macro
quadinterp x y xp yp

#x and y are columns of three (x,y) observations
#macro finds a, b, and c values that exactly fit the three points where
#y = a + bx + cx^2
#xp is an input and yp is determined by quadratic interpolation

#Copyright (c) Paul G. Mathews, 8 Oct 01, All rights reserved

mcolumn x y
mconstant a b c xp yp

let c=(y(3)-y(1)-(x(1)-x(3))/(x(1)-x(2))*(y(2)-y(1)))
let c=c/(x(3)*x(3)-x(1)*x(3)+x(1)*x(2)-x(2)*x(3))
let b=(y(2)-y(1)+c*(x(1)*x(1)-x(2)*x(2)))/(x(2)-x(1))
let a=y(1)-b*x(1)-c*x(1)*x(1)

print a b c
let yp=a+b*xp+c*xp*xp
print xp yp

endmacro