Fine timing: Curve and surface deformation by scaling derivatives

A deformation-based fine tuning technique for parametric curves and surfaces is presented. A curve or surface is deformed by scaling its derivative, instead of manipulating its control points. Since only the norm of the derivative is adjusted, the resulting curve or surface keeps the basic shape of the original profile and curvature distribution. Therefore, the new technique is especially suitable for last minute fine tuning of the design process. Other advantages include: (1) the fine tuning process is a real local method, it can be performed on any portion of a curve or a surface, not just on a set of segments or patches; (2) by allowing a user to drag a scalar function to directly adjust the curvature (and, consequently, fairness) of a curve or surface, the new technique makes the shape design process more intuitive and effective; (3) the new technique is suitable for precise shaping and deforming such as making the curvature of a specific portion twice as big. In many cases, it can achieve results that other methods such as FFD can not; (4) the fine tuning process can also be used for subdivision curves and surfaces. Related techniques and test results are included.