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
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.
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
Mail us your comments
All contents copyright (c) 1996, 1997, 1998,
Computer Science Department
University of California, Davis
All rights reserved.