CSCE 4230  Homework #2


     Due date:  Thursday, February 19


     1)  What size frame buffer is required to store an image with
         resolution 1280 by 800 with 32768 colors?


     2)  Assuming a display area aspect ratio of 16/10, specify the 
         pixel ratio for a system with screen resolution 1280 by 800:

           px/py = ______


     3)  Let p1 = (4,0,4), p2 = (2,-1,8), and p3 = (1,2,3).

         a)  Show that the three points define a right triangle.  Hint:
             the difference between two vertices is a vector whose
             direction coincides with that of a triangle side, and a
             pair of such vectors must be orthogonal in order for the
             triangle to be a right triangle.

         b)  Specify a vector N that is normal to the plane of p1, p2,
             and p3.  Hint:  N must be orthogonal to p2-p1, p3-p2, and
             p1-p3.

         c)  Specify the area of the triangle defined by p1, p2, and p3.

         d)  Specify the condition that p = (x,y,z) lies in the plane
             of p1, p2, and p3 (as an equation in x, y, and z).  Recall
             that the equation of a plane has the form Ax + By + Cz + D = 0.


     4)  Compute the following products:


             [  C  S  0 ]     [ x ]
         a)  [ -S  C  0 ]  X  [ y ]  =
             [  0  0  1 ]     [ 1 ]

             [ S_1  0   T_1 ]     [ x ]
         b)  [  0  S_2  T_2 ]  X  [ y ]  =
             [  0   0    1  ]     [ 1 ]

             [ S_1  0   0 ]     [ 1  0  T_1 ]
         c)  [  0  S_2  0 ]  X  [ 0  1  T_2 ] =
             [  0   0   1 ]     [ 0  0   1  ]

             [ 1  0  T_1 ]     [ S_1  0   0 ]
         d)  [ 0  1  T_2 ]  X  [  0  S_2  0 ] =
             [ 0  0   1  ]     [  0   0   1 ]


     5)  Evaluate the following determinant:

         | A_1  A_2  A_3 |
         | B_1  B_2  B_3 |  =
         | C_1  C_2  C_3 |