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overview.pug
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extends layout.pug
mixin refs(args)
if args && args.paper
span
a(href=args.paper) paper
if args && args.scihub
span
a(href="https://sci-hub.se/"+args.scihub) scihub
if args && args.doi
span
a(href="https://doi.org/" + args.doi) doi
if args && args.wiki
span
a(href=args.wiki) wiki
if args && args.src
span
a(href="https://rgeometry.org/rgeometry/rgeometry/" + args.src) api
mixin mark(boolean = false)
if boolean == '?'
| ?
else
span(class=boolean ? "checked" : 'unchecked').
⬤
//- Alternative: ●
mixin algo(complexity, name, args)
details(class={'has-content': args})
summary
div
div
+mark(args && args.src)
div= name
div= '\\(' + complexity + '\\)'
if args
div.content
+refs(args)
block content
article
h2 Overview of Computation Geometry
p
| This page is a summary of all the algorithms that belong in the RGeometry library.
| Green dots mark algorithms that have already been implemented and clicking on them
| will reveal a link to the API documentation.
p
| If you know of any noteworthy algorithms that are not on this list, please
|
a(href="https://github.com/rgeometry/rgeometry/issues/new") open
|
| a ticket on GitHub.
//- p
//- b How does RGeometry relate to these projects?
//- dl
//- dt HGeometry
//- dd TBD
//- dt CGAL
//- dd TBD
//- dt Geometry-Central
//- dd TBD
article.feature
h3 Polygonization
.feature-compare
+algo('O(n \\log n)', 'Convex Polygons' ,
{paper: "http://cglab.ca/~sander/misc/ConvexGeneration/convex.html"
,title: "Generating Random Convex Polygons"
,wiki: "https://en.wikipedia.org/wiki/Convex_polygon"
,src: "data/struct.PolygonConvex.html#method.random"
})
+algo('O(n \\log n)', 'Monotone Polygons' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.6026&rep=rep1&type=pdf"
,title: "Heuristics For The Generation of Random Polygons."
,wiki: "https://en.wikipedia.org/wiki/Monotone_polygon"
,src: "algorithms/polygonization/fn.new_monotone_polygon.html"
})
+algo('O(n \\log n)', 'Star-shaped Polygons' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.6026&rep=rep1&type=pdf"
,title: "Heuristics For The Generation of Random Polygons."
,wiki: "https://en.wikipedia.org/wiki/Star-shaped_polygon"
,src: "algorithms/polygonization/fn.new_star_polygon.html"
})
+algo('O(n^4)', '2-Opt Moves',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.6026&rep=rep1&type=pdf"
,title: "Heuristics For The Generation of Random Polygons."
,wiki: "https://en.wikipedia.org/wiki/2-opt"
,src: "algorithms/fn.two_opt_moves.html"
})
+algo('O(?)', 'Random Growth' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.6026&rep=rep1&type=pdf"
,title: "Heuristics For The Generation of Random Polygons."
})
+algo('O(?)', 'Skeleton holes',
{paper: "https://www.cs.umanitoba.ca/~cccg2010/electronicProceedings/paper15.pdf"
,wiki: "https://en.wikipedia.org/wiki/Straight_skeleton"
})
article.feature
h3 2D Interpolation
.feature-compare
+algo('O(n)', 'Linear')
+algo('O(?)', 'Angular')
+algo('O(?)', 'Edge+angle',
{paper: "https://www.researchgate.net/profile/Thomas_Sederberg/publication/220721162_2-D_shape_blending_An_intrinsic_solution_to_the_vertex_path_problem/links/0a85e52ec8be60e154000000/2-D-shape-blending-An-intrinsic-solution-to-the-vertex-path-problem.pdf"
,title: "2-D shape blending: An intrinsic solution to the vertex path problem"
,scihub: "10.1145/166117.166118"
,doi: "10.1145/166117.166118"
})
+algo('O(?)', 'Least-work',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.121.3736&rank=1"
,title: "A physically based approach to 2-D shape blending (1992)"
})
+algo('O(?)', 'Star-skeleton',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.116.3675"
,title: "Shape Blending Using the Star-Skeleton Representation (1995)"
})
+algo('O(?)', 'As-rigid-as-possible',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.1531&rank=1"
,title: "As-rigid-as-possible shape interpolation (2000)"
})
