Abstract: An algorithm for extending B-spline curves with a sequence of ordered points
constraint is presented based on the curve unclamping algorithm. The most important feature of
this algorithm is the ability to optimize the knots of the extended curve segment according to the
ordered points. Thus, with minimum number of interpolation points, the maximum deviation of
the extended curve segment from the ordered points is less than the given tolerance. The extended
curve segment connects to the original curve with maximum continuity intrinsically. Further more,
this algorithm can be applied to the extension of B-spline surfaces with the constraints of a
sequence of B-spline curves. Several experimental results have shown the validity and
applicability of the proposed algorithm.

Key words: B-spline, extension, ordered points constraints, knots modification