Multiple Coordinate Spaces - 3D Math Primer for Graphics and Game Development - page 82

Author City Latitude Longitude

41 o 57' 87 o 39' Fletcher Chicago North West

33 o 11' 97 o Ian Denton North West

Table 3.1. Locations of authors, including a random offset introduced to protect us from our
many obsessive stalker fans.

or even the United States is to use this information because the position is
absolute. The origin, or (0,0) point, in the world was decided for historical
reasons to be located on the equator at the same longitude as the Royal
Observatory in the town of Greenwich, England.
(The astute reader will note that these coordinates are not Cartesian
coordinates, but rather they are spherical coordinates—see Section 7.3.2.
That is not significant for this discussion. We live in a flat 2D world
wrapped around a sphere, a concept that supposedly eluded most people
until Christopher Columbus verified it experimentally.)
The world coordinate system is a special coordinate system that es-
tablishes the “global” reference frame for all other coordinate systems to
be specified. In other words, we can express the position of other coor-
dinate spaces in terms of the world coordinate space, but we cannot ex-
press the world coordinate space in terms of any larger, outer coordinate
space.
In a nontechnical sense, the world coordinate system establishes the
“biggest” coordinate system that we care about, which in most cases is not
actually the entire world. For example, if we wanted to render a view of
Cartesia, then for all practical purposes Cartesia would be “the world,”
since we wouldn't care where Cartesia is located (or even if it exists at all).
To find the optimal way to pack automobile parts into a box, we might
write a physics simulation that “jiggles” a box full of parts around until
they settle. In this case we confine our “world” to the inside of a box.
So in different situations the world coordinate space will define a different
“world.”
We've said that world coordinate space is used to describe absolute
positions. We hope you pricked up your ears when you heard this, and
you knew we weren't being entirely truthful. We already discussed in Sec-
tion 2.4.1 that there's really no such thing as “absolute position.” In this
book, we use the term “absolute” to mean “absolute with respect to the
largest coordinate space we care about.” In other words, “absolute” to us
actually means “expressed in the world coordinate space.”
The world coordinate space is also known as the global or universal
coordinate space.