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class="mw-page-title-main">List of combinatorial computational geometry topics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="This article exist only in this language. 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p> <b>List of combinatorial computational geometry topics</b> enumerates the topics of <a href="/wiki/Computational_geometry" title="Computational geometry">computational geometry</a> that states problems in terms of geometric objects as <a href="/wiki/Discrete_mathematics" title="Discrete mathematics">discrete</a> entities and hence the methods of their solution are mostly theories and <a href="/wiki/Algorithm" title="Algorithm">algorithms</a> of <a href="/wiki/Combinatorics" title="Combinatorics">combinatorial</a> character. </p><p>See <a href="/wiki/List_of_numerical_computational_geometry_topics" title="List of numerical computational geometry topics">List of numerical computational geometry topics</a> for another flavor of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Construction/representation"><span id="Construction.2Frepresentation"></span>Construction/representation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=1" title="Edit section: Construction/representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Boolean_operations_on_polygons" title="Boolean operations on polygons">Boolean operations on polygons</a></li> <li><a href="/wiki/Convex_hull" title="Convex hull">Convex hull</a></li> <li><a href="/wiki/Hyperplane_arrangement" class="mw-redirect" title="Hyperplane arrangement">Hyperplane arrangement</a></li> <li><a href="/w/index.php?title=Polygon_decomposition&action=edit&redlink=1" class="new" title="Polygon decomposition (page does not exist)">Polygon decomposition</a> <ul><li><a href="/wiki/Polygon_triangulation" title="Polygon triangulation">Polygon triangulation</a> <ul><li><a href="/w/index.php?title=Minimal_convex_decomposition&action=edit&redlink=1" class="new" title="Minimal convex decomposition (page does not exist)">Minimal convex decomposition</a></li> <li><a href="/w/index.php?title=Minimal_convex_cover&action=edit&redlink=1" class="new" title="Minimal convex cover (page does not exist)">Minimal convex cover</a> problem (<a href="/wiki/NP-hard" class="mw-redirect" title="NP-hard">NP-hard</a>)</li> <li><a href="/w/index.php?title=Minimal_rectangular_decomposition&action=edit&redlink=1" class="new" title="Minimal rectangular decomposition (page does not exist)">Minimal rectangular decomposition</a></li></ul></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tessellation</a> problems</li></ul></li> <li><a href="/wiki/Shape_dissection" class="mw-redirect" title="Shape dissection">Shape dissection</a> problems</li> <li><a href="/wiki/Straight_skeleton" title="Straight skeleton">Straight skeleton</a></li> <li><a href="/w/index.php?title=Stabbing_line_problem&action=edit&redlink=1" class="new" title="Stabbing line problem (page does not exist)">Stabbing line problem</a></li> <li><a href="/wiki/Triangulation_(geometry)" title="Triangulation (geometry)">Triangulation</a> <ul><li><a href="/wiki/Delaunay_triangulation" title="Delaunay triangulation">Delaunay triangulation</a></li> <li><a href="/wiki/Point-set_triangulation" title="Point-set triangulation">Point-set triangulation</a></li> <li><a href="/wiki/Polygon_triangulation" title="Polygon triangulation">Polygon triangulation</a></li></ul></li> <li><a href="/wiki/Voronoi_diagram" title="Voronoi diagram">Voronoi diagram</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Extremal_shapes">Extremal shapes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=2" title="Edit section: Extremal shapes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Minimum_bounding_box" title="Minimum bounding box">Minimum bounding box</a> (<a href="/wiki/Smallest_enclosing_box" class="mw-redirect" title="Smallest enclosing box">Smallest enclosing box</a>, <a href="/wiki/Smallest_bounding_box" class="mw-redirect" title="Smallest bounding box">Smallest bounding box</a>) <ul><li>2-D case: <a href="/wiki/Smallest_bounding_rectangle" class="mw-redirect" title="Smallest bounding rectangle">Smallest bounding rectangle</a> (<a href="/wiki/Smallest_enclosing_rectangle" class="mw-redirect" title="Smallest enclosing rectangle">Smallest enclosing rectangle</a>)</li> <li>There are two common variants of this problem. <ul><li>In many areas of computer graphics, the <a href="/wiki/Bounding_box" class="mw-redirect" title="Bounding box">bounding box</a> (often abbreviated to bbox) is understood to be the smallest box delimited by sides parallel to coordinate axes which encloses the objects in question.</li> <li>In other applications, such as <a href="/wiki/Packaging" title="Packaging">packaging</a>, the problem is to find the smallest box the object (or objects) may fit in ("packaged"). Here the box may assume an arbitrary orientation with respect to the "packaged" objects.</li></ul></li></ul></li> <li><a href="/wiki/Smallest_bounding_sphere" class="mw-redirect" title="Smallest bounding sphere">Smallest bounding sphere</a> (Smallest enclosing sphere) <ul><li>2-D case: <a href="/wiki/Smallest_bounding_circle" class="mw-redirect" title="Smallest bounding circle">Smallest bounding circle</a></li></ul></li> <li><a href="/wiki/Largest_empty_rectangle" title="Largest empty rectangle">Largest empty rectangle</a> (<a href="/wiki/Maximum_empty_rectangle" class="mw-redirect" title="Maximum empty rectangle">Maximum empty rectangle</a>)</li> <li><a href="/wiki/Largest_empty_sphere" title="Largest empty sphere">Largest empty sphere</a> <ul><li>2-D case: <a href="/w/index.php?title=Maximum_empty_circle&action=edit&redlink=1" class="new" title="Maximum empty circle (page does not exist)">Maximum empty circle</a> (<a href="/wiki/Largest_empty_circle" class="mw-redirect" title="Largest empty