Auto-Scale WPF TextBox/RichTextBox content to fit available space

Question

I have the following problem:

I want to setup a RichTextBox that automatically can resize the content inside to fit maximum of the available space while not change the layout of the content (e.g. Font sizes, Indent, etc.).

I saw already many questions about scaling the content of a TextBox but all questions was related to some kind of zoom slider. What I want is to really calculate the scaling so that it automatically best-fit into the TextBox.

What I have established so far is a LayoutTransform inside the AdornerDecorator of the RichTextBox template that is wrapped inside a ScrollViewer so that I can trigger a code-behind method to calculate the Scaling.

Initially the RichTextBox should not Scale when all content fit into the ViewPort. As soon as there is a need to enable the vertical ScrollBar, I change the ScaleFactor.

This works pretty good as long as it not comes to TextWrapping (so that scaling of X and Y will not cause the Text to wrap at different positions and additionally change the height). Any ideas?

I created a small demo to make things a little bit more clearer:

<Window x:Class="WpfApplication1.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Window.Resources>
    <ScaleTransform x:Key="ScaleTransform" ScaleY="{Binding ScaleFactor}"
                                           ScaleX="{Binding ScaleFactor}"/>
</Window.Resources>
<Grid>
    <RichTextBox AcceptsTab="True" 
                 Background="Transparent" 
                 BorderBrush="Transparent" 
                 VerticalScrollBarVisibility="Auto"
                 HorizontalScrollBarVisibility="Disabled"
                 HorizontalAlignment="Stretch" 
                 VerticalAlignment="Stretch">
        <RichTextBox.Template>
            <ControlTemplate TargetType="{x:Type TextBoxBase}">
                <Border CornerRadius="2" 
                        Background="{TemplateBinding Background}" 
                        BorderThickness="{TemplateBinding BorderThickness}" 
                        BorderBrush="{TemplateBinding BorderBrush}">
                    <ScrollViewer ScrollChanged="ScrollViewer_ScrollChanged">
                        <AdornerDecorator x:Name="PART_ContentHost" Focusable="False"
                                          LayoutTransform="{StaticResource ScaleTransform}"/>
                    </ScrollViewer>
                </Border>
            </ControlTemplate>
        </RichTextBox.Template>
    </RichTextBox>
</Grid>

And the code-behind:

public partial class Window1 : Window, INotifyPropertyChanged
{
    public Window1()
    {
        InitializeComponent();
        this.DataContext = this;
    }

    private double scaleFactor = 1.0;
    public double ScaleFactor
    {
        get { return scaleFactor; }
        set
        {
            scaleFactor = value;
            OnPropertyChanged("ScaleFactor");
        }
    }

    private void ScrollViewer_ScrollChanged(object sender, ScrollChangedEventArgs e)
    {
        if (e.ExtentHeightChange == 0)
            return;

        if (e.Source.GetType() == typeof(RichTextBox))
            return;

        var missingHeight = e.ExtentHeightChange;
        var heightWithoutScaling = e.ExtentHeight / ScaleFactor;

        if (e.ViewportHeight <= heightWithoutScaling)
        {
            ScaleFactor = ((e.ViewportHeight / heightWithoutScaling));
        }

    }

    #region INotifyPropertyChanged Members

    /// <summary>
    /// Raised when a property on this object has a new value
    /// </summary>
    public event PropertyChangedEventHandler PropertyChanged;

    /// <summary>
    /// Raises this object's PropertyChanged event.
    /// </summary>
    /// <param name="propertyName">The property that has a new value.</param>
    protected virtual void OnPropertyChanged(string propertyName)
    {
        PropertyChangedEventHandler handler = this.PropertyChanged;
        if (handler != null)
        {
            var e = new PropertyChangedEventArgs(propertyName);
            handler(this, e);
        }
    }

    #endregion