Methods for generating free curves and sculptured surfaces

摘要

Disclosed are methods for generating free curves and sculptured surfaces illustratively for use with a CAD/CAM designing apparatus whereby Bezier curves and surfaces are readily generated with reference to point sequences, point groups and surfaces. In operation, a starting point (P0) and an end point (P3) for a sequence of points (q1, q2...) are set as nodes, and a free curve (R(t)) is temporarily established thereby. Then control points are repeatedly established to minimize the shortest distances between the points (q1, q2...) in the sequence and the free curve (R(t)). By use of the coordinates of a plurality of points, the shortest distance (d1, d2...) is found between each of these points (q1, q2...) and a reference patch. The internal control points are set so as to minimize the total sum of these shortest distances. When a patch is generated whose external shape is represented by a plurality of points, with another plurality of points also set on the reference patch for modification, a Bezier surface is generated with respect to these point groups and surfaces.