An adaptive algorithm for efficient computation of level curves of surfaces

A new efficient algorithm for the computation of z=constant level curves of surfaces z=f (x, y) is proposed and tested on several examples. The set of z-level curves in a given rectangle of the (x, y)-plane is obtained by evaluating f on a first coarse square grid which is then adaptively refined by triangulation to eventually match a desired tolerance. Adaptivity leads to a considerable reduction in terms of evaluations of f with respect to uniform grid computation as in Matlab®’s contour. Furthermore, especially when the evaluation of f is computationally expensive, this reduction notably decreases the computational time. A comparison of performances is shown for two real-life applications such as the determination of stability charts and of ε−pseudospectra for linear time delay systems. The corresponding Matlab code is also discussed.