Alex "Akiva" Bamberger
Computer Vision HW 4

For this project, the utility class util.c was written to handle matrix operations.

We assumed the light source had direction equivalent to the normal of the brightest point. This was because the dot product <n,s> is greatest when the angle between the normal and source vectors is 0 (e.g. cos (theta) = 1).

Gradients were calculated using the following equation:
(x0-x)^2 + (y0-y)^2 + z^2 = r^2
z = sqrt(r^2 - (x0-x)^2 + (y0-y)^2)
dz/dx = -(x0-x)/sqrt(r^2 - (x0-x)^2 + (y0-y)^2)
dz/dy = -(y0-y)/sqrt(r^2 - (x0-x)^2 + (y0-y)^2)

This was useful for finding (p,q) values for each of the points on the surface.

The output of the depth map appeared to improve with more seed points, but with fewer points, noise appeared more often than desired.