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Subdivision of a planar object into triangles
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object
Triangulation_(geometry)
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
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set
Polygon_triangulation
Method of determining a location
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points
Triangulation
Simplicial complex in Euclidean geometry
and regular triangulations, several other forms and problems related to point-set triangulations have been studied in computational geometry. The minimum-weight
Point-set_triangulation
Construct in computational geometry
In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments
Constrained Delaunay triangulation
Constrained_Delaunay_triangulation
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)
Computation method in geometry
In computational geometry, the Bowyer–Watson algorithm is a method for computing the Delaunay triangulation of a finite set of points in any number of
Bowyer–Watson_algorithm
Algorithms for mesh generation
points to the geometry of an input to be meshed, in a way that causes the Delaunay triangulation or constrained Delaunay triangulation of the augmented
Delaunay_refinement
A kinetic triangulation data structure is a kinetic data structure that maintains a triangulation of a set of moving points. Maintaining a kinetic triangulation
Kinetic_triangulation
Branch of computer science
Delaunay triangulations Marching triangles: reconstruct two-dimensional surface geometry from an unstructured point cloud Polygon triangulation algorithms:
Computational_geometry
Point set triangulation minimizing total length
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge
Minimum-weight_triangulation
Subdivision of space into cells
University of Bern David Eppstein's Geometry in Action, Mesh Generation Jonathan Shewchuk's Meshing and Triangulation in Graphics, Engineering, and Modeling
Mesh_generation
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
Hypothetical approach to quantum gravity with emergent spacetime
Causal dynamical triangulation (CDT), theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum
Causal dynamical triangulation
Causal_dynamical_triangulation
Type of mathematical set
one of its vertices. Pure simplicial complexes can be thought of as triangulations and provide a definition of polytopes. A facet is a maximal simplex
Simplicial_complex
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
Shape with three sides
polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the
Triangle
Method of determining a point in 3D space
that triangulation is made on corresponding image points from two views generated by pinhole cameras. The top image illustrates the epipolar geometry of
Triangulation (computer vision)
Triangulation_(computer_vision)
Theorem on triangulation graph colorings
mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to
Sperner's_lemma
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)
Branch of mathematics
packings, triangulations, the Kneser-Poulsen conjecture, etc. It shares many methods and principles with combinatorics. Computational geometry deals with
Geometry
Topics referred to by the same term
called a triangulation of G Triangulated graph, and a chordal completion of a graph G may be called a triangulation of G Triangulation (geometry), division
Triangulation (disambiguation)
Triangulation_(disambiguation)
between binary trees and triangulations of convex polygons, rotation distance is equivalent to the flip distance for triangulations of convex polygons. Rotation
Rotation_distance
analysis on 3D random Delaunay triangulation was done by Mucke, Saias and Zhu (ACM Symposium of Computational Geometry, 1996). In both cases, a boundary
Jump-and-Walk_algorithm
This division is not a triangulation in the geometric sense. It is a topological triangulation, however. A quasi-triangulation may have some of the characteristics
Quasi-triangulation
Overview of and topical guide to geometry
Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive
Outline_of_geometry
computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of
Pitteway_triangulation
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
Polygon mesh composed of triangles
rational B-spline Point cloud Polygon mesh Triangulation (topology) Triangulation (geometry) Delaunay triangulation Triangulated irregular network Botsch,
Triangle_mesh
Method of triangulating polygons
In computational geometry, a fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing edges to all of the other vertices
Fan_triangulation
Geometry of stereo vision
the coordinates of the two image points, a process called triangulation. The epipolar geometry is simplified if the two camera image planes coincide. In
Epipolar_geometry
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
Graph formed by subdivision of triangles
Computational Geometry (PDF). Below, Alexander; De Loera, Jesús A.; Richter-Gebert, Jürgen (2000), The Complexity of Finding Small Triangulations of Convex
Apollonian_network
Covering by shapes without overlaps or gaps
tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include
Tessellation
Partition of a surface into a net of triangles
341–355 E. Hartmann: Geometry and Algorithms for COMPUTER AIDED DESIGN, p. 81 E. Hartmann: A marching method for the triangulation of surfaces, The Visual
Surface_triangulation
Set of polygons to define the surface of a 3D model
adding detail to a polygon mesh) Polygon modeling Polygonizer Triangulation (geometry) Wire-frame model Lorensen, William E.; Cline, Harvey E. (1 August
Polygon_mesh
