Approximate uniting of two adjacent B-spline curves through knot adjustment and constrained optimization

This paper explains the problem of approximate joining two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise joining of two B-spline curves, and readjusts the control points of the curves by constrained optimization in order to satisfy these conditions. To obtain a joined curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of joining curves to pass through some goal points is also discussed.