On Quadratic Splines and Their CAD-Application

Abstract

One of the important tasks of computer aided engineering design in geometric modeling. Because of theoretical and computational reasons most practical CAD-systems use parametric curves and surfaces (most commonly parametric cubic segments) in geometric modeling. Most basic ideas involved are presented in the survey paper [3] of Böhm, Farin and Kahmann, 1984. Our paper deals with quadratic splines and their application for curve and surface representation. The basic problem is to present a method for obtaining a smooth bivariate function which takes on certain prescribed values. The collection of these values is assumed to be on a rectangular grid, that is, for every point (x_i, y_j) on the rectangular grid {x_i} ⁿ_i=0 × {y_j} ^m_j=0 there is a given value z_ij.