Smooth piecewise quadric surfaces

Abstract This paper is concerned with the construction of tangent plane continuous piecewise quadric surfaces that interpolate finite sets of essentially arbitrary points in IR 3 according to a given ‘topology’ which is described in terms of a piecewise linear interpolant. Moreover, within certain ranges depending on the topology and the location of data points, given normal directions at the points are also matched by the interpolating piecewise quadric surface.