Sectional-Curvature Preserving Skinning Surfaces with a 3D Spine Curve

This work deals with the problem of constructing sectional-curvature preserving (scp) C 2-continuous surfaces, which interpolate point-sets lying on planes perpendicular to a three-dimensional spine curve. The proposed method of solution employs skinning surfaces, whose skeletal lines and blending functions belong to a special family of polynomial splines of non-uniform degree, already used for shape-preserving curve interpolation in the plane (see 4], 5]) as well as space (see 3]). Using an appropriate aane transformation, the problem simpliies to a sectional-curvature preservation problem with a straight line as spine curve, a case thoroughly studied in 2]. x1. Introduction Developing automatic algorithms for shape-preserving curve and surface interpolation , is a CAGD domain with intensive basic-research activity and a steadily increasing audience in the CAD/CAM community. While the planar problem is well studied (see 5] and the references cited therein), it seems that a lot of work has still to be done in the areas of shape-preserving interpolatory 3D curves and surfaces; see the literature review in 3] and 2]. Especially in the case of surfaces, the problem becomes really hard when con-vexity has to be preserved; see pertinent comments in the introduction in 1]. Less diicult is the problem where the designer is interested in preserving the convexity of intersections of the surface with a discrete or continuous family of planes. This is notably true when the interpolation data are point-sets lying on planes, which is likely to occur in practice when the object is characterized by a direction, directly related to its functionality, as it is, e.g., the longitudinal axis of a ship or the fuselage of an airplane. This problem has been thoroughly treated in 2], where