Deriving Hermite Splines, 1
Four constraints: value and slope (or in 3-D, position and tangent vector) at beginning and end of interval [0,1]
x(0) = x1
x(1) = x2
x’(0) = x1’
x’(1) = x2’
Assume cubic form: x(u) = au3+bu2+cu+d
Four unknowns: a, b, c, d
primes on left side denote
derivative; primes on right