Excel - Bilineare interpolatie functie

Visualisatie van bovenstaande datatabel

Berekening
X = 451 ligt tussen X = 400 en X = 500. X-fractie = (451 - 400)/(500 - 400) = 0.51
Y = 75 ligt tussen Y = 60 en Y = 80. Y-fractie = (75 - 60)/(80 - 60) = 0.75

De waarden van de 4 datapunten waartussen geïnterpoleerd moet worden (X,Y):
     1. (400,60) = 149
     2. (500,60) = 163
     3. (400,80) = 169
     4. (500,80) = 187

Interpolatie X:
     1.&2. → 149 + 0.51 × (163 - 149) = 156.14
     3.&4. → 169 + 0.51 × (187 - 169) = 178.18

Interpolatie Y:
     156.14 + 0.75 × (178.18 - 156.14) = 172.67 hetgeen de einduitkomst is.

VBA code ter plaatsing in een module

In MS Excel, druk Alt+F11 om de Visual Basic Editor te openen (Windows). Via hoofdmenu: Invoegen → Module. Kopieer onderstaande code naar de module.

Public Function InterpolateXY(ByRef X As Range, ByRef Y As Range, ByRef XRange As Range, ByRef YRange As Range, ByRef ValueTable As Range) As Double Dim iCol As Long Dim iRow As Long Dim C1 As Double Dim C2 As Double Dim C3 As Double Dim C4 As Double Dim F1 As Double Dim F2 As Double Dim C5 As Double Dim C6 As Double 'search X iCol = 1 Do While X >= XRange(1, iCol).Value And (iCol < XRange.Columns.Count) iCol = iCol + 1 Loop 'search Y iRow = 1 Do While Y >= YRange(iRow, 1).Value And (iRow < YRange.Rows.Count) iRow = iRow + 1 Loop 'if X or Y fall outside the table, the function result is an error value If (X < XRange(1, 1).Value) Or (X > XRange(1, iCol).Value) Or (Y < YRange(1, 1).Value) Or (Y > YRange(iRow, 1).Value) Then InterpolateXY = (1 / 0) Exit Function End If '4 data table points 'around' X and Y C1 = ValueTable.Cells(iRow - 1, iCol - 1).Value C2 = ValueTable.Cells(iRow - 1, iCol).Value C3 = ValueTable.Cells(iRow, iCol - 1).Value C4 = ValueTable.Cells(iRow, iCol).Value 'X and Y fractions F1 = (X - XRange.Cells(1, iCol - 1).Value) / (XRange.Cells(1, iCol).Value - XRange.Cells(1, iCol - 1).Value) F2 = (Y - YRange.Cells(iRow - 1, 1).Value) / (YRange.Cells(iRow, 1).Value - YRange.Cells(iRow - 1, 1).Value) '2 intermediate results after interpolation on X C5 = C1 + F1 * (C2 - C1) C6 = C3 + F1 * (C4 - C3) 'final result after interpolation on Y InterpolateXY = C5 + F2 * (C6 - C5) End Function