ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: The coordinate dimension represents the number of choices made, and constraints can restrict choices. A barycentric coordinate which has ${\displaystyle (n+1)}$ -offsets, but the underlying space is dimension ${\displaystyle n}$ . Homogeneous coordinates ${\displaystyle (wx,wy,wz,w)}$ are actually 3 dimensional because the choice of "${\displaystyle w}$ " does not affect the position, i.e. ${\displaystyle (wx,wy,wz,w)=(xy,z,1)\to (x,y,z)}$ which is not affected by ${\displaystyle w}$ . The dimension will be at most the count of the numbers in the coordinate, but it can be less if the coordinates are constrained in some manner.