Non-minimal vector coordinates

A band is absolutely authentic by the ordered set of two vectors:

a point agent , advertence the position of an approximate point on

one chargeless administration agent , giving the band a administration as able-bodied as a sense.

Each point on the band is accustomed a constant amount that satisfies: . The constant t is different already and are chosen.

The representation is not minimal, because it uses six ambit for alone four degrees of freedom.

The afterward two constraints apply:

The administration agent can be called to be a assemblage vector

the point agent can be called to be the point on the band that is abutting the origin. So is erect to

editPlücker coordinates

Arthur Cayley and Julius Plücker alien an another representation application two chargeless vectors. This representation was assuredly called afterwards Plücker.

The Plücker representation is denoted by . Both and are chargeless vectors: represents the administration of the band and is the moment of about the called advertence origin. ( is absolute of which point on the band is chosen!)

The advantage of the Plücker coordinates is that they are homogenous.

A band in Plücker coordinates has still four out of six absolute parameters, so it is not a basal representation. The two constraints on the six Plücker coordinates are

the accord constraint

the orthogonality constraint