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Simplicial complex in Euclidean geometry
A triangulation of a set of points P {\displaystyle {\mathcal {P}}} in the Euclidean space R d {\displaystyle \mathbb {R} ^{d}} is a simplicial complex
Point-set_triangulation
Triangulation method
In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles
Delaunay_triangulation
Partition of a simple polygon into triangles
geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with
Polygon_triangulation
Subdivision of a planar object into triangles
simplicial complex that covers the entire space. A point-set triangulation, i.e., a triangulation of a discrete set of points P ⊂ R d {\displaystyle {\mathcal
Triangulation_(geometry)
Point set triangulation minimizing total length
minimum weight triangulation has also sometimes been called the optimal triangulation. The problem of minimum weight triangulation of a point set was posed
Minimum-weight_triangulation
Topics referred to by the same term
Look up triangulation in Wiktionary, the free dictionary. Triangulation is the process of determining the location of a point by forming triangles to
Triangulation (disambiguation)
Triangulation_(disambiguation)
Using measures of converging rays to improve fixed points for mapping
In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a
Triangulation_(surveying)
Process of finding a spatial transformation that aligns two point clouds
algorithms such as triangulation, bundle adjustment, and more recently, monocular image depth estimation using deep learning. For 2D point set registration
Point-set_registration
Partition of a surface into a net of triangles
Mesh generation Tessellation (computer graphics) Marching cubes Point set triangulation M. Schmidt: Cutting Cubes – visualizing implicit surfaces by adaptive
Surface_triangulation
geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of the vertices
Pitteway_triangulation
Fixed surveying station used in geodetic surveying
A triangulation station, also known as a trigonometrical point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying
Triangulation_station
Planar graph embedding where edges map to straight-line segments
systems. Special cases of PSLGs are triangulations (polygon triangulation, point-set triangulation). Point-set triangulations are maximal PSLGs in the sense
Planar_straight-line_graph
The greedy triangulation is a method to compute a polygon triangulation or a point set triangulation using a greedy algorithm, which adds edges one by
Greedy_triangulation
Computation method in geometry
Bowyer–Watson algorithm is a method for computing the Delaunay triangulation of a finite set of points in any number of dimensions. The algorithm can be
Bowyer–Watson_algorithm
Representation of mathematical space
In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism
Triangulation_(topology)
Subdivision of space into cells
unstructured meshes. While a mesh may be a triangulation, the process of meshing is distinguished from point set triangulation in that meshing includes the freedom
Mesh_generation
Theorem in topology
entire set of n + 1 available colors. Because f is continuous, this simplex can be made arbitrarily small by choosing an arbitrarily fine triangulation. Hence
Brouwer_fixed-point_theorem
Object placed to mark a point
position). Horizontal position markers used for triangulation are also known as triangulation stations. A set of interrelated geodetic markers form a geodetic
Survey_marker
Method of determining a point in 3D space
In computer vision, triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to
Triangulation (computer vision)
Triangulation_(computer_vision)
Straight skeleton Stabbing line problem Triangulation Delaunay triangulation Point-set triangulation Polygon triangulation Voronoi diagram Minimum bounding box
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Set of data points in three-dimensional space
are many techniques for converting a point cloud to a 3D surface. Some approaches, like Delaunay triangulation, alpha shapes, and ball pivoting, build
Point_cloud
Flip distance in triangulations
flip distance between two triangulations of the same point set is the number of flips required to transform one triangulation into another. A flip removes
Flip_distance
Theorem on triangulation graph colorings
lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that
Sperner's_lemma
Type of plane partition
seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician
Voronoi_diagram
^{n}} . The example set X is not integrally convex, and indeed ch(X) does not admit an integral triangulation: every triangulation of ch(X), either has
Integrally_convex_set
Approach to quantum gravity using discrete spacetime
causal set. Monte-Carlo simulations have provided evidence for a continuum phase in 2D using the Benincasa–Dowker action. Causal dynamical triangulation (CDT)
Causal_sets
Open-source geometric modelling kernel
polyhedra Polygon and polyhedron operations Arrangements Point set triangulations Delaunay triangulations Voronoi diagrams Mesh generation Geometry processing
CGAL
cell. Point-set triangulations The triangulations of a planar point set are connected by "flip" moves that remove one diagonal from a triangulation and
