Tight linear envelopes for splines

A sharp bound on the distance between a spline and its B-spline control pol ygon is derived. The bound yields a piecewise linear envelope enclosing spl ine and polygon. This envelope is particularly simple for uniform splines a nd splines in Bernstein-Bezier form and shrinks by a factor of 4 for each u niform subdivision step. The envelope can be easily and efficiently impleme nted due to its explicit and constructive nature.