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Chapter Three

# How to Draw a Sphere Part III, The Hyperbolic Horizon

## Our Story So Far

We want to draw a sphere. Actually, we want to draw an arbitrarily scaled and oriented ellipsoid. In Chapter 1, I showed some matrix algebra for describing, transforming, and intersecting points, planes, and quadric surfaces (of which a sphere is a special case). In Chapter 2, I defined some useful coordinate systems and transformations. I'll use the same notation conventions defined there. Let's list what we have done so far.

### Inputs

We are given the following:

Qd—A matrix describing a unit radius sphere in its definition coordinate system:

${\text{Q}}_{d}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1\end{array}\right]$

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