Surface algorithms using bounds on derivatives

This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, min-max boxes, and surface/surface intersections. The class of surfaces that can be handled are all parametric C 2 surfaces. All the algorithms are related by theorems from approximation theory which give information about the maximum deviation an approximation to a surface can have if bounds on partial derivatives are known. We generalize these theorems to work with parametric geometry, and we also show how to obtain the necessary bounds.