COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	∂05-NOV-74  0936		MA,JAM
C00004 ENDMK
C⊗;
∂05-NOV-74  0936		MA,JAM
 Well, try this:
 When you fit a spline, you get a 3rd order. Well, here is a way
 to calculate the coefficient of the 4th term so as to minimize the
 second derivative (curvature) of the polynomial. If
 
 Y = A[0]+A[1]*X+A[2]*X↑2+A[3]*X↑3+A[4]*X↑4
 
 And A[0] through A[3] come from endpoint and slope considerations,
 then
 
 A[4] = -(16*A[2]+36*(X1-X0)*A[3])/(288*(X1-X0)↑2/5)
 
 To minimize Y'', where X1 and X0 are the endpoints of the interval.
 If you vary A[4] smoothly between 0 and the above value, you do not
 necessarily get a smoothly varying curve, however, but in most cases
 it should work out smooth.
 
 I tried adding in the arc length consideration and got something
 I couldn't integrate. Oh well. Maybe some numerical technique . . .