What would be a projection of a finite right cone with base radius $R$ and height $H$ which is tilted about an angle $\theta$ with the vertical on a vertical.
I have an intuition that it may look like combination of a triangle and a semi ellipse, but I can't prove it. Also it is only applicable to some extent of tilt. I wish to know the detailed analysis of the shape.
Any help is appreciated.
Whether the projection is parallel or central (which you should specify), the projection of the base is the intersection of an elliptic cylindre or an elliptic cone with the viewing plane, and is a conic. If the cone wholly lies behind the plane, that projection is an ellipse.
If the base is facing the observer, you see the whole ellipse. Otherwise only a part of it (a half for a parallel projection).
The apparent shape may also include two line segments from the apex, that tangent the ellipse. But not if the projection of the apex lies inside the ellipse.
You can see the projections when the original vertical axis of cone is tilted through angle (th) about y-axis as shown.
$(a=R)$ in parallel projection, but $b=R \cos(th)$ in projection onto original cone base plane or $(x,y)$ plane.
The cone generators are tangent to projected ellipse as per your intuition.