Closest point problem Diameter of a point set Delaunay triangulation Voronoi diagram Visibility (geometry) Art gallery problem (The museum problem) Visibility
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Method for dividing a simplicial complex
useful to replace the original spaces with simplicial complexes via triangulations: This substitution allows one to assign combinatorial invariants such
Barycentric_subdivision
Surface representing points of constant value within a volume
information about the contours of varying intensity fields. Isopotential Triangulation (geometry) Implicit surface Volume rendering "Hamilton–Jacobi equation",
Isosurface
Mathematics of smooth surfaces
decomposition, also called a triangulation. This interaction between analysis and topology was the forerunner of many later results in geometry, culminating in the
Differential geometry of surfaces
Differential_geometry_of_surfaces
Type of camera that can also capture the direction of travel of light rays
Velisavljevic, V.; Fiebig, S.; Pesch, M. (2017). "Baseline and Triangulation Geometry in a Standard Plenoptic Camera". Int. J. Comput. Vis. 126: 21–35
Light_field_camera
Embedding a graph in a topological space, often Euclidean
straight line planar embedding of a planar graph is always possible. Triangulation (geometry) Cohen, Robert F.; Eades, Peter; Lin, Tao; Ruskey, Frank (1995)
Graph_embedding
Geometric transformation
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Polygon mesh composed of triangles with no obtuse angles
Ruppert, J. (1995), "Linear-size nonobtuse triangulation of polygons", Discrete & Computational Geometry, 14 (4): 411–428, doi:10.1007/BF02570715, MR 1360945
Nonobtuse_mesh
1995 mathematics text
diagrams, and Delaunay triangulations. The book can be used as a graduate textbook, or as a reference for computational geometry research. Reviewer Peter
Algorithmic_Geometry
Quadrilateral symmetric across a diagonal
polyhedra and triangulations of the sphere", in Rivin, Igor; Rourke, Colin; Series, Caroline (eds.), The Epstein birthday schrift, Geometry & Topology Monographs
Kite_(geometry)
Shape bounded by non-intersecting line segments
computational geometry problems, including point in polygon testing, area computation, the convex hull of a simple polygon, triangulation, and Euclidean
Simple_polygon
and its applications): "Computational Geometry (Introduction)" "Line Segment Intersection", "Polygon Triangulation", "Linear Programming", "Orthogonal Range
List of books in computational geometry
List_of_books_in_computational_geometry
Type of plane partition
The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and
Voronoi_diagram
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Theorem in Euclidean geometry
two possible triangulations of the quadrilateral. The steps of this theorem require nothing beyond basic constructive Euclidean geometry. With the additional
Japanese theorem for cyclic polygons
Japanese_theorem_for_cyclic_polygons
edge endpoints. Another problem that uses Steiner points is Steiner triangulation. The goal is to partition an input (such as a point set or polygon)
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Study of systems of inequalitites
In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations
Real_algebraic_geometry
Planar movement within a Euclidean space without rotation
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction
Translation_(geometry)
Topological space that locally resembles Euclidean space
projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures
Manifold
Non-orientable surface with one edge
"Geometric realization of a triangulation on the projective plane with one face removed". Discrete & Computational Geometry. 40 (1): 141–157. doi:10
Möbius_strip
Non-convex polyhedron with no triangulation
used as gadgets in a proof that testing whether a polyhedron has a triangulation is NP-complete. Several other polyhedra, including Jessen's icosahedron
Schönhardt_polyhedron
Classical theory of gravitation
Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which
Einstein–Cartan_theory
in 2D or 3D Triangle mesh — consists of triangles in 2D or 3D Triangulation (geometry) — subdivision of given region in triangles, or higher-dimensional
List of numerical analysis topics
List_of_numerical_analysis_topics
Triangle with at least two sides congruent
Geometry (2nd, illustrated ed.), Springer, p. 27, ISBN 9783642309649 Bezdek, András; Bisztriczky, Ted (2015), "Finding equal-diameter triangulations in
Isosceles_triangle
Four-dimensional analogue of the cube
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter
Tesseract
Open-source geometric modelling kernel
operations Arrangements Point set triangulations Delaunay triangulations Voronoi diagrams Mesh generation Geometry processing Search structures (k-d tree)
CGAL
Study of graphs defined by geometric means
planar graph may be represented as a planar straight line graph. A triangulation is a planar straight line graph to which no more edges may be added
Geometric_graph_theory
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
the optimal tour is the convex hull. Similarly, the minimum-weight triangulation of planar point sets is NP-hard for arbitrary point sets, but solvable
Convex_position
Mesh generator
which is designed to partition any 3D geometry into tetrahedrons by employing a form of Delaunay triangulation whose algorithm was developed by the author
TetGen
Smallest convex set containing a given set
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined
Convex_hull
Hypothetical physical concept
needed] Alain Connes developed a geometric framework known as noncommutative geometry in which spacetime is extended via noncommutative operator algebras. When
Theory_of_everything
Feature of a polyhedron, polytope, etc.
