ON POINT CALCULATING SYSTEM OF TWO-DIMENSIONAL INTERPOLATED SPLINE

摘要

PURPOSE:To obtain efficiently an on point by finding a polygonal line, which is closest to a hit point, out of polygonal lines connecting interpolating points and decomposing the part between both ends of this polygonal line into plural polygonal lines and selecting a polygonal line, which is closest to the hit point, from them and dropping a perpendicular from the hit point. CONSTITUTION:A method is considered which obtains a point on a curve closest to a point H when the optional point H is given. Interpolating points P1-P5 are connected, and perpendiculars are dropped from the hit point H onto individual segments to select the segment from the point P2 to the point P3 closest to the hit point. This selected segment is decomposed into polygonal lines Pi...Pj, Pj+1...Pi+1, and perpendiculars are dropped from the hit point onto individual polygonal lines to obtain the polygonal line Pj closest to the hit point. The intersection between this polygonal line Pj and the perpendicular is obtained as the on point.