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Engineering spreadsheets

Can you force an Excel XY-Chart to have equal scales? by Denial
Posted: 24 Sep 15 (Edited 5 Oct 15)

The attached VBA subroutine will force an Excel XY-chart to have equal scaling on its X ("Category") and Y ("Value") axes.  It has evolved over many years, with major contributions from multiple people on this web site and elsewhere.

Why might you want to achieve equal scaling on the two axes?  In my case it was mainly for creating data-driven diagrams.  Other people have found other uses for it.

CODE

Sub GiveActivePlotEqualScales()
'
'  PURPOSE
'
'  Changes the X and Y scales of an Excel XY-Scatter chart by
'  exactly the right amount to result in the two scales being equal.
'
'  The chart, which can be embedded in a worksheet or can be on its
'  own ChartSheet, has to be "active" when this subroutine runs.
'
'  The subroutine will not run on a protected worksheet unless the
'  protection allows the user to "edit objects".  However a user who
'  can "edit objects" can also mess up the plot in various ways, so
'  the protection would seem to be somewhat pointless.
'
'  HISTORY
'
'  The original subroutine was developed by Jon Peltier, and placed
'  on his PeltierTech website at URL
'  www.peltiertech.com/Excel/Charts/SquareGrid.html
'  where it was still accessible in September 2015.
'  A modified version of the routine was placed on the "Engineering
'  spreadsheets" forum of the Eng-Tips web site (www.Eng-Tips.com)
'  by contributor Panars in December 2005, in thread 770-141275.
'  Two other EngTip-ers, Electricpete and Denial then made some
'  further modifications to it as the thread developed.
'
'  In 2010 Denial posted an improved version on Eng-Tips.  See
'  thread 770-274998.   The main problem fixed was that for
'  charts with at least one axis displayed there were still some,
'  seemingly random, circumstances under which the resulting scales
'  would not be adequately equal.
'
'  MODIFICATIONS SINCE MID 2015
'
'  Sep 2015.  Correction for where a worksheet has more than one embedded
'      chart object.  (Previously chart object 1's series were used to
'      calculate the scaling factors for all the chart objects.)
'  Sep 2015.  In charts where only one axis is utilised we now set that
'      axis's MajorUnitsIsAuto parameter to True.  This avoids some grossly
'      inappropriate label spacings under some circumstances.
'  24Sep15.  This updated version was posted on Eng-Tips
'      as thread 770-395377 and as FAQ 770-1901.
'  27Sep15.  Added check for whether a chart is actually "active".
'
Dim s As Series, PointsList As Variant, PointCount As Long
Dim PlotInHt As Double, PlotInWd As Double
Dim HaveXaxis As Boolean, HaveYaxis As Boolean
Dim PlotName As String, PlotNumb As Long
Dim TypeOfPlot As Long, SubtypeOfPlot As Long
Dim IsEmbedded As Boolean
Dim Xmax As Double, Xmin As Double, Xdel As Double
Dim Ymax As Double, Ymin As Double, Ydel As Double
Dim XmaxData As Double, XminData As Double
Dim YmaxData As Double, YminData As Double
Dim Xpix As Double, Ypix As Double
Dim Distort As Double, Distort_pc As Double
Dim CycleCount As Long, MaxCycles As Long
Dim AxisControlling As String
Dim MoveDist As Double, Shift As Long
Dim Margin As Double, Temp As Double
'
Const SubName As String = "GiveActivePlotEqualScales"
'
'  Check whether there is in fact an active chart.
'
If ActiveChart Is Nothing Then
    MsgBox "There is no active chart.", , "Subroutine " & SubName
    Exit Sub
End If
'
'  Determine whether the active chart is embedded in a worksheet or
'  is a sheet in its own right.  (If the activesheet's type is not
'  a worksheet, assume that it is a chart.)
'
IsEmbedded = (ActiveSheet.Type = xlWorksheet)
'
With ActiveChart    'The "End With" for this is at the very end of the subroutine.
'
'  Get various properties of the chart.  Check chart type.
