ABSTRACT
Three diemensional transformations are essentially extensions of concepts of 2D transformations. These are used to change the location, orientation, and shapes of splines in 3D space. These transformations are translation, rotation, scaling, reflection, and shear applied individually or in combination of two or more, known as composite transformation. Given known coordinates of a point, each of these transformations is represented by a matrix which when multiplied to the original coordinates produce a new set of transformed coordinates. This chapter formally introduces a 3D coordinate system and then uses homogeneous coordinates to derive transformation matrices for the above operations. Their applications are then illustrated using examples, MATLAB codes and graphical plots for visualization. The latter part of the chapter deals with vector alignment in 3D space and uses these concepts to derive rotation matrices in 3D space around vectors and arbitrary lines.
