Searches , social queries for DISCRETE COMPUTATIONAL-GEOMETRY
Search references for DISCRETE COMPUTATIONAL-GEOMETRY. Phrases containing DISCRETE COMPUTATIONAL-GEOMETRY
See searches and references containing DISCRETE COMPUTATIONAL-GEOMETRY!
Search references for DISCRETE COMPUTATIONAL-GEOMETRY. Phrases containing DISCRETE COMPUTATIONAL-GEOMETRY
See searches and references containing DISCRETE COMPUTATIONAL-GEOMETRY!DISCRETE COMPUTATIONAL-GEOMETRY
Academic journal
Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard
Discrete & Computational Geometry
Discrete_&_Computational_Geometry
Branch of computer science
computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is
Computational_geometry
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial
Discrete_geometry
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
Shape bounded by non-intersecting line segments
are commonly seen as the input to computational geometry problems, including point in polygon testing, area computation, the convex hull of a simple polygon
Simple_polygon
algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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 of
Polygon_triangulation
Hungarian mathematician
computer scientist working in the fields of combinatorics and discrete and computational geometry. Pach was born and grew up in Hungary. He comes from a noted
János_Pach
Conic solid with a polygonal base
"Isogonal Prismatoids", Discrete & Computational Geometry, 18: 13–52, doi:10.1007/PL00009307. O'Leary, Michael (2010), Revolutions of Geometry, John Wiley & Sons
Pyramid_(geometry)
Branch of geometry
geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry
Convex_geometry
Points separated from others by a line
In discrete geometry, a k {\displaystyle k} -set of a finite point set S {\displaystyle S} in the Euclidean plane is a subset of k {\displaystyle k} elements
K-set_(geometry)
Subdivision of the plane by lines
and order types in discrete and computational geometry", in Pach, János (ed.), New Trends in Discrete and Computational Geometry, Algorithms and Combinatorics
Arrangement_of_lines
Hungarian-Canadian mathematician
Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada
Károly_Bezdek
Edge-joined polygons which fold into a polyhedron
(2019-04-03), "Pseudo-Edge Unfoldings of Convex Polyhedra", Discrete & Computational Geometry, 64 (3): 671–689, arXiv:1709.04944, doi:10.1007/s00454-019-00082-1
Net_(polyhedron)
In computational geometry, an ε-net (pronounced epsilon-net) is the approximation of a general set by a collection of simpler subsets. In probability theory
Ε-net (computational geometry)
Ε-net_(computational_geometry)
Field of geometry closely arranging circles on a plane
packing" is concerned with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping
Circle_packing
Peak or top of a geometric figure
"Reptilings and space-filling curves for acute triangles". Discrete & Computational Geometry. 60 (1): 170–199. arXiv:1603.01382. doi:10.1007/s00454-017-9953-0
Apex_(geometry)
Farthest distance between two points
(1989), "Applications of random sampling in computational geometry II", Discrete & Computational Geometry, 4 (5): 387–421, doi:10.1007/BF02187740, MR 1014736
Diameter (computational geometry)
Diameter_(computational_geometry)
Polyhedron which tiles 3D space
(2009). "Generalizations of Schöbi's Tetrahedral Dissection". Discrete & Computational Geometry. 41 (2): 232–248. arXiv:0710.3857. doi:10.1007/s00454-008-9086-6
Space-filling_polyhedron
Analysis of datasets using techniques from topology
"Morse Theory for Filtrations and Efficient Computation of Persistent Homology". Discrete & Computational Geometry. 50 (2): 330–353. doi:10.1007/s00454-013-9529-6
Topological_data_analysis
Shortest network connecting points
"Euclidean minimum spanning trees and bichromatic closest pairs", Discrete & Computational Geometry, 6 (1), Springer: 407–422, doi:10.1007/BF02574698, MR 1115099
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Canadian computer scientist
Journal of Computational Geometry and Applications. He is also a member of the editorial board of Algorithmica, Discrete & Computational Geometry, and Computational
Timothy_M._Chan
Study of discrete mathematical structures
computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical
Discrete_mathematics
Prism with a 3-sided base
