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Computational Geometry Algorithms

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Convex Hull Algorithms

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Algorithms that find the convex hull of a set of points, which is the smallest convex polygon containing all the points. Example: Graham's Scan or Quickhull are used to solve Convex Hull determination problems.

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Range Searching

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Refers to algorithms that preprocess a set of geometric objects to answer various range queries efficiently. Examples include K-d trees and Range trees to solve problems like listing points within a rectangle.

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Line Segment Intersection

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This refers to algorithms that determine if any two of a collection of line segments intersect. Bentley-Ottmann algorithm and the Sweep line algorithm are well-known for this purpose.

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Point Location

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The problem of locating a point within a spatial subdivision of the plane efficiently. Data structures like Trapezoidal maps or the Kirkpatrick's data structure are used for solving point location queries.

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Triangulation

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The process of subdividing a polygonal area into triangles, which have various applications including computer graphics and numerical simulations. The Ear clipping method and Delaunay triangulation are common strategies.

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Voronoi Diagram

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A partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other. Used in various fields such as meteorology, biology, and mining.

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