'
If IsEmbedded Then
    PlotName = .Parent.Name
Else
    PlotName = .Name
End If
TypeOfPlot = .Type
SubtypeOfPlot = .ChartType
If TypeOfPlot <> xlXYScatter Then
    MsgBox "Scale-equalising macro is intended only for an XY Scatter chart.", , _
           PlotName & " / " & SubName
    Exit Sub
End If
'
'  Get presence/absence for each axis.
'
HaveXaxis = .HasAxis(xlCategory)
HaveYaxis = .HasAxis(xlValue)
'
'  Determine the extreme X and Y values of all the data points,
'  looping through all the data series on the chart.
'
'  Note that VBA generates an error if we try to do anything with
'  an empty series:  hence the need for the "on error" statements.
'
Xmin = 9.999999E+100:   Ymin = Xmin:   Xmax = -Xmin:   Ymax = Xmax
PointCount = 0
If IsEmbedded Then
    PlotNumb = ActiveChart.Parent.Index
    For Each s In ActiveSheet.ChartObjects(PlotNumb).Chart.SeriesCollection
        On Error Resume Next
        PointCount = PointCount + s.Points.Count
        PointsList = s.XValues
        Xmax = Application.Max(Xmax, PointsList)
        Xmin = Application.Min(Xmin, PointsList)
        PointsList = s.Values
        Ymax = Application.Max(Ymax, PointsList)
        Ymin = Application.Min(Ymin, PointsList)
        On Error GoTo 0
    Next s
Else
    For Each s In .SeriesCollection
        On Error Resume Next
        PointCount = PointCount + s.Points.Count
        PointsList = s.XValues
        Xmax = Application.Max(Xmax, PointsList)
        Xmin = Application.Min(Xmin, PointsList)
        PointsList = s.Values
        Ymax = Application.Max(Ymax, PointsList)
        Ymin = Application.Min(Ymin, PointsList)
        On Error GoTo 0
    Next s
End If
'
'  Suppress the following two error messages, because in the present
'  context the subroutine is being initiated automatically.  (And
'  we don't want to alarm the user, do we?)
'
If PointCount <= 0 Then
'    MsgBox "Chart contains no points.", , PlotName & " / " & SubName
    Exit Sub
End If
If Xmax - Xmin + Ymax - Ymin <= 1E-20 Then
'    MsgBox "Chart is of zero size.", , PlotName & " / " & SubName
    Exit Sub
End If
'
'  Expand these maximum and minimum values very slightly, so that
'  line segments running along the very edge of the graph area
'  do not get missed.  If the chart sub-type is "smoothed"
'  use a bit more expansion, to allow for the smoothed edges to
'  extend beyond the actual data points.
'
'  The sizes used for these "margins" are no better than guesses.
'
Margin = 0.005
If SubtypeOfPlot = xlXYScatterSmooth Or _
   SubtypeOfPlot = xlXYScatterSmoothNoMarkers Then Margin = 0.04
Temp = Margin * (Xmax - Xmin)
Xmax = Xmax + Temp
Xmin = Xmin - Temp
Temp = Margin * (Ymax - Ymin)
Ymax = Ymax + Temp
Ymin = Ymin - Temp
'
'  Record these max & min values for later use.
'
XminData = Xmin:   XmaxData = Xmax:   YminData = Ymin:   YmaxData = Ymax
'
'  If we have an X axis, find out what MajorUnit would auto-apply.
'
If HaveXaxis Then
    With .Axes(xlCategory)
        .MaximumScaleIsAuto = True
        .MinimumScaleIsAuto = True
        .MajorUnitIsAuto = True
        Xdel = .MajorUnit
        .MaximumScaleIsAuto = False
        .MinimumScaleIsAuto = False
        .MajorUnitIsAuto = False
    End With
    If Xmax = Xmin Then Xdel = 0
End If
'
'  If we have a Y axis, find out what MajorUnit would auto-apply.