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself
Facet_(geometry)
Class of algorithms which use a moving line to solve geometrical problems
problems in computational geometry, such as the construction of the Voronoi diagram (Fortune's algorithm) and the Delaunay triangulation or boolean operations
Sweep_line_algorithm
Theory of gravitation as curved spacetime
seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity
General_relativity
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
Branch of mathematics
Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between
Distance_geometry
Soviet mathematician
physicist, Nikolai Borisovich Delone. He is best known for the Delaunay triangulation. Boris Delone got his surname from his ancestor French Army officer
Boris_Delaunay
Canadian computer scientist (1944–2019)
linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality (unimodal function),
Godfried_Toussaint
Approach to quantum gravity using discrete spacetime
continuum phase in 2D using the Benincasa–Dowker action. Causal dynamical triangulation (CDT) Causal structure General relativity Order theory Bell, John L
Causal_sets
Description of gravity using discrete values
but no less important theories include causal dynamical triangulation, noncommutative geometry, and twistor theory. One of the difficulties of formulating
Quantum_gravity
Shortest network connecting points
the relative neighborhood graph and Delaunay triangulation. By constructing the Delaunay triangulation and then applying a graph minimum spanning tree
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
German polymath and scholar (1777–1855)
contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability. Gauss was director of the Göttingen Observatory
Carl_Friedrich_Gauss
Using distance measures along a shape's edges to determine position in space
energy waves. True-range multilateration can also be contrasted to triangulation, which involves the measurement of angles. There is no accepted or widely
True-range_multilateration
Theory extending Einstein gravity
Wheeler–DeWitt equation Loop quantum gravity Spin foam Causal dynamical triangulation Asymptotic safety in quantum gravity Causal sets DGP model Rainbow gravity
Quadratic_gravity
analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
This is a list of computer graphics and descriptive geometry topics, by article name. Contents !–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
List of computer graphics and descriptive geometry topics
List_of_computer_graphics_and_descriptive_geometry_topics
Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0
Beta_skeleton
Type of program in computer graphics
Shaders act on data such as vertices and primitives, generate or morph geometries and fragments, and calculate the colors in a rendered image. Shaders can
Shader
Multi-dimensional generalization of triangle
manifolds. 3-sphere Aitchison geometry Causal dynamical triangulation Complete graph Delaunay triangulation Distance geometry Geometric primitive Hill tetrahedron
Simplex
Cleaver (geometry) Congruence (geometry) Congruent isoscelizers point Contact triangle Conway triangle notation CPCTC Delaunay triangulation de Longchamps
List_of_triangle_topics
Open-source Java software library
Linear referencing Precision reduction Delaunay triangulation and constrained Delaunay triangulation Voronoi diagram generation Smallest enclosing rectangle
JTS_Topology_Suite
Topics referred to by the same term
operation that preserves distances Flip graph, a graph of "flips" from one triangulation or other combinatorial structure to another Coin flip, a coin toss with
Flip
Topics referred to by the same term
FAN algorithm, an algorithm for automatic test pattern generation Fan triangulation, a fast method to decompose a convex polygon in triangles .fan filename
Fan
Set of basic shapes which assemble into a polygon
Pedro; Toussaint, Godfried (1998). "Converting triangulations to quadrangulations". Computational Geometry. 9 (4): 257. doi:10.1016/s0925-7721(97)00019-9
Polygon_partition
Common point(s) shared by two lines in Euclidean geometry
Triangulation (computer vision) Intersection (Euclidean geometry) § Two line segments Cook, Jeremy (November 21, 2023). "Coplanar Lines in Geometry |
Line–line_intersection
Partition of a polygon into triangles of equal area
In geometry, an equidissection is a partition of a polygon into triangles of equal area. The study of equidissections began in the late 1960s with Monsky's
Equidissection
French computer scientist (born 1955)
