David Lutterkort

TL;DR: This paper provides a straightforward proof of quadratic convergence of the sequence of control polygons to the Bezier segment under subdivision or degree-fold degree-raising, and establishes the explicit convergence constants, and allows analyzing the optimal choice of the subdivision parameter for adaptive refinement of Quadratic and cubic segments.

TL;DR: A sharp bound on the distance between a spline and its B-spline control polygon is derived and the bound yields a piecewise linear envelope enclosingspline and polygon that can be easily and efficiently implemented.

TL;DR: This work shows how to efficiently smooth a polygon with an approximating spline that stays to one side of the polygon and how to find a smooth spline path between two polygons that form a channel.

TL;DR: An enclosure is a two-sided approximation of a uni- or multivariate function b@?B by a pair of typically simpler functions b^+,b^-@?H B such that b^-=.

TL;DR: A general framework for comparing objects commonly used to represent nonlinear geometry with simpler, related objects, most notably their control polygon, is provided and is used to compute envelopes for univariate splines, the four point subdivision scheme, tensor product polynomials and bivariate Bernstein polynmials.