.. title: CG Homework 7, due Thurs 2019-11-07 2359
.. slug: homework07
.. date: 2019-10-31
.. tags: homework
.. category: 
.. link: 
.. description: 
.. type: text
.. has_math: true

   

#. *(4 pts)*  Use the homogeneous matrix to project homogeneous points onto the plane 2x+3y+4z=5, with COP at the origin. What does the point (1,2,4,5) project to? Give the answer as a Cartesian point.

#. *(4 pts)* Repeat the previous question with the COP changed to (1,1,1,1). 

#. *(6 pts)* Do exercise 5.6 on page 272 of the text,

#. *(6 pts)* *This question will take some thinking).*

   Imagine that you have an infinitely large room illuminated
   by one infinitely long row of point lights.  This figure
   shows a side view of the room.

   The lights are **h** above the floor and are 1
   meter from each other.  Assume that the ceiling above the
   lights is black and that no light reflects off of anything.

   An object at distance **d** from a light gets illuminated
   with a brightness :math:`\frac{1}{d^2}`.

   Each point on the floor is illuminated by all the lights,
   but more brightly by the closer lights.  

   A point **p** directly below a light will be a little
   brighter than a point **q** halfway between two such
   points.  That is the problem --- we want the floor (at least
   the part directly below the line of lights) to be evenly
   lit, at least within 1%.

   However, the higher the line of lights, the more evenly the
   floor will be lit.

   Your question is to tell us what is the minimum value for
   **h** so that the line of the floor below the line of
   lights is evenly lit within 10%.

   .. image:: ../files/hw-lights.png

   E.g., the brightness at **p** is

   :math:`\sum_{i=-\infty}^{\infty} \;\; \frac{1}{\left(h^2+i^2\right)}`


*(Total: 20 points.)*