将偏移应用于缩放以保留特定点

我目前正在努力解决WPF画布和缩放问题。我希望能够围绕特定的点缩放画布（缩放后给定的点应该保持在相同的屏幕位置）。

缩放是通过简单的ScaleTransform完成的。平移存储在Point对象中，并应用于画布中的所有形状。这意味着在应用缩放后，我必须偏移所有形状（修改平移点）。为了简单起见，这里有一个简化的代码

class CanvasManager
{
    Point mTranslation; // holds the translation
    Canvas mCanvas;
    ScaleTransform mCanvasScale; // linked to mCanvas
    // Constructor omitted
    public void Scale(double factor, Point pt)
    {
        // retrieve the previous scaling factor
        double oldfactor = mCanvasScale.ScaleX;
        //apply the new factor
        mCanvasScale.ScaleX = factor;
        mCanvasScale.ScaleY = factor;
        // now offset so Point pt gets back at its original position
        mTranslation.X += ???;
        mTranslation.Y += ???;
    }
}

点pt来自相对于画布测量的鼠标事件，包括缩放。（当"比例"为2时，200的相对屏幕x坐标会给我400作为pt的值）
使用以下代码片段应用Transform（Scale）：

mCanvasScale = new ScaleTransform();
mCanvas.LayoutTransform = mCanvasScale;

如何获得mTranslation的正确偏移量？

问候
Dennis

class CanvasManager
{
    Point mTranslation; // holds the translation
    Canvas mCanvas;
    ScaleTransform mCanvasScale; // linked to mCanvas
    // Constructor omitted
    public void Scale(double factor, Point pt)
    {
        // retrieve the previous scaling factor
        double oldfactor = mCanvasScale.ScaleX;
        //apply the new factor
        mCanvasScale.ScaleX = factor;
        mCanvasScale.ScaleY = factor;
        // now offset so Point pt gets back at its original position
        mTranslation.X -= ( (pt.X * factor) - (pt.X * oldfactor) ) / factor;
        mTranslation.Y -= ( (pt.Y * factor) - (pt.Y * oldfactor) ) / factor;
    }
}