RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented.The symme- try property is realized by using symmetric knot vector and symmetric control points.Firstly,data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points.Then the divided data points are pararaeterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions.Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane.Lastly,the constrained least squares fitting problem is solved with the Lagrange multiplier method.Two examples from industry are given to show that the proposed method is efficient,robust and able to meet the general engineering requirements.