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1995 mathematics text
Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec
Algorithmic_Geometry
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
Class of algorithms in computational geometry
applications in mathematics and computer science. In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of
Convex_hull_algorithms
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Shape with three sides
Mishra, Bud (eds.). Algorithmic Foundation of Robotics VII: Selected Contributions of the Seventh International Workshop on the Algorithmic Foundations of
Triangle
Class of algorithms which use a moving line to solve geometrical problems
In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface
Sweep_line_algorithm
Subfield of mathematical topology
computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for
Computational_topology
Range Searching". Jean-Daniel Boissonnat; Mariette Yvinec (1998). Algorithmic Geometry. Cambridge University Press. ISBN 0-521-56529-4. Translation of a
List of books in computational geometry
List_of_books_in_computational_geometry
Artificial intelligence (AI) program
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language
AlphaGeometry
Mathematical abstraction of objects being "visible"
In geometry, visibility is a mathematical abstraction of the real-life notion of visibility. Given a set of obstacles in the Euclidean space, two points
Visibility_(geometry)
Method of determining minimum distance between two convex sets
Sathiya Keerthi in 1988. Unlike many other distance algorithms, it does not require that the geometry data be stored in any specific format, but instead
Gilbert–Johnson–Keerthi distance algorithm
Gilbert–Johnson–Keerthi_distance_algorithm
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
French computer scientist
project for implementing geometric algorithms. With Mariette Yvinec, he is the author of the book Algorithmic Geometry (Cambridge University Press, 1998
Jean-Daniel_Boissonnat
Art genre
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called
Algorithmic_art
Open-source geometric modelling kernel
The Computational Geometry Algorithms Library (CGAL) is an open source software library of computational geometry algorithms. While primarily written in
CGAL
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
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
Type of metric geometry
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined
Taxicab_geometry
German computer scientist
the German phrase "Algorithmische Geometrie" [algorithmic geometry] to refer to computational geometry. He is a professor of computer science at the Free
Helmut_Alt
Sequence of operations for a task
aversion Algorithm engineering Algorithm characterizations Algorithmic bias Algorithmic composition Algorithmic entities Algorithmic synthesis Algorithmic technique
Algorithm
Algorithm on linear-feedback shift registers
Berlekamp–Massey algorithm to multidimensional arrays; the resulting Berlekamp–Massey–Sakata (BMS) algorithm is used in decoding some algebraic geometry codes,
Berlekamp–Massey_algorithm
French robotician (1953–2021)
fields (graph theory, algorithmic geometry, non-linear control, optimal control, differential geometry, probabilistic algorithmics, neuroscience) applied
Jean-Paul_Laumond
triangulation was done by Mucke, Saias and Zhu (ACM Symposium of Computational Geometry, 1996). In both cases, a boundary condition was assumed, namely, Q must
Jump-and-Walk_algorithm
and applies methods and algorithms of nature characteristic to numerical analysis. This area is also called "machine geometry", computer-aided geometric
List of numerical computational geometry topics
List_of_numerical_computational_geometry_topics
French mathematician
Algorithmique (with Jean-Daniel Boissonnat, Edusciences 1995), translated as Algorithmic Geometry (Hervé Brönnimann, trans., Cambridge University Press, 1998) Geometric
Mariette_Yvinec
Curve simplification algorithm
Boost.Geometry support Douglas–Peucker simplification algorithm Implementation of Ramer–Douglas–Peucker and many other simplification algorithms with open
Ramer–Douglas–Peucker algorithm
Ramer–Douglas–Peucker_algorithm
Algorithm for computing convex hulls in a set of points
In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. In the two-dimensional
Gift_wrapping_algorithm
Research topic in computational geometry
convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami operator. Applications of geometry processing algorithms already cover a
Geometry_processing
Subfield of computer science and mathematics
and verification, algorithmic game theory, machine learning, computational biology, computational economics, computational geometry, and computational
Theoretical_computer_science
Optimization problem in computer science
classification – see k-nearest neighbor algorithm Computer vision – for point cloud registration Computational geometry – see Closest pair of points problem
Nearest_neighbor_search
Sweep line algorithm
In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e. it finds
Bentley–Ottmann_algorithm
Study of algorithms for performing number theoretic computations
as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including
Computational_number_theory
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)
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
computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in
Lists_of_mathematics_topics
mathematics, linear programming, combinatorial optimization and algorithmic geometry of numbers. Eisenbrand received his PhD at Saarland University in
Friedrich_Eisenbrand
Application of geometry in number theory
Geometry of numbers, also known as geometric number theory, is the part of number theory which uses geometry for the study of algebraic numbers. Typically
Geometry_of_numbers
Application of mathematical methods to other fields
Conte, S. D., & De Boor, C. (2017). Elementary numerical analysis: an algorithmic approach. Society for Industrial and Applied Mathematics. Greenspan,
Applied_mathematics
Israeli computer scientist
(ICRA), the European Workshop on Computational Geometry (EuroCG), and the Workshop on the Algorithmic Foundations of Robotics (WAFR). Dan Halperin at
Dan_Halperin
Non-Euclidean geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel
Elliptic_geometry
Curved curface derived from a coarse polygon mesh
specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, the underlying inner mesh, can be calculated
Subdivision_surface
Smallest box which encloses some set of points
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in
Minimum_bounding_box
Study of discrete mathematical structures
are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical problems and representations of geometrical objects
