\u011B a alternativn\u00ED p\u0159\u00EDstup vyu\u017E\u00EDvaj\u00EDc\u00ED Voronoiovy diagramy, kter\u00E9 sni\u017Euj\u00ED pravd\u011Bpodobnost koliz\u00ED s p\u0159ek\u00E1\u017Ekami. Druh\u00E1 zde zkouman\u00E1 aplika\u010Dn\u00ED oblast"@cs . "motion planning, spanning tree, Steiner tree, Delaunay triangulation, Voronoi diagram"@en . "Praha" . "Praha" . . . "Geometric Data Structures and Their Selected Applications"@en . . "1"^^ . "COMPUTICA" . "Computer Science" . . "Geometric Data Structures and Their Selected Applications"@en .