Question 5 (10 points) Consider a Lambertian circular cylinder with radius R that is viewed
under orthographic projection. Suppose that the axis of the cylinder is parallel to the x-axis
of the imaging system and the center of volume of the cylinder is at the point (0,0, zo). The
imaging system generates a 500 x 500 pixel image of the cylinder. Assume that the cylinder
is long enough so that its projection will be a horizontally oriented rectangle of size 500 × 300
pixels with a center of area at the center of the image. Assume zo < 0 and that the cylinder is
illuminated by only a single distant point light source.
a) Suppose that the unit surface normal ($n_x$, $n_y$, $n_z$) at the point projecting to the 200th row
and 400th column of the image is parallel to the direction of the incident light from the point
source. Compute ($n_x$, $n_y$, $n_z$). Simplify your answer.
b) For this direction of incident light, compute the reflectance map R(p,q). (Note: p
should be the only variables in your expression)
