| 摘要 |
PURPOSE:To generate a hyperellipse with high approximation and to respond to local shape change, etc., by dividing the hyperellipse into segments, and making them into approximate curve at every segment by the Bezier curve. CONSTITUTION:A circle setting the major axis of the hyperellipse as a radius is generated, and point groups are arranged at every segment at equal interval by dividing the circle into N segments. A corresponding secondary ellipse with a minor axis is generated by mapping the circle on an XY plane with the point group, and the intersection of a normal line at every point in the point group on the secondary ellipse with the hyperellipse is found as the point group on the hyperellipse. The Bezier curve approximating the hyperellipse from the point group and a tangent vector at the start and end points of each segment on the hyperellipse at every segment can be generated. Thereby, it is possible to obtain the hyperellipse with high approximation, and also, to respond to the local shape change. |
