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Sweep line algorithm information


Animation of Fortune's algorithm, a sweep line technique for constructing Voronoi diagrams.

In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space. It is one of the critical techniques in computational geometry.

The idea behind algorithms of this type is to imagine that a line (often a vertical line) is swept or moved across the plane, stopping at some points. Geometric operations are restricted to geometric objects that either intersect or are in the immediate vicinity of the sweep line whenever it stops, and the complete solution is available once the line has passed over all objects.

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Sweep line algorithm

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computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve...

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Sweep

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tool Sweep account, a kind of bank account Sweep line algorithm, a concept in computational geometry Sweeps, a regional English term for windmill sails...

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Multiple line segment intersection

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of segments is to use a sweep line algorithm, where we imagine a line sliding across the line segments and we track which line segments it intersects at...

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Algorithmic paradigm

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Dynamic programming Greedy algorithm Recursion Prune and search Kernelization Iterative compression Sweep line algorithms Rotating calipers Randomized...

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Rotating calipers

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calipers can be interpreted as the projective dual of a sweep line algorithm in which the sweep is across slopes of lines rather than across x- or y-coordinates...

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List of algorithms

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smoothing: an algorithm to smooth a polygonal mesh Line segment intersection: finding whether lines intersect, usually with a sweep line algorithm Bentley–Ottmann...

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Polygon triangulation

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partitioned into monotone subpolygons in O(n log n) time using a sweep-line approach. The algorithm does not require the polygon to be simple, thus it can be...

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Michael Ian Shamos

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in computational geometry, and is known for the Shamos–Hoey sweep line algorithm for line segment intersection detection and for the rotating calipers...

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Boolean operations on polygons

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on polygons tend to use plane sweep algorithms (or Sweep line algorithms). A list of papers using plane sweep algorithms for Boolean operations on polygons...

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Computational geometry

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smoothing: an algorithm to smooth a polygonal mesh Line segment intersection: finding whether lines intersect, usually with a sweep line algorithm Bentley–Ottmann...

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Tracing garbage collection

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other algorithms. The technique is also known as stop-and-copy. Cheney's algorithm is an improvement on the semi-space collector. A mark and sweep garbage...

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Closest pair of points problem

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problem. Both sweep line algorithms and divide-and-conquer algorithms with this slower time bound are commonly taught as examples of these algorithm design techniques...

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Rectilinear minimum spanning tree

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be constructed in O(n log n) using a divide and conquer algorithm or a sweep line algorithm. The problem commonly arises in physical design of electronic...

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Boundary tracing

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tracing algorithm is similar to the Square tracing algorithm with similar weaknesses but works with 8-connected (diagonal) patterns Radial sweep Theo Pavlidis’...

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Monotone priority queue

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operations are monotonic. Similarly, in sweep line algorithms in computational geometry, events at which the sweep line crosses a point of interest are prioritized...

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Vatti clipping algorithm

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the top; this is conceptually similar to the Bentley–Ottmann algorithm. This sweep line approach divides the problem space by scanlines, imaginary horizontal...

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Algorithm March

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moving canon style one at a time. After each movement, the line takes a step forward. Algorithm March lyrics, in English and Japanese (Romaji). Note: this...

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Prefix sum

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parallel algorithms, both as a test problem to be solved and as a useful primitive to be used as a subroutine in other parallel algorithms. Abstractly...

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Visibility polygon

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divide-and-conquer algorithm to compute the visibility polygon was proposed in 1987. An angular sweep, i.e. rotational plane sweep algorithm to compute the...

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Delaunay triangulation

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Delaunay triangulation that uses a radially propagating sweep-hull, and a flipping algorithm. The sweep-hull is created sequentially by iterating a radially-sorted...

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Matrix multiplication algorithm

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simultaneous sweep through a row of A and a column of B) incurs a cache miss when accessing an element of B. This means that the algorithm incurs Θ(n3)...

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Cellular evolutionary algorithm

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A cellular evolutionary algorithm (cEA) is a kind of evolutionary algorithm (EA) in which individuals cannot mate arbitrarily, but every one interacts...

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Minkowski Portal Refinement

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Refinement collision detection algorithm is a technique for determining whether two convex shapes overlap. The algorithm was created by Gary Snethen in...

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Monotone polygon

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monotone polygon is sweepable by a line which does not change its orientation during the sweep. A polygon is strictly sweepable if no portion of its...

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Stochastic gradient descent

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∇ Q i ( w ) . {\displaystyle w:=w-\eta \,\nabla Q_{i}(w).} As the algorithm sweeps through the training set, it performs the above update for each training...

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