Computer based modelling and rendering software seem to be split evenly between whether they use a left hand or right hand coordinate system, for example OpenGL uses a right hand system and PovRay a left hand system. This document describes bow to convert model coordinates and/or camera attributes when transferring models from one package to another. Each system is shown below, the difference involves how the cross product is defined...using the so-called left or right hand rule.
Note that the exact orientation of the axes above is not relevant, y need not be "pointing up", z need not be pointing "into the page". All axes orientations are equivalent to one of the above after a suitable rotation.
There are two ways to convert models between systems so that the rendered results are identical. The first involves inverting the x value (any single axes will do) of all vertices in the model and camera settings, the second uses the model and camera coordinates without change but requires a flipping of any rendered image horizontally. In what follows, the symbols p, d, and u will represent the vectors position, view direction, and up vector respectively.
Method 1 - inverting the x coordinates
Method 2 - flipping image horizontally
In this case the coordinates of the model and camera are used unchanged when transferring from one system to the other. As can be seen in the example below, the image ends up being horizontally flipped.
This is usually the preferred method, perhaps mainly because it avoids worrying about which system one is using until the end of the process, the image flipping can be built into post processing image tools. Also, it means that if one makes a mistake regarding which system is being using it doesn't affect the rendered result nearly as seriously than if one got made a mistake in the first method.
You may wonder why it is the horizontal axis that is flipped, what is so special about it? That arises because the flip is actually about the up vector which is traditionally vertical on the rendered image.