Publishing. Grünbaum, Branko (1997). "Isogonal Prismatoids". Discrete & Computational Geometry. 18: 13–52. doi:10.1007/PL00009307. Haul, Wm. S. (1893). Mensuration
Triangular_prism
Existence of a line through two points
number of ordinary lines determined by sets in complex space", Discrete & Computational Geometry, 61 (4): 778–808, arXiv:1611.08740, doi:10.1007/s00454-018-0039-4
Sylvester–Gallai_theorem
Method for computing topological features of a space at different spatial resolutions
Carlsson, Gunnar (2004-11-19). "Computing Persistent Homology". Discrete & Computational Geometry. 33 (2): 249–274. doi:10.1007/s00454-004-1146-y. ISSN 0179-5376
Persistent_homology
Area of mathematics
geometry Computational group theory Computational geometry Computational number theory Computational topology Computational statistics Algorithmic information
Computational_mathematics
Carlsson, Gunnar (2005). "Computing Persistent Homology". Discrete & Computational Geometry. 33 (2): 249–274. doi:10.1007/s00454-004-1146-y. ISSN 0179-5376
Persistence_module
Geometric graph with unit edge lengths
MR 0058193 Braß, Peter (2002), "Combinatorial geometry problems in pattern recognition", Discrete & Computational Geometry, 28 (4): 495–510, doi:10.1007/s00454-002-2884-3
Unit_distance_graph
Subfield of mathematical topology
topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational
Computational_topology
Geometric shape of rectangle and two semicircles
Yunlong (2015). "Positive center sets of convex curves". Discrete & Computational Geometry. 54 (3): 728–740. doi:10.1007/s00454-015-9715-9. MR 3392976
Stadium_(geometry)
Combinatorial approach of studying the topology of a manifold
"Morse Theory for Filtrations and Efficient computation of Persistent Homology". Discrete & Computational Geometry. 50 (2): 330–353. doi:10.1007/s00454-013-9529-6
Discrete_Morse_theory
Discrete and Computational Geometry: Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry–Ten Years
Symposium on Computational Geometry
Symposium_on_Computational_Geometry
Solid with 2 parallel n-gonal bases connected by n parallelograms
"Isogonal Prismatoids". Discrete & Computational Geometry. 18: 13–52. doi:10.1007/PL00009307. Malton, Thomas (1774). A Royal Road to Geometry: Or, an Easy and
Prism_(geometry)
In discrete geometry and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside
Relative_convex_hull
Theorem that any three objects in space can be simultaneously bisected by a plane
Conference on Computational Geometry, pp. 5–9. Lo, Chi-Yuan; Matoušek, Jiří; Steiger, William L. (1994), "Algorithms for Ham-Sandwich Cuts", Discrete & Computational
Ham_sandwich_theorem
geometry topics for another flavor of computational geometry that states problems in terms of geometric objects as discrete entities and hence the methods of
List of numerical computational geometry topics
List_of_numerical_computational_geometry_topics
Solid with six equal square faces
p. 247. Grünbaum, Branko (1997). "Isogonal Prismatoids". Discrete & Computational Geometry. 18 (1): 13–52. doi:10.1007/PL00009307. Senechal, Marjorie
Cube
Math theorem about sphere packing
Hales, Thomas C. (20 May 2002). "The Honeycomb Conjecture". Discrete & Computational Geometry. 25: 1–22. arXiv:math/9906042. doi:10.1007/s004540010071.
Kepler_conjecture
American mathematician
American mathematician working in the areas of representation theory, discrete geometry, and formal verification. In representation theory he is known for
Thomas_Callister_Hales
In discrete mathematics and theoretical computer science, reconfiguration problems are computational problems involving reachability or connectivity of
Reconfiguration
Puzzle computer game involving planar graphs
Pach, János; Tardos, Gábor (2002), "Untangling a polygon", Discrete & Computational Geometry, 28 (4): 585–592, doi:10.1007/s00454-002-2889-y Bose, Prosenjit;
Planarity
Branch of mathematics
methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or
Geometry
Polygon intersected up to twice by lines orthogonal to a given line
(1991), "Triangulating a Simple Polygon in Linear Time", Discrete & Computational Geometry, 6 (3): 485–524, doi:10.1007/BF02574703, ISSN 0179-5376 Amato
Monotone_polygon
combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects as discrete entities
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Multivariate generalization of the median
In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given
Centerpoint_(geometry)