'
If HaveYaxis Then
    With .Axes(xlValue)
        .MaximumScaleIsAuto = True
        .MinimumScaleIsAuto = True
        .MajorUnitIsAuto = True
        Ydel = .MajorUnit
        .MaximumScaleIsAuto = False
        .MinimumScaleIsAuto = False
        .MajorUnitIsAuto = False
    End With
    If Ymax = Ymin Then Ydel = 0
End If
'
'  If have both X and Y axes, use the larger MajorUnit for both.
'
If HaveXaxis And HaveYaxis Then
    If Ydel >= Xdel Then
        Xdel = Ydel
    Else
        Ydel = Xdel
    End If
End If
'
'  For directions with axes, round the minimum values down to be
'  multiples of the axis's MajorUnit.  Round only the "minimum"
'  values, since these are the ones that serve as the base for the
'  markings along the axes.  (And if we do it for the maximum
'  as well we risk overconstraining our problem.)
'
'  At the same time, set the MajorUnit.
'  Note that the calculation for the MajorUnit needs to be
'  set to "Auto" if the axis concerned is the only axis in use,
'  or the unit spacing can be badly wrong. (MajorAxisIsAuto was
'  set to False near the start of the subroutine.)
'
If HaveXaxis And Xdel <> 0 Then
    Xmin = Xdel * Round((Xmin - 0.5 * Xdel) / Xdel)
    If HaveYaxis Then
        .Axes(xlCategory).MajorUnit = Xdel
    Else
        .Axes(xlCategory).MajorUnitIsAuto = True
    End If
End If
If HaveYaxis And Ydel <> 0 Then
    Ymin = Ydel * Round((Ymin - 0.5 * Ydel) / Ydel)
    If HaveXaxis Then
        .Axes(xlValue).MajorUnit = Ydel
    Else
        .Axes(xlValue).MajorUnitIsAuto = True
    End If
End If
'
'  Get the dimensions of the part of the chart used for the actual
'  graphing, then use these to calculate the present values of the
'  relative scaling factors in the X & Y directions.
'
PlotInWd = .PlotArea.InsideWidth
PlotInHt = .PlotArea.InsideHeight
Xpix = (Xmax - Xmin) / PlotInWd
Ypix = (Ymax - Ymin) / PlotInHt
'
'  We can now set about equalising the scales.  In an ideal world
'  this would be a simple, single pass, exercise.  But it turns
'  out that, for a chart that has any axes displayed, a change to
'  the defined extents of a displayed axis will sometimes change
'  the chart's InsideWidth or InsideHeight properties.  I cannot
'  find a way to predict when this will or will not happen.
'
'  This behaviour is a major PItA.  It requires us to adopt an
'  iterative approach.  Implement the iterations with a For—Next
'  loop, and set a fairly low limit on the maximum number of
'  iterations allowed.  (But not too low:  I had one chart which
'  required 9 iterations to achieve adequately equal scales.)
'
MaxCycles = 15
For CycleCount = 1 To MaxCycles
    '
    '  Adjust one of the scales in an attempt to achieve equality.
    '
    If Ypix < Xpix Then
        '
        '  X DIRECTION CONTROLS THE SIZE OF THE CHART.
        '
        AxisControlling = "X"
        '
        'Set the X-axis extents to the data's extents.
        '
        .HasAxis(xlCategory) = True
        .Axes(xlCategory).MinimumScale = Xmin
        .Axes(xlCategory).MaximumScale = Xmax
        If Not HaveXaxis Then .HasAxis(xlCategory) = False
        '
        '  Recalculate the scaling factors, which might have changed.
        '
        PlotInWd = .PlotArea.InsideWidth
        PlotInHt = .PlotArea.InsideHeight
        Xpix = (Xmax - Xmin) / PlotInWd
        Ypix = (Ymax - Ymin) / PlotInHt
        '
        '  Calculate the value of Ymax that will result in
        '  the same value for the scale of the Y-axis as we
        '  have just defined for the scale of the X-axis.
