1. The derivative at the boundary always exists, since it is formed from the convolution of two continuous functions.
Oh, definitely, the derivative exists. It's that it's zero that bugs me. At the boundary, your constraint Jacobian is just a row of zeros. That makes it seem hard to resolve collisions. In what direction should my configuration-space particle bounce?
2. Since we end up actually low pass filtering the objects, (see below), the level set defining the boundary of the configuration space obstacle turns out to be a smooth curve and so it always has a well defined tangent and normal direction (ie it will not be 0 anywhere).[/quote]
This may address that concern; I'd need to reread that section of your paper.
