Adaptive contouring of three-dimensional surfaces (Q1064769)

This paper describes a method to compute contours, i.e. lines \(z=const\) of a bivariate function \(z=f(x,y)\). The function is assumed to be defined over a triangulation of the xy-plane and consists of a polynomial of total degree 3 over each triangle. The function is also assumed to be \(C^ 1\) and is represented in the Bernstein-Bezier form. The contouring algorithm is of the divide-and-conquer type, subdividing each triangular surface piece down to a size where it can be approximated by a linear function to within a prescribed tolerance. The decision as to whether to subdivide or not, is based on an examination of the ''roughness'' of the surface piece under consideration, hence the name ''adaptive''.