On-Line Computer Graphics Notes

Coordinate Systems

In most applications in mathematics and engineering we work in the Cartesian coordinate system. This coordinate system can take two forms : the right-handed system, and the left-handed system. These two systems are shown in the following figure.

In most applications, we preferrably use the right-handed system, however, the left-handed system does occasionally have its uses.

In the computer graphics community, we began drawing on two-dimensional screens - parameterizing in x and y - and continued by adding a z coordinate that was considered to represent depth. This representation of the Cartesian coordinate system has stuck with the field, and is represented in the figure below. Note that there are both left- and right-handed coordinate systems, depending on orientation of the z-axis.

These coordinate systems are identical to the Cartesian systems presented above, just oriented differently.

The standard coordinate system utilized in these notes will be the right-handed system.

We also make extensive use of frames in computer graphics. These are coordinate systems that are utilized to define a local representation of an object (e.g. a camera). These frame-based coordinate systems may be left- or right-handed, and are made up of three vectors and a point. The point represents the origin of the frame in the Cartesian coordinate system, and the three vectors represent a linearly independent set (basis, in this case) of vectors in three-dimensional space. A Frame is illustrated in the figure below.

See the notes on Vector Spaces for additional information on linear independence and bases.

This document maintained by Ken Joy Comments to the Author All contents copyright (c) 1996, 1997 Computer Science Department, University of California, Davis All rights reserved.