private Rect GetMaxDimensions(double aspectRatio)
{
double innerRadius = arm.GetMinReach();
double outerRadius = arm.GetMaxReach();
double sqrInnerRadius = innerRadius * innerRadius;
double sqrOuterRadius = outerRadius * outerRadius;
double sqrAspectRatio = aspectRatio * aspectRatio;
double sqrt = Math.Sqrt(outerRadius * outerRadius - (sqrAspectRatio * (sqrInnerRadius - sqrOuterRadius)) / 4.0);
double height = (2.0 * (-2.0 * innerRadius + 2.0 * sqrt)) / (4.0 + sqrAspectRatio);
double width = height * aspectRatio;
// Move the rectangle half the width to the left
double x = -width / 2.0;
// Move the the inner radius down so it is within the boundaries of the arm
double y = innerRadius;
return(new Rect(x, y, width, height));
}