### Bilinear interpolation

Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid. The underlying function f(x, y) is sampled on a regular grid and the interpolation process determines values between the grid points. Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension. Bilinear interpolation is often used in image processing to rescale images.

 First parameter X Second parameter Y 97.9 106 112
Intermediate values $$f(x,y_1) = f(x_1,y_1)+(x-x_1) \frac{f(x_2,y_1)-f(x_1,y_1)}{x_2-x_1} = 100+(14.2-10) \frac{ 95-100 }{ 20- 10 } =97.9$$ $$f(x,y_2) = f(x_1,y_2)+(x-x_1) \frac{f(x_2,y_2)-f(x_1,y_2)}{x_2-x_1} = 122+(14.2-10) \frac{ 98-122 }{ 20- 10 } =112$$ Результат $$f(x,y) = f(x,y_1)+(y-y_1) \frac{f(x,y_2)-f(x,y_1)}{y_2-y_1} = 97.9+(68-65) \frac{ 112-97.9 }{ 70- 65 } =106$$

You can see Linear interpolation calculator also