While the 3-D vector space model can nicely model directions, it is usually considered to be inadequate for use in 3-D computer graphics, primarily because of a desire to treat points and vectors as different elements that are transformed differently by translations. Instead, people commonly use an extension of linear algebra known as homogeneous coordinates. This is often described as augmenting a 3-D vector v with coordinates (v1,v2,v3)T to a4-vector v1,v2,v3,1)T. This extension makes nonlinear operations such as translations implementable as linear mappings.

For the homogeneous model in geometric algebra, the modeling principle is the same: we embed our n-dimensional base space (which you may think of as Euclidean ...

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