5. Although perspective distorts rectangles to asymmetric trapezoids in general, the properties of circles are such that they always project to an ellipse of some orientation, with the centre of the resulting ellipse generally displaced forward from the centre of the projected circle (Fig. 6). Geometrically, ellipses may be drawn by attaching a string to the foci and drawing a perimeter by keeping the string fully stretched. However, there is no known geometric method for placing the foci for a required ellipse in the perspective construction.

Fig. 6. Perspective projection of a circle to an ellipse. A: the circle inscribed on the face of a cube. B: the simple ellipse, with its centre marked. C: the projection when the cube is on the visual axis forms an ellipse whose centre (and vertical axis) is displaced from that of the projected circle. D: for a circle above the visual axis, the major axis of the ellipse is rotated from the vertical, making its construction a challenging geometric problem with no known geometric solution.