Calculate a ScrollViewer's scrollbar offsets so that an object will be centered, while maintaining a layout transform who's scale is variable

I have been fighting with this one for many hours now, and I just can't seem to arrive at an acceptable answer. I am hoping someone out there with much stronger geometry skills than my self can solve this riddle for me. Any help would be greatly appreciated. The nature of my problem, and description is below in the image that I provided.

And here is a sample project that I have built, which does not correctly fulfill the requirements.

XAML:

<Window x:Class="MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    Title="Center and Zoom ScrollViewer Test" Height="600" Width="800" WindowStartupLocation="CenterScreen">
<Grid>
    <DockPanel>
        <GroupBox Header="Parameters" DockPanel.Dock="Top" Margin="10">
            <StackPanel Orientation="Horizontal">
                <GroupBox Header="Manually Set ScrollBar Positions" Margin="10">
                    <StackPanel Orientation="Horizontal">
                        <TextBox Name="EditHorz" Width="60" Margin="10" TextChanged="EditHorz_TextChanged" />
                        <Label Content="x" Margin="0 10 0 10" />
                        <TextBox Name="EditVert" Width="60" Margin="10" TextChanged="EditVert_TextChanged" />
                    </StackPanel>
                </GroupBox>

                <GroupBox Header="Scale" Margin="10">
                    <DockPanel>
                        <Label Content="{Binding ElementName=scaleValue, Path=Value}" DockPanel.Dock="Right" VerticalContentAlignment="Center" HorizontalContentAlignment="Center" Width="40" />
                        <Slider Name="scaleValue" Minimum="1" Maximum="4" SmallChange="0.05" LargeChange="0.1" Width="200" VerticalAlignment="Center" />
                    </DockPanel>
                </GroupBox>
            </StackPanel>
        </GroupBox>

        <GroupBox Header="Debug Output" Margin="10">
            <TextBox Name="text" FontFamily="Courier New" FontSize="12" DockPanel.Dock="Left" Width="500" TextWrapping="Wrap" AcceptsReturn="True" AcceptsTab="True" Margin="10" />
        </GroupBox>

        <GroupBox Header="Proof" Margin="10">
            <DockPanel>
                <StackPanel Orientation="Horizontal" DockPanel.Dock="Bottom" HorizontalAlignment="Center">
                    <Button Width="60" HorizontalAlignment="Left" Content="Center" Click="ButtonCenter_Click" Margin="10" />
                    <Button Width="60" HorizontalAlignment="Left" Content="Reset" Click="ButtonReset_Click" Margin="10" />
                </StackPanel>
                <ScrollViewer Name="scroll" VerticalScrollBarVisibility="Hidden" HorizontalScrollBarVisibility="Hidden" Background="Green" Width="100" Height="100" VerticalAlignment="Top" Margin="10">
                    <Canvas Width="200" Height="200" Background="Red">
                        <Canvas.LayoutTransform>
                            <ScaleTransform ScaleX="{Binding ElementName=scaleValue, Path=Value}" ScaleY="{Binding ElementName=scaleValue, Path=Value}" />
                        </Canvas.LayoutTransform>
                        <Rectangle Name="rect" Width="40" Height="40" Canvas.Left="120" Canvas.Top="70" Fill="Blue" />
                    </Canvas>
                </ScrollViewer>
            </DockPanel>
        </GroupBox>
    </DockPanel>
</Grid>

Code Behind (VB.net)

Class MainWindow
''' Calculates the horizontal and vertical scrollbar offsets so that
''' the blue rectangle is centered within the scroll viewer.
Private Sub RecalculateCenter()
    ' the scale we are using
    Dim scale As Double = scaleValue.Value

    ' get the rectangles current position within the canvas
    Dim rectLeft As Double = Canvas.GetLeft(rect)
    Dim rectTop As Double = Canvas.GetTop(rect)

    ' set our point of interest "Rect" equal to the the whole coordinates of the rectangle
    Dim poi As Rect = New Rect(rectLeft, rectTop, rect.Width, rect.Height)

    ' get our view offset
    Dim ofsViewWidth As Double = (scroll.ScrollableWidth - (((scroll.ViewportWidth / 2) - (rect.ActualWidth / 2)) * scale)) / scale
    Dim ofsViewHeight As Double = (scroll.ScrollableHeight - (((scroll.ViewportHeight / 2) - (rect.ActualHeight / 2)) * scale)) / scale

    ' calculate our scroll bar offsets
    Dim verticalOffset As Double = (poi.Top - ofsViewHeight) * scale
    Dim horizontalOffset As Double = (poi.Left - ofsViewWidth) * scale

    ' record the output to the debug output window
    Dim sb As New StringBuilder()
    sb.AppendLine($"Scale      : {scale}")
    sb.AppendLine($"POI        : {poi.ToString()}")
    sb.AppendLine($"Rect       : {rectLeft}x{rectTop}")
    sb.AppendLine($"Extent     : {scroll.ExtentWidth}x{scroll.ExtentHeight}")
    sb.AppendLine($"Scrollable : {scroll.ScrollableWidth}x{scroll.ScrollableHeight}")
    sb.AppendLine($"View Offset: {ofsViewWidth}x{ofsViewHeight}")
    sb.AppendLine($"Horizontal : {horizontalOffset}")
    sb.AppendLine($"Vertical   : {verticalOffset}")

    text.Text = sb.ToString()

