Option Explicit

Function sbReducePoints(rX As Range, rY As Range, _
    Optional dMaxSlopeDelta As Double = 0.001) As Variant
'sbReducePoints eliminates points from a given set
'in case the slopes between these points do not differ
'too much.
'Source (EN): http://www.sulprobil.com/sbreducepoints_en/
'Source (DE): http://www.bplumhoff.de/sbreducepoints_de/
'(C) (P) by Bernd Plumhoff 29-Mar-2023 PB V0.1

Dim bNewSlope               As Boolean

Dim dSlope12                As Double
Dim dSlope13                As Double
Dim dSlope23                As Double

Dim i                       As Long
Dim k                       As Long
Dim lcount                  As Long

With Application.WorksheetFunction

lcount = rX.Rows.Count
If rX.Columns.Count > lcount Then
    lcount = rX.Columns.Count
End If

ReDim dX(1 To lcount) As Double
ReDim dY(1 To lcount) As Double

'read data row-wise or column-wise
If rX.Rows.Count > rX.Columns.Count Then
    For i = 1 To lcount
        dX(i) = rX.Cells(i, 1)
        dY(i) = rY.Cells(i, 1)
    Next i
Else
    For i = 1 To lcount
        dX(i) = rX.Cells(1, i)
        dY(i) = rY.Cells(1, i)
    Next i
End If

ReDim vR(1 To 2, 1 To lcount) As Variant

vR(1, 1) = dX(1)
vR(2, 1) = dY(1)
vR(1, 2) = dX(2)
vR(2, 2) = dY(2)
k = 2
bNewSlope = True
For i = 3 To lcount
    If bNewSlope Then dSlope12 = (vR(2, k) - vR(2, k - 1)) / (vR(1, k) - vR(1, k - 1))
    dSlope13 = (dY(i) - vR(2, k - 1)) / (dX(i) - vR(1, k - 1))
    dSlope23 = (dY(i) - vR(2, k)) / (dX(i) - vR(1, k))
    If Abs(dSlope13 - dSlope12) > dMaxSlopeDelta Or _
        Abs(dSlope13 - dSlope23) > dMaxSlopeDelta Then
        k = k + 1
        bNewSlope = True
    Else
        bNewSlope = False
    End If
    vR(1, k) = dX(i)
    vR(2, k) = dY(i)
Next i
    
ReDim Preserve vR(1 To 2, 1 To k) As Variant

If rX.Rows.Count > rX.Columns.Count Then
    sbReducePoints = .Transpose(vR)
Else
    sbReducePoints = vR
End If

End With

End Function