Modification of Free-Form Surfaces Using Correction Functions for Specified Points and Curves

This paper describes a technique which modifies shapes with free-form surfaces using correction functions to the given surface equations. The modification is executed by indicating points or curves through which the shape passes smoothly. A correction function is introduced to define the effect over the whole shape according to the distance along the normal direction of the given surface. The values of the correction function are 1 at the indicated point and 0 at the boundaries, and the shape should be modified to keep the original smoothness. The distance values of the correction functions at the indicated points are determined to satisfy all the given positions by solving linear equations. As for the function for curves, Cardinal spline is used to prevent the oscillation caused by many input points. The correction function for a surface is generated by multiplying two types of functions defined along u and v directions. The same types of correction functions are used in case of points, while the correction functions for the curves, the point fuction is changed across the specified curve according to the parameter values on the curve. The paper also introduces a method for treating a trimmed surface. Smooth free-form surfaces have been obtaind in real time modification. The approximation method of the deformed free-form surface is also presented, which is a fifth degree C 2 spline surface.