Reverse-search_algorithm
2004 mathematics textbook
diagrams and Gale diagrams, irrational polytopes, point set triangulations, regular triangulations and their polyhedral representation by secondary polytopes
Lectures in Geometric Combinatorics
Lectures_in_Geometric_Combinatorics
United States historic place
The Meades Ranch Triangulation Station is a survey marker in Osborne County in the state of Kansas in the Midwestern United States. The marker was initially
Meades Ranch Triangulation Station
Meades_Ranch_Triangulation_Station
equal to 90° Point-set triangulation — triangle mesh such that given set of point are all a vertex of a triangle Polygon triangulation — triangle mesh
List of numerical analysis topics
List_of_numerical_analysis_topics
Points usable to draw any planar graph
universal point sets of subquadratic size? More unsolved problems in mathematics In graph drawing, a universal point set of order n is a set S of points
Universal_point_set
Shape with three sides
[citation needed] Triangulation means the partition of any planar object into a collection of triangles. For example, in polygon triangulation, a polygon is
Triangle
In discrete mathematics, a discrete fixed-point is a fixed-point for functions defined on finite sets, typically subsets of the integer grid Z n {\displaystyle
Discrete_fixed-point_theorem
Combinatorial analog of the Borsuk-Ulam theorem
of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball B n {\displaystyle B_{n}} . Assume
Tucker's_lemma
Open-source algorithm library
by scanning. Greedy Projection Triangulation implements an algorithm for fast surface triangulation on an unordered PointCloud with normals. The result
Point_Cloud_Library
Algorithm for computing convex hulls in a set of points
Science, pp 50–59 Fortune, Steven (1989). "Stable maintenance of point set triangulations in two dimensions" (PDF). 30th Annual Symposium on Foundations
Graham_scan
Largest distance between two points
graph of triangulations of a point set, the minimum number of local moves needed to transform one triangulation into another for two triangulations chosen
Diameter_of_a_set
Family of problems in computational geometry
plane sweep (it can also be performed in linear time, using polygon triangulation). Therefore, there is no loss of generality, if we restrict our data
Point_location
Type of mathematical set
Abstract simplicial complex Barycentric subdivision Causal dynamical triangulation Delta set Loop quantum gravity Polygonal chain – 1 dimensional simplicial
Simplicial_complex
1791–1853 geodetic survey of Britain
The Principal Triangulation of Britain was the first high-precision triangulation survey of the whole of Great Britain and Ireland, carried out between
Principal Triangulation of Great Britain
Principal_Triangulation_of_Great_Britain
Graph representing faces of another graph
circumcenter of the corresponding triangle of the Delaunay triangulation, but this point may lie outside its triangle. The concept of duality can be
Dual_graph
Representation of a surface as a triangle mesh with elevated vertices
on a Delaunay triangulation or constrained Delaunay. Delaunay conforming triangulations are recommended over constrained triangulations. This is because
Triangulated irregular network
Triangulated_irregular_network
Branch of computer science
Find the intersections between a given set of line segments. Delaunay triangulation Voronoi diagram: Given a set of points, partition the space according
Computational_geometry
1995 mathematics text
hull algorithms, low-dimensional randomized linear programming, point set triangulation for two- and three-dimensional data, arrangements of hyperplanes
Algorithmic_Geometry
Point with known height used in surveying when levelling
for triangulation. In the United Kingdom, triangulation points are often set in large concrete markers that, as well as functioning as triangulation points
Benchmark_(surveying)
Every simple polygon with more than three vertices has at least two ears
crossings. The two ears theorem is equivalent to the existence of polygon triangulations. It is frequently attributed to Gary H. Meisters, but was proved earlier
Two_ears_theorem
Tree data structure that partitions a 2D area
essentially the triangulation of a point set for which further processing may be performed. As such, it is desirable for the resulting triangulation to have certain
Quadtree
Smallest convex set containing a given set
an intersection of sublevel sets of holomorphic functions containing a given set. The Delaunay triangulation of a point set and its dual, the Voronoi diagram
Convex_hull
Geolocation system
device can be employed to determine the device's location based on triangulation algorithms. A combination of these techniques may be used to improve
Wi-Fi_positioning_system
Scanning of an object or environment to collect data on its shape
a 2D configuration. This is referred to as a time-of-flight camera. Triangulation based 3D laser scanners are also active scanners that use laser light
3D_scanning
Algorithms and methods of plotting the Mandelbrot set on a computing device
representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
Type of weighted geometric graph
