Abstract: A new method for modification of curves is described in this paper. To modify an initial G 2 rational cubic Bezier curve, we give constrained boundaries, replace the curve segment intersecting the boundaries with one of its curve family, which is either tangent to the boundaries or passes their vertexes, and restore G 2 continuity according to the curvature. The modified curve does not intersect the boundaries and keeps geometric continuity. Numerical examples are given, showing that the method is simple, fast and efficient.

Key words: modification of curves, constrained interpolation, rational cubic Bezier splines