e/Plucker coordinates

Information
has gloss	eng: In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogenous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P3 and points on a quadric in P5 (projective 5-space). A predecessor and special case of Grassmann coordinates (which describe k-dimensional linear subspaces, or flats, in an n-dimensional Euclidean space), Plücker coordinates arise naturally in geometric algebra. They have proved useful for computer graphics, and also can be extended to coordinates for the screws and wrenches in the theory of kinematics used for robot control.
lexicalization	eng: Plucker co-ordinates
lexicalization	eng: Plucker coordinates
lexicalization	eng: Pluecker co-ordinates
lexicalization	eng: Pluecker coordinates
lexicalization	eng: Plücker co-ordinates
lexicalization	eng: Plücker coordinates
instance of	(noun) a system that uses coordinates to establish position reference system, coordinate system, frame of reference, reference frame

Meaning
French
has gloss	fra: Définition On considère la grassmannienne G(2,4) formé par les sous-espaces de dimension 2 dans un espace de dimension 4, cest-à-dire la plus simple des Grassmanniennes qui ne soit pas un espace projectif. Elle a été identifiée par Julius Plücker, comme lensemble des droites de l'espace projectif de dimension 3.
lexicalization	fra: coordonnées plückeriennes
Chinese
has gloss	zho: 数学上，普吕克坐标是将射影三维空间中的每条线给予6个齐次坐标，也就是一个射影5维空间中的一点。普吕克坐标由尤利乌斯·普吕克于1844年给出。
lexicalization	zho: 普吕克坐标

Media
media:img	Plücker line coordinate geometry.png