There are two types of oblique projections. One assumes that the measurements in the depth direction (45° in your problem) are measured at the same scale as the horizontal and vertical directions. The second type assumes a foreshortening in the depth direction. A value of 50% is often used. This projection is called a cabinet projection.
The circle lying on the top plane is a true ellipse in the full oblique projection. It has a major and minor axis as noted in the image below. The angle of rotation for the ellipse (relative to the major axis) is 22.5°. This is the angle of the diagonal. AutoCAD's ellipse command does not have an option to construct an ellipse via conjugate axis points. These points use the base circle radius and would not require knowing major and minor axes values.
The circle representation in the cabinet projection is a bit more complex. In effect, the ellipse from the full oblique projection needs to be scale by 1/2 in a 45°direction while not scaling in the horizontal direction. One way to create this curve is by using the Control Vertex method of making a spline. I used 4 CVs to define each quadrant of the "ellipse".
The following image shows the 4 CVs used to create the 4 splines. The 2 intermediate CVs are located at the midpoints of the bounding parallelogram.
The "faking" referenced in earlier posts is a part of all drawings since they are an attempt to represent in 2D a real 3D object. The drawings are not the object but a representation. A photograph is a fake. It is not the real object.
As noted earlier, a CAD assignment to generate an oblique projection is not recommended. It is an interesting academic exercise but of little value in learning CAD.
lee.minardi