Discrete_mathematics
Biennial conference series on computational number theory
devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers
Algorithmic Number Theory Symposium
Algorithmic_Number_Theory_Symposium
Symposium on Algorithms SODA – ACM–SIAM Symposium on Discrete Algorithms SWAT and WADS – SWAT and WADS conferences Conferences on computational geometry, graph
List of computer science conferences
List_of_computer_science_conferences
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
Class of algorithms
flood fill algorithm is a simple but relatively robust algorithm that works for intricate geometries and can determine which part of the (target) area that
Flooding_algorithm
Computational problem
object from the source to destination. The term is used in computational geometry, computer animation, robotics and computer games. For example, consider
Motion_planning
Topics referred to by the same term
three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations Euclidean geometry, the study of the properties of Euclidean
Euclidean
Branch of discrete mathematics
of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking
Combinatorics
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
American computer scientist and mathematician (born 1963)
University of California, Irvine, known for his work in computational geometry, graph algorithms, and recreational mathematics. Eppstein is also a Wikipedia editor
David_Eppstein
Line-drawing algorithm
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form
Bresenham's_line_algorithm
Mathematical treatise by Euclid
Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest
Euclid's_Elements
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
Algorithm for computing convex hulls in a set of points
analyze the algorithm, but rather to provide a textbook example of what and how may fail due to floating-point computations in computational geometry. Later
Graham_scan
Measure of algorithmic complexity
known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It
Kolmogorov_complexity
Vector quantization algorithm minimizing the sum of squared deviations
the mean, and this way minimizes L 1 {\displaystyle L_{1}} norm (Taxicab geometry). k-medoids (also: Partitioning Around Medoids, PAM) uses the medoid instead
K-means_clustering
Sequence of points far from previous points
In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected
Farthest-first_traversal
Computational Geometry. 39 (1–3): 174–190. doi:10.1007/s00454-008-9050-5. David Avis; Komei Fukuda (December 1992). "A pivoting algorithm for convex hulls
Vertex_enumeration_problem
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
Search for an atomic arrangement with the lowest inter-atomic force
chemistry, energy minimization (also called energy optimization, geometry minimization, or geometry optimization) is the process of finding an arrangement in
Energy_minimization
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)
Area of research
Architectural geometry is an area of research which combines applied geometry and architecture, which looks at the design, analysis and manufacture processes
Architectural_geometry
Sums vector sets A and B by adding each vector in A to each vector in B
∈ A , b ∈ B } . {\displaystyle A+B=\{a+b\mid a\in A,\ b\in B\}.} In geometry, the Minkowski sum of two subsets A and B of a Euclidean space is the set
Minkowski_addition
Term in computer science
objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games
Collision_detection
Iterative design process
constructive solid geometry (CSG)-based technique to create smooth topology shapes with precise geometric control. Then, a genetic algorithm is used to optimize
Generative_design
Area of mathematics
algebraic geometry Computational group theory Computational geometry Computational number theory Computational topology Computational statistics Algorithmic information
Computational_mathematics
Polygon visible from one of its points
In geometry, a star-shaped polygon is a polygonal region in the euclidean plane which is a star domain, that is, a polygon that contains a point from which
Star-shaped_polygon
Polish computer scientist
Indyk's research focuses primarily on computational geometry in high-dimensions, streaming algorithms, and computational learning theory. He has made a
Piotr_Indyk
Book by Marvin Minsky and Seymour Papert
Perceptrons: An Introduction to Computational Geometry is a book written by Marvin Minsky and Seymour Papert and published in 1969. An edition with handwritten
Perceptrons_(book)
theories and algorithms of combinatorial character. See List of numerical computational geometry topics for another flavor of computational geometry that deals
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
In computational geometry, the multiple line segment intersection problem supplies a list of line segments in the Euclidean plane and asks whether any
Multiple line segment intersection
Multiple_line_segment_intersection
Yvinec, Mariette (1998), "15.3.2 Computing the lower envelope", Algorithmic Geometry, Cambridge University Press, p. 358, ISBN 9780521565295 Choquet (1966)
Lower_envelope
Voronoi tessellation where the generating point of each Voronoi cell is also its centroid
Three centroidal Voronoi tessellations of five points in a square In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation
Centroidal Voronoi tessellation
Centroidal_Voronoi_tessellation
Unsolved problem in graph theory
In mathematics, the Gilbert–Pollak conjecture is an unproven conjecture on the ratio of lengths of Steiner trees and Euclidean minimum spanning trees for
Gilbert–Pollak_conjecture
In proof theory, the Geometry of Interaction (GoI) was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs can
Geometry_of_interaction
Problem in computational complexity theory
H. (1995), "On a class of O(n2) problems in computational geometry", Computational Geometry: Theory and Applications, 5 (3): 165–185, doi:10.1016/0925-7721(95)00022-2
3SUM
Historical development of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry
History_of_geometry
Determining whether a knot is the unknot
crossings. Understanding the complexity of these algorithms is an active field of study. Algorithmic topology Unknotting number Hard unknot Mentioned
Unknotting_problem
Computer hardware technology that uses quantum mechanics
scientific and algorithmic discovery". arXiv:2506.13131 [cs.AI]. Zhang, C.; et al. (22 October 2025). "Quantum computation of molecular geometry via many-body
Quantum_computing
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
Adjusting the complexity of a 3D model representation to save storage and computation
what will be discussed here. After introducing some available algorithms for geometry management, it is stated that most fruitful gains came from ".
