Construction of Monotone Extensions to Boundary Functions

Abstract

Suppose we are given monotonically increasing, smooth, univariate functions along the edges of the unit square. The problem is to construct an extension F(x, y) to the whole square which is monotone and of class C ¹. A nonlinear method is presented which defines F in terms of a set of level lines, each of which is represented as a cubic Bézier curve. As the level changes, the corresponding control points shift along trajectories which contain appropriate kinks.