Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous 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.
sameAs
primaryTopic
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous 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.
has abstract
In geometry, Plücker coordinat ...... matics used for robot control.
@en
Les coordonnées plückeriennes ...... et 1839 par Hermann Grassmann.
@fr
Плюккеровы координаты — коорди ...... ю и для векторных пространств.
@ru
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。
@zh
Link from a Wikipage to an external page
Wikipage page ID
Wikipage revision ID
636,472,522
hypernym
comment
In geometry, Plücker coordinat ...... matics used for robot control.
@en
Les coordonnées plückeriennes ...... et 1839 par Hermann Grassmann.
@fr
Плюккеровы координаты — коорди ...... ю и для векторных пространств.
@ru
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。
@zh
label
Coordonnées plückeriennes
@fr
Plücker coordinates
@en
Плюккеровы координаты
@ru
普吕克坐标
@zh