Interior improvement of piecewise linear interpolants defined over Delaunay triangulations

Given a set of points and corresponding function values we construct a piecewise linear C0 interpolant defined over the Delaunay triangulation of the data set. The approximation quality of the interpolant is then improved by detecting badly shaped interior triangles, adding suitable points and updating the triangulation to form the new Delaunay triangulation and the new interpolant. Some of the developed schemes and repeated application of the idea can yield very impressive improvements of mean, maximum, and root mean square errors, as well as, of contour line plots.