Abstract: In commercial geometric engines‚intersection curves of surfaces are expressed procedurally by position operators that can evaluate the curve position information precisely.To be able to use such kinds of procedural curves in geometric modelling operations‚intersection curves should be output as system available forms‚such as B-spline.The existing approximation algorithms in the geometry engines have the disadvantages that：（1） The number of B-spline control points is unnecessarily large；and （2） the B-spline curves have low continuity （C1）.A novel algorithm to optimally approximate intersection curves of surfaces with C2 B-spline curves is presented that have approximately only 1／3of the number of control points of the B-spline output from geometry engines.Our algorithm has been integrated into SolidWorks system successfully with very good application performances.