O(n^{2})} space. Chew's main result was that for a set of points in the plane there is a triangulation of this pointset such that for any two points there
Geometric_spanner
Electro-optical instrument used in surveying and building construction
distance from the instrument to a particular point, and an on-board computer to collect data and perform triangulation and position resection and intersection
Total_station
Approximation to shape of a point cloud
finite point set is its ordinary convex hull. Alpha shapes are closely related to alpha complexes, which are subcomplexes of the Delaunay triangulation of
Alpha_shape
Shape with three inward-curved sides
boundaries of these three convex sets. A pseudotriangulation (pseudo-triangulations) is a partition of a region of the plane into pseudotriangles, and a
Pseudotriangle
problem that uses Steiner points is Steiner triangulation. The goal is to partition an input (such as a point set or polygon) into triangles, meeting edge-to-edge
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Shape that blocks all lines of sight
solution has a special structure: a Steiner tree for one triangle in a triangulation of the polygon, and a segment in each remaining triangle from one vertex
Opaque_set
Mathematical software
of simplifications to find a locally minimal ideal triangulation. Once a suitable ideal triangulation is found, SnapPea can try to find a hyperbolic structure
SnapPea
Well-spaced set of points in a metric space
polyhedra called plesiohedra. Clarkson, Kenneth L. (2006), "Building triangulations using ε-nets", STOC'06: Proceedings of the 38th Annual ACM Symposium
Delone_set
Reference frame for geodesy on the continent
an initial point (Meades Ranch Triangulation Station in Kansas), the direction of a line between this point and a specified second point, and two dimensions
North_American_Datum
Shortest network connecting points
turns out to be. For uniformly random point sets in any bounded dimension, the Yao graph or Delaunay triangulation have linear expected numbers of edges
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Topological manifold with a piecewise linear structure on it
functions. This is slightly stronger than the topological notion of a triangulation. An isomorphism of PL manifolds is called a PL homeomorphism. PL sits
Piecewise_linear_manifold
Optical ranging devices
coincidence telemeter is a type of rangefinder that uses the principle of triangulation and an optical device to allow an operator to determine the distance
Coincidence_rangefinder
Use of distances for determining unknown coordinates of a point
multilateration. Trilateration or multilateration should not be confused with triangulation, which uses angles for positioning; and direction finding, which determines
Trilateration
Possibility of a consistent definition of "clockwise" in a mathematical space
any n {\displaystyle n} -manifold having a triangulation. However, some 4-manifolds do not have a triangulation, and in general for n > 4 {\displaystyle
Orientability
Computer graphics algorithm
added four new cases to the Marching Cubes triangulation table (subcases of the cases 3, 4, 6 and 7). At this point, even with all the improvements proposed
Marching_cubes
Geometric graph connecting nearby points
neighborhood graph can be computed in linear time from the Delaunay triangulation of the point set. Because it is defined only in terms of the distances between
Relative_neighborhood_graph
point sets whose β-skeletons are paths of arbitrarily large length within a unit square. Therefore, unlike the closely related Delaunay triangulation
Beta_skeleton
Lighthouse
Passamaquoddy Bay, including Green's Point. Diving info "Green's Point Lighthouse". 29 May 2025. "Triangulation in Maine", U.S. Government Printing Office
Green's_Point_Lighthouse
concept of a triangulation in topology. This can mean simply that a neighborhood of each vertex (i.e. the set of simplices that contain that point as a vertex)
Simplicial_manifold
Independent set in a graph
associated with a set S = {Vi1, …, Vik} of colors. Each point x of the triangulation is labeled with a vertex g(x) of G such that: (a) For each point x on a face
Rainbow-independent_set
(induced) forbidden subgraphs. Characterise word-representable near-triangulations containing the complete graph K4 (such a characterisation is known for
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Attempt to find a consistent theory of quantum gravity
also used). Physics portal Asymptotic freedom Causal dynamical triangulation Causal sets Critical phenomena Euclidean quantum gravity Fractal cosmology
Asymptotic_safety
Chess opening
Opening Repertoire" (pp. 95–125) and "The King's Indian Attack, from White's Point of View" (pp. 126–155), both contributed by Dvoretsky. Edition Olms, 2007
King's_Indian_Attack
Geodetic reference system
Additional surface gravity observations, results from the extension of triangulation and trilateration networks, and large amounts of Doppler and optical
World_Geodetic_System
Optical surveying instrument
of his own design. Ramsden's instruments were used for the Principal Triangulation of Great Britain. At this time the highest precision instruments were
Theodolite
