Surface algorithms using bounds on derivatives
The given paper draws a general conclusion about three main algorithms important mostly for their surface application. The mentioned algorithms can be applied for calculation of piecewise linear approximations, all- size-boxes and surface/surface intersections. The best results are achieved by handling all parametric \(C^ 2\) surfaces. These algorithms are related by theorems from approximation theory concerning the maximum deviation possible for an approximation to a surface. Bounds on the partial derivatives have to be known. The generalization of these theorems enables one to work with parametric geometry and shows how to get the necessary bounds.
scientific article; zbMATH DE number 4028719