Jim Blinn's Corner: Notation, Notation, Notation

Chapter Three

How to Draw a Sphere Part III, The Hyperbolic Horizon

September 1995

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:

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

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