If we assume that the spine curve is regular, i.e. is simple and , there exist two kinds of singularities on pipe surfaces: those that arise from local differential geometry properties of the surface and those that come from global distance properties of the surface. The first type of singularity occurs when the radius of the pipe surface exceeds the minimum radius of curvature of the spine curve; we refer to this singularity as local self-intersection. The second one happens, for example, when twice the radius of the pipe surface is larger than the minimum distance between two interior points (excluding the two end points) on the spine curve; we refer to this singularity as global self-intersection. Kreyszig , doCarmo  and Rossignac  derive the condition for local self-intersection of a pipe surface and Shani and Ballard  describe a method to prevent local self-intersection of a generalized cylinder. So far the discussion was based on ``Given a spine curve and a radius, does the pipe surface self-intersect? If so, where does it self-intersect?'' However in some applications, we may encounter the case ``Given a spine curve, what is the maximum radius such that the pipe surface does not self-intersect?'' More precisely, given a regular space curve we want to find the maximum , so that the pipe surface is nonsingular, whenever . In  it is discussed how to find this maximum possible radius .
One immediate application lies in the area of finding a topologically reliable approximation of a space curve . More precisely, suppose we are given a regular space curve , and would like to approximate with another curve -within a prescribed tolerance- in a natural way; that is, there is a space homeomorphism that carries onto . One important consequence of such a homeomorphism is that and have the same knot type. To do this, we first construct a nonsingular pipe surface . Then, we construct a curve that lies inside , and ``looks like'' . By taking to be the tolerance we have a reliable approximation of the given curve. Sakkalis and Charitos  apply the concepts of pipe surfaces and alpha shapes  to ambiently approximate a nonsingular space curve with a piecewise linear curve.