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.
We are given the following:
■ Qd—A matrix describing a unit radius sphere in its definition coordinate system: