For problems $($A$)$ through $($C$),$ please prepare your solution in a PDF file. You can either type and export to a PDF$,$ or hand write and scan$/$photograph and convert to

PDF$.$ For problem $($D$),$ please develop a WebGL project. We will need your complete program along with a demo of it$.$

$($A$)$ In computer graphics, objects such as spheres are usually approximated by simpler objects constructed from flat polygons $($polyhedra$).$ Using lines of

longitude and latitude, define a set of simple polygons that approximate a sphere centered at the origin. Can you use only quadrilaterals or only triangles?

$($B$)$ Consider the perspective views of the cube shown in figure below. The one on the left is called a one$-$point perspective because parallel lines in one direction

of the cube$-$along the sides of the top$-$converge to a vanishing point in the image. In contrast, the image on the right is a two$-$point perspective. Characterize

the particular relationship between the viewer, or a simple camera, and the cube that determines why one is a two$-$point perspective and the other a one$-$point

perspective.

$($C$)$ The memory in a framebuffer must be fast enough to allow the display to be refreshed at a rate sufficiently high to avoid flicker. A typical workstation display

can have a resolution of $12801024$ pixels. If it is refreshed $72$ times per second, how fast must the memory be$?$ That is$,$ how much time can we take to read

one pixel from memory? What is this number for a $640480$ display that operates at $60$ Hz but is interlaced?

$($D$)$ Write a WebGL $2\mathrm{.}0$ application that will display three different $2$D shapes, one at a time. A left mouse click will toggle among the shapes.

The initial canvas will display the first shape. A left mouse click will cause the second shape to be displayed, another left mouse click will result in the third shape

to be displayed, and finally another left click will display the first shape. So$,$ every time there is a left mouse click, the next shape will be displayed.