# Bilinear Interpolation Formula

Bilinear interpolation interpolates functions of the two variables X and Y on a rectilinear 2D grid. The page presents the bilinear interpolation formula to calculate the bilinear interpolation. It is performed similarly like the linear interpolation in one direction and then in the other direction. To calculate the double interpolation, compute the values of X1, X2, Y1 and Y2, coordination value of X and position of Q11, Q12, Q21 and Q22 as in the double interpolation formula.

# Double Interpolation Formula

#### Formula:

p = [[(b - e) x (d - f) / (b - a) (d - c)] x p1] + [[(e - a) x (d - f) / (b - a) (d - c)]x p3] + [[(b - e) x (f - c) / (b - a) (d - c)] x p2] + [[(e - a) x (f - c) / (b - a) (d - c)] x p4]

Where,

p = The Interpolated Value
a = Value of X1
b = Value of X2
c = Value of Y1
d = Value of Y2
e = Coordination Value of x
f = Coordination Value of y
p1 = Position of Q11
p2 = Position of Q12
p3 = Position of Q21
p4 = Position of Q22

#### Related Calculator:

Double interpolation is one of the important resampling techniques used in the computer vision and image processing technology. It is also referred as bilinear filtering or bilinear texture mapping for producing realistic images in the text mapping. Feel free to refer this bilinear interpolation formula for your educational purpose.