But now let's look at those variables in the transfer function domain, where (as before) we have data value, not position, on the horizontal axis, with gradient magnitude on the vertical axis. As we traverse the boundary, the relationship between the data value and gradient magnitude forms an arch, like this.
Boundaries in the volume appear as arches in the transfer function domain. That basic idea underlies my VolVis 98 paper, in which transfer functions were specified semi-automatically. Now, we're specifying transfer functions manually, but we're still guided by the same kinds of considerations. Specifically, we still locate the boundary at those data values associated with a maximum in the first derivative, and zero crossing in the second.
Remember this arch, you'll see it again in Joe's section.