** Overview**

Translation is one of the simplest transformations. A translation moves all points of an object a fixed distance in a specified direction. It can also be expressed in terms of two frames by expressing the coordinate system of object in terms of translated frames.

For a pdf version of these notes look here.

** Development of the Transformation in Terms of Frames**

Translation is a simple transformation. We can develop the matrix involved in a straightforward manner by considering the translation of a single frame. If we are given a frame , a translated frame would be one that is given by - that is, the origin is moved, the vectors stay the same.

If we write in terms of the previous frame by

** Applying the Transformation Directly to the Local
Coordinates of a Point**

Given a frame and a point that has coordinates in , if we apply the transformation to the coordinates of the point we obtain

** Summary**

Translation is a simple transformation that is calculated directly from the conversion matrix for two frames, one a translate of the other. The translation matrix is most frequently applied to all points of an object in a local coordinate system resulting in an action that moves the object within this system.

**Return to
the Graphics Notes Home Page**

**Return
to the Geometric Modeling Notes Home Page**

**Return
to the UC Davis Visualization and Graphics Group Home Page**

**This document maintained by Ken
Joy**

All contents copyright (c) 1996, 1997, 1998,
1999

Computer Science Department

University of California, Davis

All rights reserved.

1999-12-06