Homework #2
OpenGL, Lighting, Shading, and Viewing
Question #1 - Basic OpenGL: (25 points)
(a) (5 pts) Consider that you have a function listOfVertices() that generates a list of
properly formatted vertices in OpenGL. Write the OpenGL code needed to draw a red
polygon composed of these vertices.
(b) (10 pts) Consider that you have a function drawShape() that draws an arbitrary
polygon in OpenGL centered at (0,0). Write the OpenGL code needed to scale the
shape by a factor of 2 in x and a factor of 3 in y, then rotate by 45º in the xy-plane,
then translate by 5 in x and -1 in y.
(c) (7 pts) Write the OpenGL commands needed to choose the projection matrix as the
active matrix, reset it to the identify matrix, then set it to a perspective projection with
a 20 degree field of view, an aspect ratio of 1024/768, a near plane at 0.1 and a far
plane at 10.
(d) (3 pts) What is the other OpenGL command you could use to define a perspective
projection matrix?
Question #2 - Lighting and Shading: (20 points)
Assume you are viewing the point at (0, 0, 1) on the surface of a radius-1 sphere centered
at the origin. There is a viewer at (2, 2, 2) and a point light at (-3, 3, 3). Compute the n, l, v, and r
vectors (normalized, please) required for the Phong lighting equations.
Question #3 - Viewing: (15 points)
The equation on slide 39 of the September 27 lecture projects space onto a single plane.
Starting from this equation, derive the equation for projecting space into a volume defined by 2
planes, znear and zfar. How x and y are projected is unchanged, but z should now map to a range,
not to a single value. (i.e. znear should map to 1, and zfar should map to -1, and the values in
between should decrease monotonically with distance)
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