Category: Geometric algorithms

Fixed-radius near neighbors
In computational geometry, the fixed-radius near neighbor problem is a variant of the nearest neighbor search problem. In the fixed-radius near neighbor problem, one is given as input a set of points
Largest empty sphere
In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in d-dimensional space whose interior does not overlap with any given obstacles.
Hierarchical RBF
In computer graphics, a hierarchical RBF is an interpolation method based on Radial basis functions (RBF). Hierarchical RBF interpolation has applications in the construction of shape models in 3D com
Gradient pattern analysis
Gradient pattern analysis (GPA) is a geometric computing method for characterizing geometrical bilateral symmetry breaking of an ensemble of symmetric vectors regularly distributed in a square lattice
The Computational Geometry Algorithms Library (CGAL) is an open source software library of computational geometry algorithms. While primarily written in C++, Scilab bindings and bindings generated wit
Minkowski addition
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously,
Steiner tree problem
In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Ste
Visibility polygon
In computational geometry, the visibility polygon or visibility region for a point p in the plane among obstacles is the possibly unbounded polygonal region of all points of the plane visible from p.
Spatial database
A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools f
Bregman divergence
In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function
Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that
Point in 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. It is a special case of point location prob
Space partitioning
In geometry, space partitioning is the process of dividing a space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divid
Mesh generation
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells.Often these cells form a simplicial complex.Usually the
Vertex enumeration problem
In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the ob
Visibility (geometry)
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 in the space are said to be visible to each oth
Criss-cross algorithm
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear ineq
Nearest neighbor search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically
Star-shaped polygon
In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible. Formally, a pol
Visvalingam–Whyatt algorithm
The Visvalingam–Whyatt algorithm, also known as the Visvalingam's algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points.
Möller–Trumbore intersection algorithm
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dim
Fan triangulation
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 of the polygon. Not every polygon can be tri
Weighted Voronoi diagram
In mathematics, a weighted Voronoi diagram in n dimensions is a generalization of a Voronoi diagram. The Voronoi cells in a weighted Voronoi diagram are defined in terms of a distance function. The di
Delaunay tessellation field estimator
The Delaunay tessellation field estimator (DTFE), (or Delone tessellation field estimator (DTFE)) is a mathematical tool for reconstructing a volume-covering and continuous density or intensity field
Minimum bounding box algorithms
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to v
Bowyer–Watson algorithm
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 dimensions. The algorithm can be also used to obt
Greedy geometric spanner
In computational geometry, a greedy geometric spanner is an undirected graph whose distances approximate the Euclidean distances among a finite set of points in a Euclidean space. The vertices of the
Closest pair of points problem
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The clos
Gilbert–Johnson–Keerthi distance algorithm
The Gilbert–Johnson–Keerthi distance algorithm is a method of determining the minimum distance between two convex sets. Unlike many other distance algorithms, it does not require that the geometry dat
Midpoint circle algorithm
In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. Bresenham's circle algorithm is derived from the midpoint circle algor
Katchalski-Katzir algorithm
The Katchalski-Katzir algorithm is an algorithm for docking of rigid molecules, developed by Ephraim Katchalski-Katzir, Isaac Shariv and Miriam Eisenstein. In 1990 Professor Ephraim Katchalski-Katzir,
Monotone polygon
In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects the boundary of P at most twice. Similarly, a polygonal chain C is
Rectilinear Steiner tree
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plan
Rotating calipers
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.
Geometric algorithms
No description available.
Geometric design
Geometrical design (GD) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes and is closely related to geometric modeling.
Line–line intersection
In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer
Prune and search
Prune and search is a method of solving optimization problems suggested by Nimrod Megiddo in 1983. The basic idea of the method is a recursive procedure in which at each step the input size is reduced
Euclidean shortest path
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that doe
Linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by
Minimum bounding rectangle
In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, p
Stencil jumping
Stencil jumping, at times called stencil walking, is an algorithm to locate the grid element enclosing a given point for any structured mesh. In simple words, given a point and a structured mesh, this
Gilbert–Pollack conjecture
No description available.
