Minimum displacement bounds are a rendering setting that allows the render to account for displacements that cross the boundaries between render buckets, although trying to account for a (possibly near) infinite displacement may not be worth the trouble. You're right about the formula, the additional bias does eliminate the possibility of divide-by-zero problems. On the other hand, it does occur to me that any sinusoidal function (or cosines for that matter) would inherently suffer from discontinuities at a radial center. If you take any cross-section of the curve through the radius, it's obvious that, except when the phase is other than +/-PI/2 (?), there is going to be a sharp peak or trough at the origin with the cross section reflected on both sides. This may be a lot more apparent with displacement, since the accuracy of the sampling is always a pixel or less, than with other (geometrical deformation) techniques where there is an element of mesh smoothing between sample (vertex) points. It may be that you need to add an additional smoothing function to compensate for the discontinuity at the center. Bill