Deriving Hermite Splines, 2
Since x(u) = au3+bu2+cu+d,
its derivative is x’(u) = 3au2+2bu+c
Rewriting the constraints yields four linear equations:
x(0) = x1 = d
x(1) = x2 = a+b+c+d
x’(0) = x1’ = c
x’(1) = x2’ = 3a+2b+c
Solve for a, b, c, d:
a=2x1-2x2+x1’+x2’, b=-3 x1+3x2-2x1’-x2’, c= x1’, d= x1
Simpler if we use matrix notation…