
Calculation explanation of above example - Bilinear interpolation
Visualisation of the data table above

Calculation
X = 451 lies between X = 400 and X = 500. X-fraction = (451 - 400)/(500 - 400) = 0.51
Y = 75 lies between Y = 60 and Y = 80. Y-fraction = (75 - 60)/(80 - 60) = 0.75
The 4 data point values to interpolate between are (X,Y):
1. (400,60) = 149
2. (500,60) = 163
3. (400,80) = 169
4. (500,80) = 187
Interpolation X:
1.&2. → 149 + 0.51 × (163 - 149) = 156.14
3.&4. → 169 + 0.51 × (187 - 169) = 178.18
Interpolation Y:
156.14 + 0.75 × (178.18 - 156.14) = 172.67 = final bilineair interpolation result.
The Cubic spline based interpolation brings 173.44, which is 0.4% higher. If your data is about a concave curved surface, it is obvious that the bilinear interpolation result will always slightly underestimate, except on a data point itself. The above example is slightly convex in Y direction, but more dominantly concave in X direction.
X = 451 lies between X = 400 and X = 500. X-fraction = (451 - 400)/(500 - 400) = 0.51
Y = 75 lies between Y = 60 and Y = 80. Y-fraction = (75 - 60)/(80 - 60) = 0.75
The 4 data point values to interpolate between are (X,Y):
1. (400,60) = 149
2. (500,60) = 163
3. (400,80) = 169
4. (500,80) = 187
Interpolation X:
1.&2. → 149 + 0.51 × (163 - 149) = 156.14
3.&4. → 169 + 0.51 × (187 - 169) = 178.18
Interpolation Y:
156.14 + 0.75 × (178.18 - 156.14) = 172.67 = final bilineair interpolation result.
The Cubic spline based interpolation brings 173.44, which is 0.4% higher. If your data is about a concave curved surface, it is obvious that the bilinear interpolation result will always slightly underestimate, except on a data point itself. The above example is slightly convex in Y direction, but more dominantly concave in X direction.