Base de Hermite :

X
f(X)
f '(X)
  
Xa =
Ya =
Y'a =
Point A
Xb =
Yb =
Y'b =
Point B
H00 =
H01 =
H10 = H11 =
X =
fH( )
(Remplir les cases grises)

Base de Hermite sur [a,b]

Ya = f(Xa) , dYa = f '(Xa)
Yb = f(Xb) , dYb = f '(Xb)

T = ( x - Xa ) / ( Xb - Xa)

H00(T) = 2 * T3-3 * T2 + 1
H01(T) = T3 - 2 * T2 + T
H10(T) = 3 * T2 - 2 * T3
H11(T) = T3 - T2

fH(x) = Ya * H00(T) + Yb * H10(T) + ( Xb - Xa) * [ dYa * H01(T) + dYb * H11(T) ]

fH(x) ≈ f(x) avec x dans le domaine [a,b]


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