        '
        Ymax = Ymin + Xpix * PlotInHt
        '
        '  The available space in the Y-direction will be greater
        '  than what is needed by the actual graphing.  Attempt
        '  to position the graphing centrally in this space.  If
        '  the chart has its Y-axis displayed, then any shift
        '  must be a multiple of the MajorUnit.
        '
        MoveDist = 0.5 * (Ymax + Ymin - YmaxData - YminData)
        If HaveYaxis Then
            Shift = Round(MoveDist / Ydel, 0)
            Ymin = Ymin - Shift * Ydel
            Ymax = Ymax - Shift * Ydel
        Else
            Ymin = Ymin - MoveDist
            Ymax = Ymax - MoveDist
        End If
        '
        '  Set the Y-axis extents to these calculated values.
        '
        .HasAxis(xlValue) = True
        .Axes(xlValue).MinimumScale = Ymin
        .Axes(xlValue).MaximumScale = Ymax
        If Not HaveYaxis Then .HasAxis(xlValue) = False
    Else
        '
        '  Y DIRECTION CONTROLS THE SIZE OF THE CHART.
        '
        AxisControlling = "Y"
        '
        '  Set the Y-axis extents to the data's extents.
        '
        .HasAxis(xlValue) = True
        .Axes(xlValue).MinimumScale = Ymin
        .Axes(xlValue).MaximumScale = Ymax
        If Not HaveYaxis Then .HasAxis(xlValue) = False
        '
        '  Recalculate the scaling factors, which might have changed.
        '
        PlotInWd = .PlotArea.InsideWidth
        PlotInHt = .PlotArea.InsideHeight
        Xpix = (Xmax - Xmin) / PlotInWd
        Ypix = (Ymax - Ymin) / PlotInHt
        '
        '  Calculate the value of Xmax that will result in
        '  the same value for the scale of the X-axis as we
        '  have just defined for the scale of the Y-axis.
        '
        Xmax = Xmin + Ypix * PlotInWd
        '
        '  The available space in the X-direction will be greater
        '  than what is needed by the actual graphing.  Attempt
        '  to position the graphing centrally in this space.  If
        '  the chart has its X-axis displayed, then any shift
        '  must be a multiple of the MajorUnit.
        '
        MoveDist = 0.5 * (Xmax + Xmin - XmaxData - XminData)
        If HaveXaxis Then
            Shift = Round(MoveDist / Xdel, 0)
            Xmin = Xmin - Shift * Xdel
            Xmax = Xmax - Shift * Xdel
        Else
            Xmin = Xmin - MoveDist
            Xmax = Xmax - MoveDist
        End If
        '
        '  Set the X-axis extents to these calculated values.
        '
        .HasAxis(xlCategory) = True
        .Axes(xlCategory).MinimumScale = Xmin
        .Axes(xlCategory).MaximumScale = Xmax
        If Not HaveXaxis Then .HasAxis(xlCategory) = False
    End If
    '
    '  Recalculate the scaling factors, which might have changed yet again.
    '
    PlotInWd = .PlotArea.InsideWidth
    PlotInHt = .PlotArea.InsideHeight
    Xpix = (Xmax - Xmin) / PlotInWd
    Ypix = (Ymax - Ymin) / PlotInHt
    '
    '  If the discrepancy between the scaling factors is less than
    '  say 0.5%, then we can apply the Bobby McFerrin / Meher Baba
    '  algorithm ("Don't worry, be happy").
    '
    '  Otherwise, sigh deeply and begin another iteration.
    '
    Distort = Abs((Xpix - Ypix) / (Xpix + Ypix))
    If Distort < 0.0025 Then GoTo Finish_Off
Next CycleCount
'
'  Tell the long-suffering user that adequate convergence
'  has not been achieved.  Then carry on regardless.
'
Distort_pc = Round(100 * Distort, 1)
MsgBox "Discrepancy between scales is " & Distort_pc & "%" & Chr(13) & _
       "after " & MaxCycles & " iterations.", , _
       PlotName & " / " & SubName
'
Finish_Off:
'
End With        'Terminates the "With ActiveChart" near the top of the subroutine.
'
End Sub 

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