Degrees of Freedom, Pose, Displacement and Perspective

  • Matjaž MiheljEmail author
  • Domen Novak
  • Samo Begus
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 68)


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.


Reference Frame Virtual Environment Mass Particle Coordinate Frame Euler Angle 
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    Bajd T, Mihelj M, Lenarčič J, Stanovnik A, Munih M (2010) Robotics. SpringerGoogle Scholar
  2. 2.
    Bajd T, Mihelj M, Munih M (2013) Introduction to Robotics. SpringerGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia

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