Title: Tight linear tolerance envelopes for curved geometry

Abstract: 

We consider two problems: (1) constructing a spline that stays above, but
close to, a given polygon (2) constructing a spline that stays in the
channel between two given nonintersecting polygons. The problems can be
solved by a linear or a quadratic program.

The constraints for the programs are based on a new tight bound on the
distance between a spline and its B-spline control polygon. This bound can
be efficiently computed from the nonuniform knot sequence and the second
differences of the control polygon. For low degrees, the resulting
piecewise linear envelope follows the spline more closely than comparable
constructive bounds like the min-max or convex hull envelopes.