Why does a circle project its shadow as an upside down heart shape onto a corner instead of as an ellipse?

Question

I was walking by a street corner and saw the attached image of a disc and its shadow. I was somewhat surprised to see an upside down heart shape instead of an ellipse projected onto the wall corner as the disc's shadow. disc shadow projected onto 2 planes How can one predict if a shadow of a disc onto two planes will be primarily convex or include concave elements?

Answer 1

What the sun sees of the disk is an ellipse. Hence, the shadowed area is the intersection of an elliptic cylinder with a dihedron. The two half-planes intersect the cylindre along two different ellipses, which meet at the common edge.

Answer 2

There are two walls with some $ 20^{\circ}$ turn about a common discontinuous vertical edge AD.

The shadow of ellipse major axis makes different angles to the vertical due to inclination of sun's rays.

It should be noted that the wall edge, vertical diameter of disc and the sun are in the same plane.

From the boundary of two semicircles in the projection we have two different tilted ellipse intersections as shadows cast through B and E on either wall around the discontinuity edge.

You can choose coloring to get an upright heart too :)