    ' set the EditHorz and EditVert text box values, this will trigger the scroll
    ' bar offsets to fire via the TextChanged event handlers
    EditHorz.Text = horizontalOffset.ToString()
    EditVert.Text = verticalOffset.ToString()
End Sub

''' Try and parse the horizontal text box to a double, and set the scroll bar position accordingly
Private Sub SetScrollBarHorizontalOffset()
    Dim ofs As Double = 0
    If Double.TryParse(EditHorz.Text, ofs) Then
        scroll.ScrollToHorizontalOffset(ofs)
    End If
End Sub

''' Try and parse the vertical text box to a double, and set the scroll bar position accordingly
Private Sub SetScrollBarVerticalOffset()
    Dim ofs As Double = 0
    ofs = 0
    If Double.TryParse(EditVert.Text, ofs) Then
        scroll.ScrollToVerticalOffset(ofs)
    End If
End Sub

''' Parse and set scrollbars positions for both Horizontal and Vertical
Private Sub SetScrollBarOffsets()
    SetScrollBarHorizontalOffset()
    SetScrollBarVerticalOffset()
End Sub

Private Sub ButtonCenter_Click(sender As Object, e As RoutedEventArgs)
    RecalculateCenter()
End Sub

Private Sub ButtonReset_Click(sender As Object, e As RoutedEventArgs)
    scroll.ScrollToVerticalOffset(0)
    scroll.ScrollToHorizontalOffset(0)
End Sub

Private Sub EditHorz_TextChanged(sender As Object, e As TextChangedEventArgs)
    SetScrollBarOffsets()
End Sub

Private Sub EditVert_TextChanged(sender As Object, e As TextChangedEventArgs)
    SetScrollBarOffsets()
End Sub

End Class

Solution

After much more trial and error, and breaking it apart piece by piece, I was able to finally get this code to work. I hope someone else will find this useful. Solution is as follows:

XAML:

<Window x:Class="MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    Title="Center and Zoom ScrollViewer Test" Height="600" Width="800" WindowStartupLocation="CenterScreen">
<Grid>
    <DockPanel>
        <GroupBox Header="Parameters" DockPanel.Dock="Top" Margin="10">
            <StackPanel Orientation="Horizontal">
                <GroupBox Header="Manually Set ScrollBar Positions" Margin="10">
                    <StackPanel Orientation="Horizontal">
                        <TextBox Name="EditHorz" Width="60" Margin="10" TextChanged="EditHorz_TextChanged" />
                        <Label Content="x" Margin="0 10 0 10" />
                        <TextBox Name="EditVert" Width="60" Margin="10" TextChanged="EditVert_TextChanged" />
                    </StackPanel>
                </GroupBox>

                <GroupBox Header="Scale" Margin="10">
                    <DockPanel>
                        <Label Content="{Binding ElementName=scaleValue, Path=Value, StringFormat={}{0:F2}}" DockPanel.Dock="Right" VerticalContentAlignment="Center" HorizontalContentAlignment="Center" Width="40" />
                        <Slider Name="scaleValue" Minimum="1" Maximum="4" SmallChange="0.05" LargeChange="0.1" Width="200" VerticalAlignment="Center" />
                    </DockPanel>
                </GroupBox>
            </StackPanel>
        </GroupBox>

        <GroupBox Header="Debug Output" Margin="10">
            <TextBox Name="text" FontFamily="Courier New" FontSize="12" DockPanel.Dock="Left" Width="500" TextWrapping="Wrap" AcceptsReturn="True" AcceptsTab="True" Margin="10" />
        </GroupBox>

        <GroupBox Header="Proof" Margin="10">
            <DockPanel>
                <StackPanel Orientation="Horizontal" DockPanel.Dock="Bottom" HorizontalAlignment="Center">
                    <Button Width="60" HorizontalAlignment="Left" Content="Center" Click="ButtonCenter_Click" Margin="10" />
                    <Button Width="60" HorizontalAlignment="Left" Content="Reset" Click="ButtonReset_Click" Margin="10" />
                </StackPanel>
                <ScrollViewer Name="scroll" VerticalScrollBarVisibility="Hidden" HorizontalScrollBarVisibility="Hidden" Background="Green" Width="100" Height="100" VerticalAlignment="Top" Margin="10">
                    <Canvas Width="200" Height="200" Background="Red">
                        <Canvas.LayoutTransform>
                            <ScaleTransform ScaleX="{Binding ElementName=scaleValue, Path=Value}" ScaleY="{Binding ElementName=scaleValue, Path=Value}" />
                        </Canvas.LayoutTransform>
                        <Rectangle Name="rect" Width="40" Height="40" Canvas.Left="120" Canvas.Top="70" Fill="Blue" />
                    </Canvas>
                </ScrollViewer>
            </DockPanel>
        </GroupBox>
    </DockPanel>
</Grid>

