September 1999
The purpose of knot removal for a B-spline curve is to obtain a new B-spline curve defined on the knot sequence from which some knots are removed out of an initial sequence, so that the curve has the least difference with the initial curve with respect to some norms.
In this thesis, the problem of removing one inner knot from the knot sequence of a B-spline curve is discussed. Doing so, a local geometric construction of the new control points is introduced based on two special inverses of knot insertion matrices. Then the free weight coefficients appearing in this general construction are determined by minimizing three norms of discrete $L_\infty$ , $L_2$ and continiuous $L_\infty$, between the old and new curves. Depending on each of the three norms, an approximation problem comes into consideration, the best of which is continiuous $L_\infty$ approximation, calculated by a particular type of Remez algorithm.
By implementing some composition and decomposition algorithms of B-spline, based on the methods of removing a single knot, some applications can be considered such as the problem of knot ranking for joint removal of many knots as a special application, and also many practical applications like curve and surface fiiting, signal processing, image compression and approximation of functions out of spline space with free-knot sequence.
Full thesis (in Persian):