Quad-edge

Quad-edge

A quad-edge data structure is a computer representation of the topology of a two-dimensional or three-dimensional map, that is, a graph drawn on a (closed) surface.

Overview

The quad-edge data structure:
* represents simultaneously both the map, its dual and mirror image.
* can represent the most general form of a map, admitting vertices and faces of degree 1 and 2.
* is a variant of the earlier winged edge data structure.

The fundamental idea behind the quad-edge structure is the recognition that a single edge, in a closed polygonal mesh topology, sits between exactly two faces and exactly two vertices. Thus, it can represent a dual of the graph simply by reversing the convention on what is a vertex and what is a face.

Details

The quad-edge structure gets its name from the general mechanism by which they are stored. A single Edge structure conceptually stores references to up to two faces, two vertices, and 4 edges. The four edges stored are the edges starting with the two vertices that are attached to the two stored faces.

Uses

Much like Winged Edge, quad-edge structures are used in programs to store the topology of a 2D or 3D polygonal mesh. The mesh itself does not need to be closed in order to form a valid quad-edge structure.

Using a quad-edge structure, iterating through the topology is quite easy. Often, the interface to quad-edge topologies is through directed edges. This allows the two vertices to have explicit names (start and end), and this gives faces explicit names as well (left and right, relative to a person standing on start and looking in the direction of end). The 4 edges are also given names, based on the vertices and faces: start-left, start-right, end-left, and end-right. A directed edge can be reversed to generate the edge in the opposite direction.

Iterating around a particular face only requires having a single directed edge to which that face is on the left (by convention) and then walking through all of the start-left edges until the original edge is reached.

References

* The quad-edge data structure was described in the paper by Leonidas J. Guibas and Jorge Stolfi, "Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams", "ACM Transactions on Graphics", 4(2), 1985, 75-123

External links

* http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/quadedge.html A quad-edge implementation in C++.
* http://www.ic.unicamp.br/~stolfi/EXPORT/software/c/2000-05-04/libquad/ A quad-edge implementation in C.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Edge detection — is a terminology in image processing and computer vision, particularly in the areas of feature detection and feature extraction, to refer to algorithms which aim at identifying points in a digital image at which the image brightness changes… …   Wikipedia

  • Quad band — (also known as quad band or quadband ) literally means four bands. Most people come across the term when it is used to describe a mobile phone supporting four frequency bands. Having more than one frequency in one device is useful to enable… …   Wikipedia

  • Quad Data Rate SRAM — Quad Data Rate (QDR) SRAM is a type of static RAM computer memory that can transfer up to four words of data in each clock cycle. Like Double Data Rate (DDR) SDRAM, QDR SRAM transfers data on both rising and falling edges of the clock signal.… …   Wikipedia

  • Quad-City Times — The July 27, 2005 front page of the Quad City Times Type Daily newspaper Format Broadsheet Owner …   Wikipedia

  • Quad-flat no-leads package — 28 pin QFN, upside down to show contacts and thermal/ground pad Flat no leads packages such as QFN (quad flat no leads) and DFN (dual flat no leads) physically and electrically connect integrated circuits to printed circuit boards. Flat no leads …   Wikipedia

  • Quad-Ominos — This article is about the 1978 game published by Pressman. Quad Ominos is a game published by Pressman beginning in 1978. It is permanently out of production but generally available on the secondhand market. It is similar in theory to Triominoes… …   Wikipedia

  • Doubly connected edge list — The doubly connected edge list (DCEL) is a data structure to represent an embedding of a planar graph in the plane and polytopes in 3D. This data structure provides efficient manipulation of the topological information associated with the objects …   Wikipedia

  • Winged edge — The winged edge data structure is a commonly used data representation used to describe polygon models in computer graphics. It explicitly describes the geometry and topology of faces, edges, and vertices when three or more surfaces come together… …   Wikipedia

  • Doubly-connected edge list — Die Doubly connected edge list (DCEL, doppelt verkettete Kantenliste) ist eine Datenstruktur, die einen zusammenhängenden planaren Graphen repräsentiert, der in die Ebene eingebettet ist. Die Datenstruktur wird in der algorithmischen Geometrie… …   Deutsch Wikipedia

  • MotorStorm: Arctic Edge — MotorStorm Arctic Edge Éditeur Sony Computer Entertainment Développeur Bigbig Studios …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”