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# Vertex (geometry)

In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes. [1]

## Angle

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

## Computer graphics

Computer graphics are pictures and movies created using computers - usually referring to image data created by a computer specifically with help from specialized graphical hardware and software.

## Convex polygon

A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.

## Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

## Convex set

In Euclidean space, a convex set is the region such that, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region.

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

## CW complex

In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.

## Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

## Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler&ndash;Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

## Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

## Günter M. Ziegler

Günter Matthias Ziegler (born 19 May 1963) is a German mathematician.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Internal and external angle

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## John M. Sullivan (mathematician)

John Matthew Sullivan (born February 25, 1963) is an American mathematician who works in Germany as a professor at the Technical University of Berlin.

## Joseph O'Rourke (professor)

Joseph O'Rourke is the Olin Professor of Computer Science at Smith College and the founding chair of the Smith computer science department.

## Khronos Group

The Khronos Group is an American not-for-profit member-funded industry consortium based in Beaverton, Oregon, focused on the creation of open standard, royalty-free application programming interfaces (APIs) for authoring and accelerated playback of dynamic media on a wide variety of platforms and devices.

## N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

## Peter McMullen

Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

## Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit.

## Polyhedron

In elementary geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

## Polytope

In elementary geometry, a polytope is a geometric object with flat sides, and may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope.

## Princeton University Press

The Princeton University Press is an independent publisher with close connections to Princeton University.

## Right angle

In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line.

Satyan Linus Devadoss is a professor of mathematics at Williams College.

In the field of computer graphics, a shader is a computer program that is used to do shading: the production of appropriate levels of color within an image, or, in the modern era, also to produce special effects or do video post-processing.

## Simplicial complex

In mathematics, a simplicial complex is a topological space of a certain kind, constructed by "gluing together" points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

## Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball, (viz., analogous to a circular object in two dimensions).

## Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

## Vertex (computer graphics)

A vertex (plural vertices) in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space.

## Vertex (curve)

In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.

## Vertex (graph theory)

In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

## Vertex normal

In the geometry of computer graphics, a vertex normal at a vertex of a polyhedron is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of the surface.

## Vertex pipeline

The function of the vertex pipeline in any GPU is to take geometry data (usually supplied as vector points), work with it if needed with either fixed function processes (earlier DirectX), or a vertex shader program (later DirectX), and create all of the 3D data points in a scene to a 2D plane for display on a computer monitor.

## References

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