Code Behind (VB.net):

Class MainWindow
' Calculates the horizontal and vertical scrollbar offsets so that
' the blue rectangle is centered within the scroll viewer.
Private Sub RecalculateCenter()
    ' the scale we are using
    Dim scale As Double = scaleValue.Value

    ' get our rectangles left and top properties
    Dim rectLeft As Double = Canvas.GetLeft(rect) * scale
    Dim rectTop As Double = Canvas.GetTop(rect) * scale
    Dim rectWidth As Double = rect.Width * scale
    Dim rectHeight As Double = rect.Height * scale

    ' set our point of interest "Rect" equal to the the whole coordinates of the rectangle
    Dim poi As Rect = New Rect(rectLeft, rectTop, rectWidth, rectHeight)

    ' get top and left center values
    Dim horizontalCenter As Double = ((scroll.ViewportWidth / 2) - (rectWidth / 2))
    Dim verticalCenter As Double = ((scroll.ViewportHeight / 2) - (rectHeight / 2))

    ' get our center of viewport with relation to the poi
    Dim viewportCenter As New Rect(horizontalCenter, verticalCenter, rectWidth, rectHeight)

    ' calculate our scroll bar offsets
    Dim verticalOffset As Double = (poi.Top) - (viewportCenter.Top)
    Dim horizontalOffset As Double = (poi.Left) - (viewportCenter.Left)

    ' record the output to the debug output window
    Dim sb As New StringBuilder()
    sb.AppendLine($"Scale .............. {scale,0:F2}")
    sb.AppendLine($"rectLeft ........... {rectLeft,0:F0}")
    sb.AppendLine($"rectTop ............ {rectTop,0:F0}")
    sb.AppendLine($"POI ................ {poi.Left,0:F0},{poi.Top,0:F0},{poi.Width,0:F0},{poi.Height,0:F0}")
    sb.AppendLine($"Horz Center ........ {horizontalCenter,0:F0}")
    sb.AppendLine($"Vert Center ........ {verticalCenter,0:F0}")
    sb.AppendLine($"View Center ........ {viewportCenter.Left,0:F0},{viewportCenter.Top,0:F0},{viewportCenter.Width,0:F0},{viewportCenter.Height,0:F0}")
    sb.AppendLine($"Horizontal ......... {horizontalOffset,0:F0}")
    sb.AppendLine($"Vertical ........... {verticalOffset,0:F0}")
    sb.AppendLine($"------------------------------------")
    sb.AppendLine($"ViewPort ........... {scroll.ViewportWidth,0:F0} x {scroll.ViewportHeight,0:F0}")
    sb.AppendLine($"Extent ............. {scroll.ExtentWidth,0:F0} x {scroll.ExtentHeight,0:F0}")
    sb.AppendLine($"Scrollable ......... {scroll.ScrollableWidth,0:F0} x {scroll.ScrollableHeight,0:F0}")

    text.Text = sb.ToString()

    ' set the EditHorz and EditVert text box values, this will trigger the scroll
    ' bar offsets to fire via the TextChanged event handlers
    EditHorz.Text = $"{horizontalOffset,0:F2}"
    EditVert.Text = $"{verticalOffset,0:F2}"
End Sub

' Try and parse the horizontal text box to a double, and set the scroll bar position accordingly
Private Sub SetScrollBarHorizontalOffset()
    Dim ofs As Double = 0
    If Double.TryParse(EditHorz.Text, ofs) Then
        scroll.ScrollToHorizontalOffset(ofs)
    Else
        scroll.ScrollToHome()
    End If
End Sub

' Try and parse the vertical text box to a double, and set the scroll bar position accordingly
Private Sub SetScrollBarVerticalOffset()
    Dim ofs As Double = 0
    ofs = 0
    If Double.TryParse(EditVert.Text, ofs) Then
        scroll.ScrollToVerticalOffset(ofs)
    Else
        scroll.ScrollToHome()
    End If
End Sub

' Parse and set scrollbars positions for both Horizontal and Vertical
Private Sub SetScrollBarOffsets()
    SetScrollBarHorizontalOffset()
    SetScrollBarVerticalOffset()
End Sub

Private Sub ButtonCenter_Click(sender As Object, e As RoutedEventArgs)
    RecalculateCenter()
End Sub

Private Sub ButtonReset_Click(sender As Object, e As RoutedEventArgs)
    EditHorz.Text = String.Empty
    EditVert.Text = String.Empty
End Sub

Private Sub EditHorz_TextChanged(sender As Object, e As TextChangedEventArgs)
    SetScrollBarOffsets()
End Sub

Private Sub EditVert_TextChanged(sender As Object, e As TextChangedEventArgs)
    SetScrollBarOffsets()
End Sub

Private Sub scaleValue_ValueChanged(sender As Object, e As RoutedPropertyChangedEventArgs(Of Double)) Handles scaleValue.ValueChanged
    Dispatcher.BeginInvoke(Sub() RecalculateCenter())
End Sub

End Class