convex hull. Similarly, the minimum-weight triangulation of planar point sets is NP-hard for arbitrary point sets, but solvable in polynomial time by dynamic
Convex_position
Outdoor game
certain elevation, but hobbyists often use the term benchmarks to include triangulation stations or other reference marks. Like geocaching, the activity has
Benchmarking_(hobby)
Survey of the distance between Greenwich and Paris
position of the Royal Greenwich Observatory and the Paris Observatory via triangulation. The English operations, executed by the Scottish military surveyor
Anglo-French Survey (1784–1790)
Anglo-French_Survey_(1784–1790)
Graph defined from a set of points in the Euclidean plane
Like beta-skeletons, and unlike Delaunay triangulations, it is not a geometric spanner: for some point sets, distances within the Gabriel graph can be
Gabriel_graph
Connected triangles that share a central vertex
a single fan, by arbitrarily selecting any point inside it as the center. Triangle strip Fan triangulation "In depth explanation why triangle fans do
Triangle_fan
Type of directed graph
nearest neighbors allowed) of a set of points in the plane or any higher dimension is a subgraph of the Delaunay triangulation, the Gabriel graph, and the
Nearest_neighbor_graph
1935–1962 geodetic survey of Great Britain
The Retriangulation of Great Britain was a triangulation project carried out between 1935 and 1962 that sought to improve the accuracy of maps of Great
Retriangulation of Great Britain
Retriangulation_of_Great_Britain
German mathematician (1905–1980)
property of a partially ordered set. Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains
Emanuel_Sperner
Graph that encodes local operations in mathematics
generalized in a number of ways. Let T {\displaystyle T} be a triangulation of a finite set of points A ⊂ R d {\displaystyle {\mathcal {A}}\subset \mathbb
Flip_graph
Unit of information
scientific journal). Data analysis methodologies vary and include data triangulation and data percolation. The latter offers an articulate method of collecting
Data
Lubiw, Anna; Pathak, Vinayak (2015), "Flip distance between two triangulations of a point set is NP-complete", Computational Geometry, 49: 17–23, arXiv:1205
Reconfiguration
Shape bounded by non-intersecting line segments
geometry problems, including point in polygon testing, area computation, the convex hull of a simple polygon, triangulation, and Euclidean shortest paths
Simple_polygon
Geometry of stereo vision
calculated from the coordinates of the two image points, a process called triangulation. The epipolar geometry is simplified if the two camera image planes
Epipolar_geometry
Device for measuring the geometry of objects
known as noncontact scanning, which includes high speed laser single point triangulation, laser line scanning, and white light scanning, is advancing very
Coordinate-measuring_machine
Graph that can be embedded in the plane
then bounded by three edges, explaining the alternative term plane triangulation (which technically means a plane drawing of the graph). The alternative
Planar_graph
Study of graphs defined by geometric means
a graph formed from the triangulations of a point set, in which each vertex represents a triangulation and two triangulations are connected by an edge
Geometric_graph_theory
Concept in algebraic geometry
intersections. When discussing Voronoi tessellations and Delaunay triangulations in the plane, a set of points in the plane is said to be in general position only
General_position
Polygon mesh composed of triangles
Nonuniform rational B-spline Point cloud Polygon mesh Triangulation (topology) Triangulation (geometry) Delaunay triangulation Triangulated irregular network
Triangle_mesh
Computing the fixed point of a function
can be reduced to 2D-SPERNER (computing a fully-labeled triangle in a triangulation satisfying the conditions to Sperner's lemma), and therefore it is PPAD-complete
Fixed-point_computation
Mathematical problem
because the existence of triangulations is proven under certain verified conditions. The vertices of the resulting triangulation graph may be 3-colored
Art_gallery_problem
Shortest paths on a bounded deformed sphere-like quadric surface
straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry (Euler
Geodesics_on_an_ellipsoid
Austrian-American film director (1894–1969)
Exquisite Sinner. A romance set in post-World War I Brittany, the movie was withheld from release for failing to clearly set forth its narrative, though
Josef_von_Sternberg
Science of determining the positions of points and the distances and angles between them
to a point could be deduced. Dutch mathematician Willebrord Snellius (a.k.a. Snel van Royen) introduced the modern systematic use of triangulation. In
Surveying
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Girl/Female
Tamil
Bindushri | பீநà¯à®¤à¯à®·à¯à®°à¯€Â
Point
Bindushri | பீநà¯à®¤à¯à®·à¯à®°à¯€Â
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Boy/Male
Indian
Point
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Girl/Female
Hindu, Indian
Point
Girl/Female
Norse
Beautiful point.
Female
Egyptian
, an uncertain goddess.
Surname or Lastname
English and French
English and French : probably an altered form of French Pons, a habitational name from places so named in Bourgogne and Franche-Comté.
