Degrees of Freedom, Pose, Displacement and Perspective

Abstract

A virtual environment is composed of entities such as objects, avatars and sound sources. The number of independent axes of translation and rotation along and around which an entity can move defines the number of degrees of freedom of the particular entity. The pose (position and orientation) and displacement (translation and rotation) of an entity can be defined with the use of homogenous transformation matrices. Rotations and orientations can also be expressed in terms of Euler angles or quaternions. Homogenous transformation matrices also make it possible to define perspective transformations. In this chapter the basic mathematical tools in the study of rigid body kinematics will be introduced.