+algo('O(?)', 'Guaranteed intersection-free',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.4852&rank=1"
,title: "Guaranteed Intersection-Free Polygon Morphing (2001)"
})
article.feature
h3 Visibility
.feature-compare
+algo('O(n^2)', 'Naive Visibility',
{wiki: "https://en.wikipedia.org/wiki/Visibility_polygon#Naive_algorithms"
,wikiTitle: "Visibility polygon"
,src: "algorithms/visibility/naive/index.html"
})
+algo('O(n)', 'Linear Visibility',
{paper: "https://link.springer.com/article/10.1007%2FBF01937271"
,title: "Corrections to Lee's visibility polygon algorithm (1987)"
,scihub: "10.1007/BF01937271"
,doi: "10.1007/BF01937271"
})
+algo('O(n \\log n)', 'Sweep Visibility' ,
{paper: "https://dl.acm.org/doi/10.1145/10515.10517"
,title: "Worst-case optimal algorithms for constructing visibility polygons with holes (1986)"
,scihub: "10.1145/10515.10517"
,doi: "10.1145/10515.10517"
})
+algo('O(k)', 'Output-sensitive visibility' ,
{paper: "https://link.springer.com/article/10.1007/BF01840360"
,title: "Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons (1987)"
,scihub: "10.1007/BF01840360"
,doi: "10.1007/BF01840360"
})
+algo('O(n)', 'Minimum-link path' ,
{paper: "https://www.sciencedirect.com/science/article/abs/pii/0734189X86901271"
,title: "A linear time algorithm for minimum link paths inside a simple polygon (1986)"
,scihub: "10.1016/0734-189X(86)90127-1"
,doi: "10.1016/0734-189X(86)90127-1"
})
+algo('O(n)', 'Visibility window',
{paper: "https://www.sciencedirect.com/science/article/abs/pii/0734189X86901271"
,title: "A linear time algorithm for minimum link paths inside a simple polygon (1986)"
,scihub: "10.1016/0734-189X(86)90127-1"
,doi: "10.1016/0734-189X(86)90127-1"
})
+algo('O(n)', 'Single-source shortest path' ,
{paper: "https://link.springer.com/article/10.1007/BF01840360"
,title: "Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons (1987)"
,scihub: "10.1007/BF01840360"
,doi: "10.1007/BF01840360"
})
+algo('O(n \\log n)', 'Shortest path' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.2037&rank=2"
,title: "An Optimal Algorithm for Euclidean Shortest Paths in the Plane"
})
article.feature
h3 Convex
.feature-compare
+algo('O(n)', 'Polygon Kernel',
{paper: "http://www.dtic.mil/get-tr-doc/pdf?AD=ADA056887"
,title: "An Optimal Algorithm For Finding The Kernel Of A Polygon (1979)"
,scihub: "10.1145/322139.322142"
,doi: "10.1145/322139.322142"
,wiki: "https://en.wikipedia.org/wiki/Star-shaped_polygon"
,wikiTitle: "Star-shaped Polygon"
})
+algo('O(n)', 'Polygon Convex Hull',
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.512.9681&rep=rep1&type=pdf"
,title: "Online Construction of the Convex Hull of a Simple Polyline"
,wiki: "https://en.wikipedia.org/wiki/Convex_hull_of_a_simple_polygon"
,wikiTitle: "Convex hull of a Simple Polygon"
,api: "algorithms/convex_hull/melkman/index.html"
})
+algo('O(n \\log n)', 'Point Set Convex Hull' ,
{paper: "https://www.math.ucsd.edu/~ronspubs/72_10_convex_hull.pdf"
,wiki: "https://en.wikipedia.org/wiki/Graham_scan"
,src: "algorithms/fn.convex_hull.html"
})
+algo('O(nh)', 'Point Set Convex Hull' ,
{doi: "10.1016/0020-0190(73)90020-3"
,wiki: "https://en.wikipedia.org/wiki/Gift_wrapping_algorithm"
})
+algo('O(n \\log h)', 'Point Set Convex Hull' ,
{doi: "10.1137/0215021"
})
+algo('O(\\log n)', 'Convex point locator' ,
{paper: "https://cp-algorithms.com/geometry/point-in-convex-polygon.html"
,src: "data/struct.PolygonConvex.html#method.locate"
})
+algo('O(\\log n)', 'Convex extremes')
+algo('O(n + m)', 'Convex Minkowski sum')
+algo('O(\\log n + \\log m)', 'Convex intersection' ,
{paper: "https://arxiv.org/pdf/1312.1001.pdf"
,title: "Optimal detection of intersections between convex polyhedra"
})
+algo('O(nr^2)', 'Optimal Convex Decomposition')
+algo('O(nr)', 'ACD Lien/Amato' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.115.477&rep=rep1&type=pdf"
,title: "Approximate Convex Decomposition of Polygons"
})
+algo('O(n)', 'ACD Hertel/Mehlhorn',
{paper: "https://core.ac.uk/download/pdf/82318242.pdf"