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' Edward Poins, an irregular humorist.
Girl/Female
Norse
Point.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : from the medieval personal name Ponc(h)e, Pons (see Ponce).English (of Norman origin) : habitational name from Ponts in La Manche and Seine-Maritime, Normandy, from Latin pontes ‘bridges’ (see Pont).English (of Norman origin) : nickname for a fop or dandy, from points ‘laces for hose’ (see Pointer 1).
Girl/Female
Indian
Drop, Point
Surname or Lastname
English
English : variant spelling of See.
Girl/Female
Tamil
Bindu Priya | பிஂத௠பà¯à®°à®¿à®¯à®¾Â
Drop, Point
Bindu Priya | பிஂத௠பà¯à®°à®¿à®¯à®¾Â
Girl/Female
Norse
New point.
Male
English
Short form of English Stephen, STE means "crown."
Surname or Lastname
English, Scottish, French, and Catalan
English, Scottish, French, and Catalan : topographic name for
someone who lived near a bridge, Middle English, Old French, Catalan
pont (Latin pons, genitive pontis).Catalan : habitational name from any of the numerous places named
with Pont.Dutch : variant of
Pond 2.A Pont from the Lorraine region of France is documented in Quebec City in
1640; Pont appears to be a secondary surname to
Girl/Female
Hindu, Indian
Point
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
Girl/Female
Hebrew
Life.
Biblical
distillation from the mouth
Boy/Male
German
Strong Judgment
Girl/Female
Indian
Honest
Girl/Female
Indian, Tamil
Carrier of Elixer
Girl/Female
Hebrew
Dove.
Surname or Lastname
English
English : habitational name from a place in West Yorkshire, probably named with the genitive case of the Old English personal name StÄn ‘stone’, a byname or short form of any of various compound names with this as the first element (compare, for example, Stammer, Stannard) + Old English feld ‘pasture’, ‘open country’.English : alternatively, it may be a topographic name from Middle English stanesfeld ‘open country of the (standing) stone’, with reference to a prominent monolith. There are other places so called, for example in Suffolk, but the distribution suggests that the one in Yorkshire is the source of the surname.
Girl/Female
Indian
Soft and warm
Boy/Male
Gujarati, Hindu, Indian, Kannada, Sanskrit, Telugu
Compassionate
Boy/Male
Tamil
Indrajeet | இநà¯à®¤à¯à®°à®œà®¿à®¤
Conqueror of Indra, One who got victory over Indra
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
POINT SET-TRIANGULATION
n.
A fixed conventional place for reference, or zero of reckoning, in the heavens, usually the intersection of two or more great circles of the sphere, and named specifically in each case according to the position intended; as, the equinoctial points; the solstitial points; the nodal points; vertical points, etc. See Equinoctial Nodal.
n.
To supply with punctuation marks; to punctuate; as, to point a composition.
n.
Lace wrought the needle; as, point de Venise; Brussels point. See Point lace, below.
n.
Printed letters; the impression taken from type, as to excellence, form, size, etc.; as, small print; large print; this line is in print.
n.
One of the points of the compass (see Points of the compass, below); also, the difference between two points of the compass; as, to fall off a point.
n.
To direct toward an abject; to aim; as, to point a gun at a wolf, or a cannon at a fort.
n.
A movement executed with the saber or foil; as, tierce point.
n.
To mark (as Hebrew) with vowel points.
n.
A standard unit of measure for the size of type bodies, being one twelfth of the thickness of pica type. See Point system of type, under Type.
n.
A core print. See under Core.
n.
A joining of two things or parts so as to admit of motion; an articulation, whether movable or not; a hinge; as, the knee joint; a node or joint of a stem; a ball and socket joint. See Articulation.
adv.
In a point-blank manner.
n.
To give a point to; to sharpen; to cut, forge, grind, or file to an acute end; as, to point a dart, or a pencil. Used also figuratively; as, to point a moral.
adv.
Alt. of Point-devise
n.
The attitude assumed by a pointer dog when he finds game; as, the dog came to a point. See Pointer.
a.
Alt. of Point-devise
n.
Whatever serves to mark progress, rank, or relative position, or to indicate a transition from one state or position to another, degree; step; stage; hence, position or condition attained; as, a point of elevation, or of depression; the stock fell off five points; he won by tenpoints.
n.
A short piece of cordage used in reefing sails. See Reef point, under Reef.
v. t.
To point out the seat or position of, as birds, or other game; -- said of hunting dogs.