A Method For The Modification Of Curves And Surfaces With Rational Bezier

Curve modification is a research focus in Computer Aided Geometry Design (CAGD). It is generally used in shape design modeling and outline design.To modify the initial curve, the traditional methods can be classified into two groups: the first one modifies the initial curve by adjusting the controlling vertices; another is by constructing and adjusting some shape control parameters. Although both methods will provide many free degrees for designers, the process of manipulation is always laborious and troubled.Based on analyzing the two methods above and combining the mechanism of avoiding obstructs, a new method for G~2 rational cubic Bezier curves modification is described in this paper: give constrained boundaries first, then replace the curve segment which intersects the boundaries with one of its curve family, which either is tangent to the boundaries or interpolates its vertex. Finally, restore G~2 continuity by the curvature. The modified curve will not intersect the boundaries and keep the geometric continuity. Numerical examples are given to show that the method is simple, fast and efficient. In addition, the method can be extended to space curves and developable surfaces modification.