,title: "Fast Triangulation of the Plane with Respect to Simple Polygons (1985)"
,scihub: "10.1016/S0019-9958(85)80044-9"
,doi: "10.1016/S0019-9958(85)80044-9"
})
article.feature
h3 Triangulation
.feature-compare
+algo('O(n \\log n)', 'Ear clipping' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49.3013&rep=rep1&type=pdf"
,doi: "10.1007/s00453-001-0028-4"
,wiki: "https://en.wikipedia.org/wiki/Polygon_triangulation#Ear_clipping_method"
,src: "algorithms/triangulation/earclip/index.html"
})
+algo('O(n \\log n)', 'Monotone Triangulation' ,
{paper: "https://www.ibr.cs.tu-bs.de/courses/ws2021/ag/Papers/Ch5/Garey-etal_Triangulating_1978.pdf"
,wiki: "https://en.wikipedia.org/wiki/Polygon_triangulation#Monotone_polygon_triangulation"
})
+algo('O(n \\log^\\star n)', 'Trapezoidal Triangulation' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.6973&rank=1"
,title: "A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons (1991)"
,wiki: "https://en.wikipedia.org/wiki/Polygon_triangulation"
})
+algo('O(n)', 'Randomised Linear Triangulation' ,
{paper: "https://www.ics.uci.edu/~goodrich/pubs/dcg-tri.pdf"
,wiki: "https://en.wikipedia.org/wiki/Polygon_triangulation"
})
+algo('O(n)', 'Linear Triangulation' ,
{paper: "https://link.springer.com/article/10.1007/BF02574703"
,title: "Triangulating a simple polygon in linear time (1990)"
,scihub: "10.1109/fscs.1990.89541"
,doi: "10.1109/fscs.1990.89541"
,wiki: "https://en.wikipedia.org/wiki/Polygon_triangulation"
})
+algo('O(n^2)', 'Constrained Delaunay Triangulation',
{wiki: "https://en.wikipedia.org/wiki/Constrained_Delaunay_triangulation"})
+algo('O(n\\log n)', 'Constrained Delaunay Triangulation' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.8264&rank=2"
,title: "Constrained Delaunay triangulations (1989)"
,wiki: "https://en.wikipedia.org/wiki/Constrained_Delaunay_triangulation"
})
+algo('O(n\\log n)', 'Constrained Delaunay Triangulation' ,
{paper: "https://dl.acm.org/doi/10.1080/13658810701492241"
,doi: "10.1080/13658810701492241"
,scihub: "10.1080/13658810701492241"
,title: "Sweep-line algorithm for constrained Delaunay triangulation (2008)"
,wiki: "https://en.wikipedia.org/wiki/Constrained_Delaunay_triangulation"
})
+algo('O(n \\log n)', 'Delaunay Triangulation' ,
{paper: "https://link.springer.com/article/10.1007%2FBF00977785"
,title: "Two algorithms for constructing a Delaunay triangulation (1980)"
,doi: "10.1007/BF00977785"
,scihub: "10.1007/BF00977785"
,wiki: "https://en.wikipedia.org/wiki/Delaunay_triangulation"
})
+algo('O(?)', 'Compatible triangulation')
article.feature
h3 Misc
.feature-compare
+algo('O((n+k)\\log n)', 'Segment intersections' ,
{wiki: "https://en.wikipedia.org/wiki/Bentley–Ottmann_algorithm"
,wikiTitle: "Bentley–Ottmann algorithm"
})
+algo('O(n\\log n+k)', 'Segment intersections' ,
{paper: "https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.7188"
,title: "An optimal algorithm for finding segments intersections (1995)"
,doi: "10.1145/220279.220302"
})
+algo('O(n)', 'Douglas Peucker\'s simplification')
+algo('O(n \\log n)', 'Euclidean Minimum Spanning Tree')
+algo('O(n \\log n)', '2D closest pair')
+algo('O(n)', 'Polygon point locator',
{wiki: "https://en.wikipedia.org/wiki/Point_in_polygon"
,src: "data/struct.Polygon.html#method.locate"
})
+algo('O(\\log n)', 'Planar point location')
+algo('O(nm)', 'Boolean operations' ,
{paper: "https://www.inf.usi.ch/hormann/papers/Foster.2019.CSP.pdf"
,title: "Clipping simple polygons with degenerate intersections"
,scihub: "10.1016/j.cagx.2019.100007"
,doi: "10.1016/j.cagx.2019.100007"
,wiki: "https://en.wikipedia.org/wiki/Boolean_operations_on_polygons"
})
+algo('O((n+k) \\log n)', 'Boolean operations' ,
{paper: "https://doi.org/10.1016/j.advengsoft.2013.04.004"
,paperTitle: "A simple algorithm for Boolean operations on polygons."
,scihub: "10.1016/j.advengsoft.2013.04.004"
,doi: "10.1016/j.advengsoft.2013.04.004"
,wiki: "https://en.wikipedia.org/wiki/Boolean_operations_on_polygons"
})