The following questions are a compilation of exercises from the books this class is based upon.
You must support all your answers with graphical explanations and sketches!
Consider a satellite orbiting the earth. Its position above the earth is specified in polar coorindates. Find a model-view matrix that keeps the viewer looking at the earth. Such a matrix could be used to show the earth as it rotates. (2 points)
Can we obtain an isometric of a cube by a single rotation about a suitably chosen axis? Explain your answer. (2 points)
Show that perspective projection preserves lines. (2 points)
Define one or more APIs to specify oblique projections. You do not need to write the function; just decide which parameters the user must specify (and show what they represent). (2 points)
As geometric data passes through the viewing pipeline, a sequence of rotations, translations, scaling, and a projection transformation are applied to the vectors that determine the cosine terms in the Phong reflection model.
a) Which, if any, of these operations preserve(s) the angles between the vectors? (1 point)
b) Estimate the amount of extra calculations required for Phong shading as compared to Gouraud shading, taking into account the previously mentioned transformations. (1 point)