Ellipse construction in perspective
Hi, lately I had some doubts about the construction of ellipses in cylinders. In the art books dealing with perspective (e.g. Scott Robertson - How to draw, p.72) it is said that the minor axes of the ellipses will vanish to the same vanishing point as the middle axis of the cylinder and its sides. I was not fully convinced and therefore did some research on the topic. I found a math forum where people were discussing just that topic. The mathematicians seem to be of the opinion that the minor axes do have a different vanishing point than the sides of the cylinder without actually giving a proof. Check the thread here: https://math.stackexchange.com/questions/3823048/is-the-line-created-by-the-minor-axis-of-an-ellipse-concurrent-to-the-lines-runn Does anybody have an actual formal proof for the theory of the minor axes sharing the vanishing point with the sides of the cylinder? I did some drawings and tried to be accurate with the construction. In my drawings the vanishing points of the minor axes and the sides of the cylinder aligned. My drawing process was first constructing a cube in perspective, then transferring the cube and the vanishing points to another sheet of paper and constructing the ellipses inside of the squares in perspective. After inserting the minor axes I checked whether they were in the correct spot or not with a small mirror.
The rule mentioned by Robertson and others is a rule of thumb. It is not mathematically correct. However, it is the only practical guideline known to mankind, so let's stick to it...