Level of detail (computer graphics)
Level_of_detail_(computer_graphics)
geometry Gauss–Bonnet theorem, a theorem about curvature in differential geometry for 2d surfaces Chern–Gauss–Bonnet theorem in differential geometry
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Measure method in computational geometry
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including
Rotating_calipers
Czech mathematician (1963–2015)
Mathematical and algorithmic applications of linear algebra. American Mathematical Society, 2010, ISBN 978-0-8218-4977-4. Approximation Algorithms and Semidefinite
Jiří_Matoušek_(mathematician)
Computational geometry problem
of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find a pair of points
Closest pair of points problem
Closest_pair_of_points_problem
Sub-field of computer science
graphics might be: Geometry: ways to represent and process surfaces Animation: ways to represent and manipulate motion Rendering: algorithms to reproduce light
Computer graphics (computer science)
Computer_graphics_(computer_science)
Measure of similarity between curves
the Computational Geometry Algorithms Library de Berg, Mark, "Analyzing Trajectories of Moving Objects", Computational Geometry, Two Selected Topics
Fréchet_distance
Algorithms for mesh generation
generation, Delaunay refinements are algorithms for mesh generation based on the principle of adding Steiner points to the geometry of an input to be meshed, in
Delaunay_refinement
Technique or strategy underlying a variety of algorithms
algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic
Algorithmic_paradigm
Subspace of n-space whose dimension is (n-1)
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like
Hyperplane
Part of a line that is bounded by two distinct end points; line with two endpoints
is a triangle. Chord (geometry) Diameter Radius Polygonal chain Interval (mathematics) Line segment intersection, the algorithmic problem of finding intersecting
Line_segment
Connected series of line segments
In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain P {\displaystyle P} is a curve specified by
Polygonal_chain
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
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)
is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes
Geometric_modeling
Determining where a point is in relation to a coplanar polygon
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon
Point_in_polygon
Finding the smallest circle that contains all given points
circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set
Smallest-circle_problem
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
Boy/Male
Indian, Tamil, Telugu
Lord Muruga; Happy; Joy; Beauty
Girl/Female
Native American
Independent.
Boy/Male
Muslim/Islamic
Star celestial body
Girl/Female
Hindu, Indian, Marathi, Tamil
Lamp; Light
Girl/Female
Muslim
She was a companion
Boy/Male
Arabic, Muslim
Gift of the Merciful Allah
Female
Scottish
Variant form of Scottish Gaelic Oighrig, possibly EIRIC means "new speckled one."
Male
Portuguese
Galician-Portuguese form of Latin Johannes, XOÃN means "God is gracious."
Boy/Male
Muslim
A companion of the prophet
Girl/Female
Gujarati, Hindu, Indian, Kannada
Gift of God
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
ALGORITHMIC GEOMETRY
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
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.
The art of calculating by nine figures and zero.
n.
That branch of geometry which treats of the cone and the curves which arise from its sections.
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.
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.
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.
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.
n.
A Greek geometer of the 3d century b. c.; also, his treatise on geometry, and hence, the principles of geometry, in general.
n.
That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
n.
Related to Euclid, or to the geometry of Euclid.
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.
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.
n.
That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.
n.
Alt. of Algorithm
n.
A treatise on this science.
n.
The four "liberal arts," arithmetic, music, geometry, and astronomy; -- so called by the schoolmen. See Trivium.
a.
Well versed in any branch of learning; qualified by study; learned; as, a man well studied in geometry.