/// <summary>
        /// Handles changes to the AlphaTicksPercentage property.
        /// </summary>
        private static void OnAlphaTicksPercentageChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            SprocketControl sprocket = (SprocketControl)d;
            double          oldAlphaTicksPercentage = (double)e.OldValue;
            double          newAlphaTicksPercentage = sprocket.AlphaTicksPercentage;

            sprocket.OnAlphaTicksPercentageChanged(oldAlphaTicksPercentage, newAlphaTicksPercentage);
        }