Envelopes of nonlinear geometry

A general framework for comparing objects commonly used to represent nonlinear geometry with simpler, related objects, most notably their control polygon, is provided. The framework enables the efficient computation of bounds on the distance between the nonlinear geometry and the simpler objects and the computation of envelopes of nonlinear geometry. The framework is used to compute envelopes for univariate splines, the four point subdivision scheme, tensor product polynomials and bivariate Bernstein polynomials. The envelopes are used to approximate solutions to continuously constrained optimization problems.

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