Choosing coordinate axes

One often neglected point is the choice of coordinates for the models, in terms of their placement and scale. If these are defined cleverly at the outset, then many tedious complications can be avoided. If the virtual world is supposed to correspond to familiar environments from the real world, then the axis scaling should match common units. For example, $ (1,0,0)$ should mean one meter to the right of $ (0,0,0)$. It is also wise to put the origin $ (0,0,0)$ in a convenient location. Commonly, $ y=0$ corresponds to the floor of a building or sea level of a terrain. The location of $ x=0$ and $ z=0$ could be in the center of the virtual world so that it nicely divides into quadrants based on sign. Another common choice is to place it in the upper left when viewing the world from above so that all $ x$ and $ z$ coordinates are nonnegative. For movable models, the location of the origin and the axis directions become extremely important because they affect how the model is rotated. This should become clear in Sections 3.2 and 3.3 as we present rotations.

Steven M LaValle 2020-01-06