An algorithm is presented for calculating an osculatory quadratm sphne that preserves the monotonmlty and convexity of the data when consmtent with the given derivatives at the data points A method is also presented for calculatmn of an mterpolatory quadratm sphne with monotonicity and convexity consistent with that of the data Included is a discussion of pathologms that can occur when these algorithms are maplemented.Examples are given that illustrate the dependence of the method on only local informatmn and its usefulness m geometrm design.

This algorithm is a FORTRAN implementation for the procedure developed in [3].Let n data points {(x,, y,)} n.1 and n first derivatives {rn,),"-1 at these data points be given, with x, <_-X,+l, 1 __ i __.n -1.The algorithm constructs a smooth osculatory quadratic spline S, which satisfies (1) S(x,) = y,, 1 <_ i <_ n;(2) S'(xi) = m,, 1 <_ i <_ n;(3) S preserves monotonicity and convexity in the case that the slopes rn, are consistent with the shape of the data; (4) the knots of the spiine S include the data points and at most two additional knots between adjacent data points.The spline S is a piecewise quadratic Bernstein polynomial with a continuous first derivative.

The Integrated Photogrammetric Instrument Network (IPIN) is being designed and developed by the Defense Mapping Agency Aerospace Center in St. Louis, Mo. to meet database demands for terrain elevation information. IPIN is a network of computers and instrumentation dedicated to digitizing and editing photo-source terrain data [1]. Editing procedures are required because of digitizing errors inherent in the data-collection process. Some of these errors are random; others are systematic and predictable.