CG_VoronoiExtraCh7

# CG_VoronoiExtraCh7 - Voronoi diagrams of line segments...

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams More on Voronoi diagrams Computational Geometry Lecture 13: More on Voronoi diagrams Computational Geometry Lecture 13: More on Voronoi diagrams

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Motion planning for a disc Can we move a disc from one location to another amidst obstacles? Computational Geometry Lecture 13: More on Voronoi diagrams
Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Motion planning for a disc Since the Voronoi diagram of point sites is locally “furthest away” from those sites, we can move the disc if and only if we can do so on the Voronoi diagram Computational Geometry Lecture 13: More on Voronoi diagrams

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Retraction Global idea for motion planing for a disc: 1. Get center from start to Voronoi diagram 2. Move center along Voronoi diagram 3. Move center from Voronoi diagram to end This is called retraction Computational Geometry Lecture 13: More on Voronoi diagrams
Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Voronoi diagram of points Computational Geometry Lecture 13: More on Voronoi diagrams

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Voronoi diagram of line segments For a Voronoi diagram of other objects than point sites, we must decide to which point on each site we measure the distance This will be the closest point on the site Computational Geometry Lecture 13: More on Voronoi diagrams
Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Voronoi diagram of line segments Computational Geometry Lecture 13: More on Voronoi diagrams

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Voronoi diagram of line segments Computational Geometry Lecture 13: More on Voronoi diagrams
Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Voronoi diagram of line segments The points of equal distance to two points lie on a line The points of equal distance to two lines lie on a line (two lines) The points of equal distance to a point and a line lie on a parabola Computational Geometry Lecture 13: More on Voronoi diagrams

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Voronoi diagrams of line segments Farthest-point Voronoi diagrams Motion planning for a disc Geometry Plane sweep algorithm Bisector of two line segments Two line segment sites have a bisector with up to 7 arcs Computational Geometry Lecture 13: More on Voronoi diagrams
Voronoi diagrams of line segments Farthest-point Voronoi diagrams

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