(2021). "The Multi-Cover Persistence of Euclidean Balls". Discrete & Computational Geometry. 65 (4): 1296–1313. doi:10.1007/s00454-021-00281-9. ISSN 0179-5376
Multicover_bifiltration
Geometry without using coordinates
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic
Synthetic_geometry
Convex polytope whose vertices all have integer Cartesian coordinates
MR 1997998 Stanley, Richard P. (1986), "Two poset polytopes", Discrete & Computational Geometry, 1 (1): 9–23, doi:10.1007/BF02187680, MR 0824105 Lovász, László
Integral_polytope
list of books in computational geometry. There are two major, largely nonoverlapping categories: Combinatorial computational geometry, which deals with
List of books in computational geometry
List_of_books_in_computational_geometry
Natural number
"Closed-Form Expressions for Uniform Polyhedra and Their Duals". Discrete & Computational Geometry. 27 (3). Springer: 353–355, 372–373. doi:10.1007/s00454-001-0078-2
44_(number)
Toroidal polyhedron with 7 faces
Alexander (2024), "Adjacency Graphs of Polyhedral Surfaces", Discrete & Computational Geometry, 71 (4): 1429–1455, doi:10.1007/S00454-023-00537-6 Jungerman
Szilassi_polyhedron
Continuous unfolding of a polyhedron
convex polyhedra: Cut loci and nonoverlapping unfoldings", Discrete & Computational Geometry, 39 (1–3): 339–388, doi:10.1007/s00454-008-9052-3, MR 2383765
Blooming_(geometry)
Discrete (i.e., incremental) version of infinitesimal calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of
Discrete_calculus
Problem in discrete geometry
In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly linear number of distinct distances
Erdős distinct distances problem
Erdős_distinct_distances_problem
Graph formed by touching unit circles
"On the independence number of minimum distance graphs", Discrete & Computational Geometry, 20 (2): 179–187, doi:10.1007/PL00009381, MR 1637884 Brass
Penny_graph
Shape with three sides
in Discrete and Computational Geometry: Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry—Ten
Triangle
Partition of Earth's surface into subdivided cells
2019-02-18. "Computational geometry and spatial indexing on the sphere: Google/s2geometry". GitHub. 2019-02-18. OGC DGGS Standards Working Group Discrete Global
Discrete_global_grid
Flat-sided three-dimensional shape
(1993), Computational Geometry in C, Cambridge University Press, pp. 113–116. Grünbaum, Branko (1999), "Acoptic polyhedra" (PDF), Advances in discrete and
Polyhedron
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical
Numerical_algebraic_geometry
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Roman (2012-07-20). "Notes About the Carathéodory Number". Discrete & Computational Geometry. 48 (3): 783–792. arXiv:1112.5942. doi:10.1007/s00454-012-9439-z
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
Deals with digitized models or images of objects of the 2D or 3D Euclidean space
Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean
Digital_geometry
Bound on the number of incidences between points and lines in the plane
Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean plane
Szemerédi–Trotter_theorem
Hungarian-Canadian mathematician
Columbia. His main research interests are arithmetic combinatorics, discrete geometry, graph theory, and combinatorial number theory. Solymosi earned his
József_Solymosi
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
Set of mathematical concepts in quantum gravity
principles" is Discrete Lorentzian quantum gravity. Noncommutative geometry Quantum spacetime Tomasiello, Alessandro (2022). Geometry of String Theory
Quantum_geometry
Non-orientable surface with one edge
3-space of the six-pentagon map of the projective plane". Discrete & Computational Geometry. 40 (3): 395–400. doi:10.1007/s00454-007-9033-y. MR 2443291
Möbius_strip
On tangency patterns of circles
J. (2021), "Packing disks by flipping and flowing" (PDF), Discrete & Computational Geometry, 66 (4): 1262–1285, arXiv:1910.02327, doi:10.1007/s00454-020-00242-8
Circle_packing_theorem
In computational geometry, a Steiner point is a point that is not part of the input to a geometric optimization problem but is added during the solution
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Study of systems of inequalitites
computing the Euler characteristic of semi-algebraic sets". Discrete & Computational Geometry. 22 (1): 1–18. doi:10.1007/PL00009443. hdl:2027.42/42421.
