Game Development Reference
In-Depth Information
•
Section 3.4
discusses nested coordinate spaces, commonly used for
animating hierarchically segmented objects in 3D space.
•
Section 3.5
is a political campaign for more human readable code.
3.1
Why Bother with Multiple Coordinate Spaces?
Why do we need more than one coordinate space? After all, any one 3D
coordinate system extends infinitely and thus contains all points in space.
So we could just pick a coordinate space, declare it to be the “world”
coordinate space, and all points could be located using this coordinate
space. Wouldn't that be easier? In practice, the answer to this is “no.”
Most people find it more convenient to use different coordinate spaces in
different situations.
The reason multiple coordinate spaces are used is that certain pieces of
information are known only in the context of a particular reference frame.
It might be true that theoretically all points could be expressed using a
single “world” coordinate system. However, for a certain point
a
, we may
not know the coordinates of
a
in the “world” coordinate system. But we
may be able to express
a
relative to some other coordinate system.
For example, the residents of Cartesia (see Section 1.2.1) use a map
of their city with the origin centered quite sensibly at the center of town
and the axes directed along the cardinal points of the compass. The res-
idents of Dyslexia use a map of their city with the coordinates centered
at an arbitrary point and the axes running in some arbitrary directions
that probably seemed a good idea at the time. The citizens of both cities
are quite happy with their respective maps, but the State Transportation
Engineer assigned the task of running up a budget for the first highway
between Cartesia and Dyslexia needs a map showing the details of both
cities, which therefore introduces a third coordinate system that is superior
to him, though not necessarily to anybody else. Each major point on both
maps needs to be converted from the local coordinates of the respective city
to the new coordinate system to make the new map.
The concept of multiple coordinate systems has historical precedent.
While Aristotle (384-322 BCE), in his topics On the Heavens and Physics,
proposed a geocentric universe with Earth at the origin, Aristarchus (ca.
310-230 BCE) proposed a heliocentric universe with the sun at the origin.
So we can see that more than two millennia ago the choice of coordinate
system was already a hot topic for discussion. The issue wasn't settled for
another couple of millennia until Nicolaus Copernicus (1473-1543) observed
in his book De Revolutionibus Orbium Coelestium (On the Revolutions of
the Celestial Orbs) that the orbits of the planets can be explained more
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