warner@orca.UUCP (Ken Warner) (06/27/84)
I solved a similar problem once. My solution was without reguard to
"best fit" as it didn't pass through the "middle" point. Simple
mathematicaly, it was done with a recursive procedure that accepted
three points. It might be applied here if some method was devised for
extrapolating two more points from the original three points.
Brief description of the method:
Calculate the mid points of the lines between the "end" points and
the "middle" point, i.e. between 1,2 and 2,3. You now have five points.
(2).
(4).
(5). (3).
(1).
Pass the original procedure 1,5,4 then 5,4,3 .. repeat.
When the the distance between the points is "small enough" ..
connect them with a line.
If the original problem required a point through 1,3,X then 2 would
have been extrapolated, somehow, from 1,3,X.
The curves made this way look nice and smooth on a macro scale but
look wiggly on a micro scale.
Ken Warner
..tektronix!tekecs!warner