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Unformatted text preview: Motivation Doublyconnected edge list Map overlay Subdivision representation and map overlay Computational Geometry Lecture 2b: Subdivision representation and map overlay Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Map overlay Map overlay Map overlay is the combination of two (or more) map layers It is needed to answer questions like: What is the total length of roads through forests? What is the total area of corn fields within 1 km from a river? What area of all lakes occurs at the geological soil type “rock”? Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Map overlay Map overlay To solve map overlay questions, we need (at the least) intersection points from two sets of line segments (possibly, boundaries of regions) Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Map overlay Map overlay To solve map overlay questions, we also need to be able to represent subdivisions clay clay sand sand loess rock rock sand sand loess clay rock rock clay Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Subdivisions Representing subdivisions DCEL structure Subdivisions A planar subdivision is a structure induced by a set of line segments in the plane that can only intersect at common endpoints. It consists of vertices, edges, and faces face vertex edge Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Subdivisions Representing subdivisions DCEL structure Subdivisions Vertices are the endpoints of the line segments Edges are the interiors of the line segments Faces are the interiors of connected twodimensional regions that do not contain any point of any line segment Objects of the same dimensionality are adjacent or not; objects of different dimensionality are incident or not adjacent incident Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Subdivisions Representing subdivisions DCEL structure Subdivisions Exactly one face is unbounded, the outer face Every other face is bounded and has an outer boundary consisting of vertices and edges Any face has zero or more inner boundaries Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Subdivisions Representing subdivisions DCEL structure Subdivisions Vertices, edges, and faces form a partition of the plane If a planar subdivision is induced by n line segments, it has exactly n edges, and at most 2 n vertices Computational Geometry Lecture 2b: Subdivision representation and map overlay Motivation Doublyconnected edge list Map overlay Subdivisions Representing subdivisions...
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 Fall '08
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 Geometric algorithms, Line segment intersection, Sweep line algorithm, map overlay

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