PRODUCTION OF FREE CURVED SURFACE

摘要

PURPOSE:To easily and quickly obtain a desired free curved surface by producing a secondary Bezier curve and converting this curve into a cubic one to decide a cubic Bezier curve connecting end points of picture elements as a boundary line between picture elements to be interpolated. CONSTITUTION:A plane pi1 passing the control points around an end point P1 is formed at the point P1 of a boundary line C3 of one of two picture elements touching a picture element S3 to be interpolated. Then a plane pi2 which passes an end point P2 of a boundary line C4 of the other picture element and is defined by the control points around the point P2 is obtained. A point Q1 is obtained on an intersecting line between both planes pi1 and pi2 which are formed in 1st and 2nd processes. Thus a secondary Bezier curve is produced with points P1, P2 and Q1 defined as control points and then converted into a cubic Bezier curve C1. Furthermore a cubic Bezier curve C2 is produced in terms of the end points at the other side of both boundary lines C3 and C4 respectively. Then an interpolated picture element S3 is obtained from a bicubic Bezier curved surface where those curves C1-C4 are defined as four sides respectively.