﻿ Excel - Bilinear / bicubic / spline based 2D-interpolation functions (UDF & VBA)

# Excel - Bilinear interpolation functions

Interpolating within a 2-dimensional table is easier done by using a LAMBDA or VBA function than by using regular Excel formulas. Source: wikipedia
• Bilineair interpolation functions InterpolateXY (UDF) and L_InterpolateXY (LAMBDA equivalent). LAMBDA functionality is new in Office365/Excel 2021 (beta). It enables you to create new functions directly within Name Manager.

• Three spline based 2D-interpolation functions (UDF). A spline is a curve that goes through the data points (see also Excel splines). More accurate for convex/concave surfaces, as bilinear interpolation always overestimates/underestimates, except on datapoints itself.
• InterpolateXY_CubicSpline: also known as bicubic interpolation
• InterpolateXY_MonotoneCubicSpline: based on monotone cubic splines that do not 'wobble' like the other two types of splines
• InterpolateXY_CardinalSpline: based on a cardinal spline with parameter tension between 0.0 and 1.0 (default 0.5; at 0.0 it 'becomes' bilinear interpolation).

If you want to interpolate within a 1-dimensional table, then see Linear interpolation. ## 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.

## Bilinear interpolation - VBA code to be put in a module

In MS Excel, press Alt+F11 to open the Visual Basic Editor (Windows). Via top menu: Insert → Module. Copy the code below into the module.

## LAMBDA function L_InterpolateXY

Based on L_InterpolateX, so you need to copy in both functions.