ABSTRACT
In order to transform and project points and objects in three dimensional (3D) we need vector and matrix algebra just as in the two dimensional (2D)-case. The matrices for all these transforms look much the same as their 2D-analogs except that adding one dimension results in more basic cases. In a 2D-case the question of orientation was very simple – there was just one possible rotation. But in a 3D-situation it is much more complex and there are many different ways to specify orientation. Just as in a 2D-case a simple translation by a give n vector is not a linear transformation and cannot be represented by a 3×3 matrix. The rigid-body transformations preserves lengths of the vectors and angles between vectors. Another form of specifying the orientation in a 3D-space are quaternions, which provide a non-redundant way of storing orientations and a simple way to work with and interpolate them.