circle">largest empty circle</a>)</li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="Interaction/search"><span id="Interaction.2Fsearch"></span>Interaction/search</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=3" title="Edit section: Interaction/search"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Collision_detection" title="Collision detection">Collision detection</a></li> <li><a href="/wiki/Line_segment_intersection" class="mw-redirect" title="Line segment intersection">Line segment intersection</a></li> <li><a href="/wiki/Point_location" title="Point location">Point location</a> <ul><li><a href="/wiki/Point_in_polygon" title="Point in polygon">Point in polygon</a></li></ul></li> <li><a href="/w/index.php?title=Polygon_intersection&action=edit&redlink=1" class="new" title="Polygon intersection (page does not exist)">Polygon intersection</a></li> <li><a href="/wiki/Range_searching" title="Range searching">Range searching</a> <ul><li><a href="/wiki/Orthogonal_range_searching" class="mw-redirect" title="Orthogonal range searching">Orthogonal range searching</a></li> <li><a href="/w/index.php?title=Simplex_range_searching&action=edit&redlink=1" class="new" title="Simplex range searching (page does not exist)">Simplex range searching</a></li></ul></li> <li><a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a> (not to be confused with <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> of computer graphics)</li> <li><a href="/wiki/Slab_method" title="Slab method">Slab method</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Proximity_problems"><a href="/wiki/Proximity_problems" title="Proximity problems">Proximity problems</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=4" title="Edit section: Proximity problems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Closest_pair_of_points" class="mw-redirect" title="Closest pair of points">Closest pair of points</a></li> <li><a href="/wiki/Nearest_neighbor_search" title="Nearest neighbor search">Closest point problem</a></li> <li><a href="/wiki/Diameter_of_a_point_set" class="mw-redirect" title="Diameter of a point set">Diameter of a point set</a></li> <li><a href="/wiki/Delaunay_triangulation" title="Delaunay triangulation">Delaunay triangulation</a></li> <li><a href="/wiki/Voronoi_diagram" title="Voronoi diagram">Voronoi diagram</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Visibility">Visibility</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=5" title="Edit section: Visibility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Visibility_(geometry)" title="Visibility (geometry)">Visibility (geometry)</a></li> <li><a href="/wiki/Art_gallery_problem" title="Art gallery problem">Art gallery problem</a> (<a href="/wiki/The_museum_problem" class="mw-redirect" title="The museum problem">The museum problem</a>)</li> <li><a href="/wiki/Visibility_graph" title="Visibility graph">Visibility graph</a></li> <li><a href="/wiki/Watchman_route_problem" title="Watchman route problem">Watchman route problem</a></li> <li>Computer graphics applications: <ul><li><a href="/wiki/Hidden_surface_determination" class="mw-redirect" title="Hidden surface determination">Hidden surface determination</a></li> <li><a href="/wiki/Hidden_line_removal" class="mw-redirect" title="Hidden line removal">Hidden line removal</a></li></ul></li> <li><a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a> (not to be confused with <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> of computer graphics)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Other">Other</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_combinatorial_computational_geometry_topics&action=edit&section=6" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Happy_ending_problem" title="Happy ending problem">Happy ending problem</a></li> <li><a href="/wiki/Ham_sandwich_problem" class="mw-redirect" title="Ham sandwich problem">Ham sandwich problem</a></li> <li><a href="/w/index.php?title=Shape_assembly&action=edit&redlink=1" class="new" title="Shape assembly (page does not exist)">shape assembly</a> problems</li> <li><a href="/w/index.php?title=Shape_matching&action=edit&redlink=1" class="new" title="Shape matching (page does not exist)">shape matching</a> problems</li> <li><a href="/wiki/Klee%27s_measure_problem" title="Klee's measure problem">Klee's measure problem</a></li> <li>Problems on <a href="/wiki/Isothetic_polygon" title="Isothetic polygon">isothetic polygons</a> and <a href="/w/index.php?title=Isothetic_polyhedra&action=edit&redlink=1" class="new" title="Isothetic polyhedra (page does not exist)">isothetic polyhedra</a> <ul><li><a href="/wiki/Orthogonal_convex_hull" title="Orthogonal convex hull">Orthogonal convex hull</a></li></ul></li> <li><a href="/wiki/Path_planning" class="mw-redirect" title="Path planning">Path planning</a> <ul><li><a href="/w/index.php?title=Paths_among_obstacles&action=edit&redlink=1" class="new" title="Paths among obstacles (page does not exist)">Paths among obstacles</a></li> <li><a href="/w/index.php?title=Shortest_path_in_a_polygon&action=edit&redlink=1" class="new" title="Shortest path in a polygon (page does not exist)">Shortest path in a polygon</a></li></ul></li> <li><a href="/w/index.php?title=Polygon_containment&action=edit&redlink=1" class="new" title="Polygon containment (page does not exist)">Polygon containment</a></li> <li><a href="/wiki/Robust_geometric_computation" title="Robust geometric computation">Robust geometric computation</a> addresses two main issues: fixed-precision representation of <a href="/wiki/Real_number" title="Real number">real numbers</a> in computers and possible geometrical <a href="/wiki/Degeneracy_(mathematics)" title="Degeneracy (mathematics)">degeneracy (mathematics)</a> of input data</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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