Please name all the possible shapes produced in an image under perspective of:

$($a$).$ A scene containing an infinite slender rod with circular cross section.

$($b$).$ A scene containing one disk, you may assume the disk has a non$-$zero radius, and the disk is very thin.

$(2).$ Suppose you have a camera $($unit aspect ratio, optical center at $(0,0),$ no skew$)$ that takes a picture here on earth. Now suppose we have a new world where everything is half $(1/2)$ as large, including distances

between objects. Assuming perspective projection, compare the two images and provide your explanation as to how does the two images differ from each other with proper reasoning.