Real_algebraic_geometry
Type of plane partition
Conference on Computational Geometry (CCCG 2016). Edelsbrunner, Herbert (2012) [1987]. "13.6 Power Diagrams". Algorithms in Combinatorial Geometry. EATCS Monographs
Voronoi_diagram
Quickly growing function
made faster within the cell-probe model of computational complexity. Certain problems in discrete geometry related to Davenport–Schinzel sequences have
Ackermann_function
Algorithm to compute rounding error
Floating-Point Arithmetic and Fast Robust Geometric Predicates". Discrete & Computational Geometry. 18 (3): 305–363. doi:10.1007/PL00009321. Knuth, Donald E
2Sum
Fundamental object of geometry
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical
Point_(geometry)
Cube with notched surfaces
partitions for hidden-surface removal and solid modeling". Discrete & Computational Geometry. 5 (5): 485–503. doi:10.1007/BF02187806. Erickson, Jeff (June
Chazelle_polyhedron
Concept in three-dimensional geometry
"Dense crystalline dimer packings of regular tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. doi:10.1007/s00454-010-9273-0
Tetrahedron_packing
Does the plane contains a dense set of points whose distances are all rational
de Zeeuw, Frank (2010), "On a question of Erdős and Ulam", Discrete & Computational Geometry, 43 (2): 393–401, arXiv:0806.3095, doi:10.1007/s00454-009-9179-x
Erdős–Ulam_problem
American mathematician
collection of original research papers in discrete and computational geometry entitled Discrete and Computational Geometry: The Goodman–Pollack Festschrift was
Richard_M._Pollack
American geometer (1933–2021)
American Mathematical Society (1): 301–309 "Discrete & Computational Geometry". Discrete & Computational Geometry. Springer Science+Business Media. Archived
Jacob_E._Goodman
Smallest convex set containing a given set
"A polynomial solution for the potato-peeling problem", Discrete & Computational Geometry, 1 (2): 155–182, doi:10.1007/BF02187692, MR 0834056 Chazelle
Convex_hull
Infinite regular skew polyhedron
Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete & Computational Geometry. 17 (47): 449–478. doi:10.1007/PL00009304. McMullen, Peter;
Regular_skew_apeirohedron
American computer scientist
(1994). "Helly theorems and generalized linear programming". Discrete & Computational Geometry. 12 (3): 241–261. Amenta, Nina; Bern, Marshall; Eppstein,
Nina_Amenta
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
Numerical method
A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of
Discrete_element_method
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a
Constructive_solid_geometry
Branch of mathematics
theory and computational technique. In the 20th century, algebraic geometry split into several subareas. The mainstream of algebraic geometry is devoted
Algebraic_geometry
conjecture (discrete geometry) Kirchberger's theorem (discrete geometry) Krein–Milman theorem (mathematical analysis, discrete geometry) Minkowski's
List_of_theorems
Form of plane tiling without repeats at scale
Grünbaum, Branko; Shephard, G. C. (1992). "Aperiodic tiles". Discrete & Computational Geometry. 8 (1): 1–25. doi:10.1007/BF02293033. MR 1156132. Gardner
Aperiodic_tiling
Unsolved geometry problem about planar regions
"An improved upper bound for Leo Moser's worm problem", Discrete and Computational Geometry, 29 (3): 409–417, doi:10.1007/s00454-002-0774-3, MR 1961007
Moser's_worm_problem
Four-dimensional analogue of the cube
Satisfying Conway's Criterion (PDF). 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG3 2016). Tokyo. Kemp, Martin (1
Tesseract
Mexican mathematician and computer scientist
University of Mexico (UNAM). His research primarily concerns discrete and computational geometry. Urrutia earned his Ph.D. from the University of Waterloo
Jorge_Urrutia_Galicia
Open-source geometric modelling kernel
; Näher, S. (2004). "Two computational geometry libraries: LEDA and CGAL". Handbook of Discrete and Computational Geometry. pp. 1435–1464.. CGAL User
CGAL
Graph of intervisible locations in computational geometry
In computational geometry and robot motion planning, a visibility graph is a graph of intervisible locations, typically for a set of points and obstacles
Visibility_graph
American mathematician
Heptagons, no Three Points on a Line, no Four on a Circle" (PDF). Discrete & Computational Geometry. 39 (4): 786–790. doi:10.1007/s00454-007-9038-6. ISSN 0179-5376
Sarah_Peluse
Study of geometry using a coordinate system
foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system
Analytic_geometry
Triangle with at least two sides congruent
"Reptilings and space-filling curves for acute triangles", Discrete & Computational Geometry, 60 (1): 170–199, arXiv:1603.01382, doi:10.1007/s00454-017-9953-0
Isosceles_triangle
On point sets with no small-area triangles
chosen to maximize this area? More unsolved problems in mathematics In discrete geometry and discrepancy theory, the Heilbronn triangle problem asks how to
Heilbronn_triangle_problem
Overview of and topical guide to geometry
solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic
Outline_of_geometry
Combinatorial theory of mechanics and discrete geometry
In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected
Structural_rigidity
Ziegler, G. M. (2000-09-01). "Neighborly Cubical Polytopes". Discrete & Computational Geometry. 24 (2): 325–344. arXiv:math/9812033. doi:10.1007/s004540010039
Graph_of_a_polytope
travel, tourism, insurance
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
DISCRETE COMPUTATIONAL-GEOMETRY
travel, tourism, insurance