7
2 — In each control the points situated in one side are separated from those situated
in the other side of the axis of the strip.
The average of the corrections of X and Y is taken for each one of those
groups of points.
For each control two sets of values are obtained:
Cx+ Cy+ Xp+ Yp+
Cx~ Cy~ Xp~ Yp~
defining corrections Cx+, Cy+ and Cx~, Cy~ in fictitious points, situated
respectively in Xp+, Yp+ and Xp-, Yp~.
By means of linear interpolation, the correction and the value of Xp over the
line Yp = 0 is calculated.
We shall have in each control i
Cxi Cyi Xpi
The parameters a 1, a2 and a3 are obtained by resolution of the systems:
| Cxl = a‘2 Xp 2 1 + al Xpl
[ Cx2 = a2 Xp 2 2 + al Xp2
in the case of one intermediary control, or
Cxi — a3 X 3 p 1 +a2 X 2 pl + al Xpl
Cx2 = a3 X 3 p2 + a2 X 2 p2 + al Xp2
Cx3 = a3 X 3 p3 + a2 X 2 p3 + al Xp3
in the case of two intermediary controls.
The parameters dl, d2 and d3 are then obtained by resolution of the systems:
Cxl + -Cxl-~a2 [(Xpl+) 2 - {Xpl~) 2 ]-al Xpi+-Xpl~)-Al= (d2 Xp\ +
+ dl Xpi) (Ypi + -Ypl ~)
Cx2+ - Cx2~ -a2 [ {Xp2+) 2 - {Xp2~) 2 ] - al (Xp2+-Xp2~) = A2 = (d2 Xp 2 2 +
+ dl Xp2) (Yp2+ - Yp2~)
in the case of one intermediary control, or
Cxl + -Cxl~-a3 [{Xpl+y- {Xpi-) 3 ] - a2 [(Xpl + ) 2 -{Xpi~) 2 ]-
-al(Xpl+-Xpl~)=Xl=(d3 Xp 3 1 + d2 Xp 2 1 + dl Xpl) (Ypl + ~Ypl-)
Cx2+-Cx2~-a3 [(Xp2 + ) 3 -(Xp2~) 3 ] -a2 r L (Xp2+) 2 -(Xp2~) 2 ]-
-al (Xp2+ -Xp2~) = A2= (d3 Xp\ + d2 Xp 2 2 + dl Xp2) (Yp2 + -Yp2~)
Cx3 + — Cx3~ — a3 [{Xp3+) 3 -{Xp3~) 3 ]-a2 [(Xp3+) 2 -(Xp3~) 2 ]-
-al(Xp3+-Xp3~)=\3=(d3 Xp\ + d2 Xp 2 3 + dl Xp3)(Yp3+-Yp3~)
in the case of two intermediary controls.