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simply in a heliocentric universe without all the mucking about with wheels
within wheels in a geocentric universe.
In Sand-Reckoner, Archimedes (d. 212 BCE), perhaps motivated by
some of the concepts introduced in Section 1.1, developed a notation for
writing down very large numbers—numbers much larger than anybody had
ever counted at that time. Instead of choosing to count dead sheep, as
in Section 1.1, he chose to count the number of grains of sand it would
take to fill the universe. (He estimated that it would take 8 × 10 63 grains
of sand, but he did not, however, address the question of where he would
get the sand.) In order to make the numbers larger, he chose not the
geocentric universe generally accepted at the time, but Aristarchus' revolu-
tionary new heliocentric universe. In a heliocentric universe, Earth orbits
the sun, in which case the fact that the stars show no parallax means that
they must be much farther away than Aristotle could ever have imagined.
To make his life more di cult, Archimedes deliberately chose the coordi-
nate system that would produce larger numbers. We will use the direct
opposite of his approach. In creating our virtual universe inside the com-
puter we will choose coordinate systems that make our lives easier, not
harder.
In today's enlightened times, we are accustomed to hearing in the media
about cultural relativism, which promotes the idea that it is incorrect to
consider one culture or belief system or national agenda to be superior to
another. It's not too great a leap of the imagination to extend this to
what we might call “transformational relativism”—the contention that no
place or orientation or coordinate system can be considered superior to
others. In a certain sense that's true, but to paraphrase George Orwell
in Animal Farm: “All coordinate systems are considered equal, but some
are more equal than others.” Now let's look at some examples of common
coordinate systems that you will meet in 3D graphics.
3.2
Some Useful Coordinate Spaces
Different coordinate spaces are needed because some information is mean-
ingful or available only in a particular context. In this section, we give some
examples of common coordinate spaces.
3.2.1 World Space
The authors wrote this topic from Chicago, Illinois, and Denton, Texas.
More precisely, their locations are as shown in Table 3.1.
These latitude and longitude values express our “absolute” position in
the world. You don't need to know where Denton, Chicago, Texas, Illinois,
 
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