$1$ Exercises

$(10$ points$)$ Consider three different raster systems with resolutions of $800$ by $600,1280$

by $960,$ and $1680$ by $1050.$ What size frame buffer $($in bytes$)$ is needed for each of these

systems to store $16$ bits per pixel? How much storage is required for each system if $32$

bits per pixel are to be stored?

$(5$ points$)$ Suppose an RGB raster system is to be designed using an $8$ inch by $10$ inch

screen with a resolution of $100$ pixels per inch in each direction. If we want to store

$6$ bits per pixel in the frame buffer, how much storage $($in bytes$)$ do we need for the

frame buffer?

$(10$ points$)$ List the statements needed to

set up an OpenGL display window whose lower$-$left corner is at pixel position $(75,$

and has a window width of $200$ pixels and a height of $150$ pixels.

and draw a rectangle at the middle of display window with the aspect ratio equal

to the aspect ratio of the display window. The area of rectangle must be a quarter

of the display window area.

$(5$ points$)$ Explain what is meant by the term "OpenGL display callback function".

$(10$ points$)$ Split a convex octagon given by the list of vertices $V_1,V_2,V_3,V_4,V_5,V_6,$

$V_7,V_8$ into a set of triangles and give the vertices that make up each triangle.

$(10$ points$)$ First prove that the pentagon with the following vertices is concave. Then,

convert it into a set of convex polygons:

$A_1=(2,2),A_2=(5,3),A_3=(4,7),A_4=(-1,6),A_5=(1,5)$