Construction of Monotone Extensions to Boundary Functions

摘要

The construction of monotone extensions to boundary functions is studied: givenmonotonically increasing, smooth, univariate functions along the edges of the unit square, the problem is to construct an extension towards the interior of the square such, that the resulting F(x,y) is monotone and of class C(sup 1). A nonlinear method which defines F in terms of a set of level lines, each of which is represented as a cubic Bezier curve, is presented. Considering a sequence of these level lines, the corresponding control points shift along trajectories which contain kinks.