For example, take the tilted torus shown below. If you stare at the picture and think about it, you'll see that we chose to project the points where the tangent plane to the torus is parallel to the z-axis. We will call this set the z-profile of the surface. So first we need to figure out what those equations are. This is exactly what we did for the tilted torus.
C t is said to be part of the envelope of C t .
Try to write down a polynomial equation, i.e. one that avoids square roots. The resulting implicit equation for the envelope can then be plotted to obtain the red curves in the 4th figure on this page. For an even deeper discussion, see Bruce and Giblin.