Recall that we use the convention that \(\vec{\ell}\) points towards the infinitely distant directional light source, while a point light source is specified by the position of the source \(\vec{s}\).
Given a ray (\(\mathbf{p} + t \mathbf{d}\)) and the t at which it intersects a surface, calculate a unit vector giving the direction from the surface towards:
point light source at position \(\vec{s}\)
a directional light source with direction \(\vec{\ell}\)
A scene contains a unit sphere centered at the origin. A directional light with direction \(\vec{\ell}\) shines on the scene.
Give the coordinates of the brightest point on the sphere.
Describe (mathematically) the set of points on the sphere where the amount of light hitting the sphere goes from nonzero to zero.