his work is in computational geometry, where he is known for his study of algorithms, such as linear-time triangulation of a simple polygon, as well as
Bernard_Chazelle
Theory proposed by Roger Penrose
Roger Penrose in 1967 as a unification of general relativity (space-time geometry) and quantum mechanics (quantum theory) and has subsequently evolved into
Twistor_theory
Set of data points in three-dimensional space
converting a point cloud to a 3D surface. Some approaches, like Delaunay triangulation, alpha shapes, and ball pivoting, build a network of triangles over
Point_cloud
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
Difference in apparent position with viewing angle
angles, and using geometry, one can determine distance. Distance measurement by parallax is a special case of the principle of triangulation, which states
Parallax
Cube with notched surfaces
Computational Geometry. 43 (2): 73–83. doi:10.1016/j.comgeo.2009.04.003. Bern, Marshall; Eppstein, David (1995). "Mesh Generation and Optimal Triangulation". Computing
Chazelle_polyhedron
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
Girl/Female
American, Australian
God's Grace
Boy/Male
Indian, Sanskrit
Worthy of Salutation; Worshipping
Boy/Male
Latin
Calm.
Boy/Male
Hindu
Embodiment of philosophy of life
Girl/Female
Hebrew
Tenderness; barren.
Boy/Male
British, Christian, English, German, Norse, Teutonic
Divinely Good
Girl/Female
Hindu
Winning girl
Boy/Male
Muslim
Seeds, Spice, Seeds Man, One who sows, The Persian scribe and memorizer of tradition, Abu-ishaq Ibrahim had this name
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
A Rishi in Indian Mythology
Boy/Male
Hindu, Indian, Punjabi, Sikh
The New Warrior
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
TRIANGULATION GEOMETRY
n.
Formerly, strangulation, as in hernia.
v. t.
To affect with a sense of strangulation by passion or strong feeling.
n.
A stoppage or irritation of the windpipe, producing the feeling of strangulation.
p. pr. & vb. n.
of Triangulate
n.
The act of superposing, or the state of being superposed; as, the superposition of rocks; the superposition of one plane figure on another, in geometry.
v. t.
To determine the form, extent, position, etc., of, as a tract of land, a coast, harbor, or the like, by means of linear and angular measurments, and the application of the principles of geometry and trigonometry; as, to survey land or a coast.
n.
That branch of applied geometry which gives rules for finding the length of lines, the areas of surfaces, or the volumes of solids, from certain simple data of lines and angles.
a.
That chokes; producing the feeling of strangulation.
n.
An examination of a region as to its general natural features, preparatory to a more particular survey for the purposes of triangulation, or of determining the location of a public work.
n.
The act of strangling, or the state of being strangled.
n.
A disease of bovine cattle, consisting of a swelling under the throat, which, unless checked, causes strangulation.
n.
The art of delineating the forms of solid bodies on a plane; a branch of solid geometry which shows the construction of all solids which are regularly defined.
a.
Well versed in any branch of learning; qualified by study; learned; as, a man well studied in geometry.
n.
Inordinate compression or constriction of a tube or part, as of the throat; especially, such as causes a suspension of breathing, of the passage of contents, or of the circulation, as in cases of hernia.
n.
The series or network of triangles into which the face of a country, or any portion of it, is divided in a trigonometrical survey; the operation of measuring the elements necessary to determine the triangles into which the country to be surveyed is supposed to be divided, and thus to fix the positions and distances of the several points connected by them.
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
a.
Having familiar knowledge united with readiness and dexterity in its application; familiarly acquainted with; expert; skillful; -- often followed by in; as, a person skilled in drawing or geometry.
n.
A Spanish mode of execution by strangulation, with an iron collar affixed to a post and tightened by a screw until life become extinct; also, the instrument by means of which the punishment is inflicted.
n.
A constriction of the hernial sac, rendering it irreducible, but not great enough to cause strangulation.
n.
the science or art of conducting ships or vessels from one place to another, including, more especially, the method of determining a ship's position, course, distance passed over, etc., on the surface of the globe, by the principles of geometry and astronomy.