Watchman route problem
The Watchman Problem is an optimization problem in computational geometry where the objective is to compute the shortest route a watchman should take to guard an entire area with obstacles given only
Line–plane intersection
In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is th
Cone algorithm
In computational geometry, the cone algorithm is an algorithm for identifying the particles that are near the surface of an object composed of discrete particles. Its applications include computationa
Proximity problems
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects. A subset of these problems stated in terms of points only are somet
Bounding volume
In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to im
Wiener connector
In network theory, the Wiener connector is a means of maximizing efficiency in connecting specified "query vertices" in a network. Given a connected, undirected graph and a set of query vertices in a
Sweep line algorithm
In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space. I
JTS Topology Suite
JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functio
Bounding sphere
In mathematics, given a non-empty set of objects of finite extension in -dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an -dimen
Geometric modeling
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modelin
Marching triangles
In computer graphics, the problem of transforming a cloud of points on the surface of a three-dimensional object into a polygon mesh for the object can be solved by a technique called marching triangl
Surface-to-surface intersection problem
The surface-to-surface intersection (SSI) need. is a basic workflow in computer-aided geometric design: Given two intersecting surfaces in R3, compute all parts of the intersection curve. If two surfa
Bitonic tour
In computational geometry, a bitonic tour of a set of point sites in the Euclidean plane is a closed polygonal chain that has each site as one of its vertices, such that any vertical line crosses the
Fréchet distance
In mathematics, the Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. It is named after Maurice Fréchet.
Bentley–Ottmann 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 the intersection points (or, simply, intersections
Geometric median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the
Line–sphere intersection
In analytic geometry, a line and a sphere can intersect in three ways: 1. * No intersection at all 2. * Intersection in exactly one point 3. * Intersection in two points. Methods for distinguishing
Rectangle packing
Rectangle packing is a packing problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon, such that no two small rectangles overlap
Local feature size
Local feature size refers to several related concepts in computer graphics and computational geometry for measuring the size of a geometric object near a particular point. * Given a smooth manifold ,
Planar straight-line graph
In computational geometry and geometric graph theory, a planar straight-line graph, in short PSLG, (or straight-line plane graph, or plane straight-line graph) is a term used for an embedding of a pla
Shoelace formula
The shoelace formula, shoelace algorithm, or shoelace method (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose
Lloyd's algorithm
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points i
List of numerical computational geometry topics
List of numerical computational geometry topics enumerates the topics of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature ch
HyperFun (from Hyperdimensional Functions) is a programming language and software used to create, visualize, and fabricate volumetric 3D and higher-dimensional models. The team maintaining the HyperFu
Ramer–Douglas–Peucker algorithm
The Ramer–Douglas–Peucker algorithm, also known as the Douglas–Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar cu
Geometric spanner
A geometric spanner or a t-spanner graph or a t-spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a t-path between any pair of vertices for a
Minimum bounding box
In geometry, the minimum or smallest bounding or enclosing box for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which a
Symmetrization methods
In mathematics the symmetrization methods are algorithms of transforming a set to a ball with equal volume and centered at the origin. B is called the symmetrized version of A, usually denoted . These
Line fitting
Line fitting is the process of constructing a straight line that has the best fit to a series of data points. Several methods exist, considering: * Vertical distance: Simple linear regression * Resi
Geometric primitive
In vector computer graphics, CAD systems, and geographic information systems, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (d
Boolean operations on polygons
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR, ...) operating on one or more sets of polygons in computer graphics. These sets of operations are widely used in comp
Multiple line segment intersection
In computational geometry, the multiple line segment intersection problem supplies a list of line segments in the Euclidean plane and asks whether any two of them intersect (cross). Simple algorithms
Function representation
Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementatio
Centroidal Voronoi tessellation
In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation in which the generating point of each Voronoi cell is also its centroid (center of mass). It can be viewe
Minkowski Portal Refinement
The Minkowski Portal Refinement collision detection algorithm is a technique for determining whether two convex shapes overlap. The algorithm was created by in 2006 and was first published in Game Pro
Largest empty rectangle
In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed a
Nesting algorithm
Nesting algorithms are used to make the most efficient use of material or space by evaluating many different possible combinations via recursion. 1. * Linear (1-dimensional): The simplest of the algo
Velocity obstacle
In robotics and motion planning, a velocity obstacle, commonly abbreviated VO, is the set of all velocities of a robot that will result in a collision with another robot at some moment in time, assumi