The Study On Smooth Connection Between Two Spline Curves

In the field of computer-aided geometric design, it is very important for the problem of smooth connection between two spline curves, in this paper, we study the problem of smooth connection for two segregated spline curves. We propose the conditions of two spline fuctions with degree n to realize C^n-1 continuity by using the methods of spline interpolation, and obtain the conditions for the smooth connection of spline parametric curves with degree n. And we propose the solution of reparametrization to the problem of non—smooth connection, when two spline parametric curves are connected in parametric continuity, cusp or point of intersection comes into being where they connect. According to the fact that geometric continuity in CAGD can accurately and objectively measure the degree of smooth for the connection between two spline parameter curves, by inserting control point, we research the smooth connection between two low degree Bezier curves in Gⁿ continuity, and proposes the conditions of smooth connection between two Bezier curves, and generalizes them to more general situations. According to the special advantage of trigonometric polynomial, we study some properties of a kind of trigonometric B—spline curves with 2, by using some methods and properties of uniform B—spline curve, and discover the conditions of realizing smooth connection between two trigonometric B—spline curves with degree 2. Hence, the smooth connection between two spline curves can be used to free form curves and surfaces modeling.