.. title: CG Homework 3, due Thurs 2019-09-26 2359
.. slug: homework03
.. date: 2019-09-16
.. tags: homework
.. category: 
.. link: 
.. description: 
.. type: text


Homework 3, due Thu 2017-09-26 2359
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#. *(10 pts)*    Part of changing from one coordinate system to another is scaling and making things fit. E.g., suppose that you had a square with lower left corner (llc) (0,0) and upper right corner (urc) (1,1). You want to scale and center it to just fit into a rectangle with llc (0,0) and urc (2,3). The square stays a square but is probably larger or smaller. Then, these equations would do it:

   |   x' = 2x
   |   y' = 2y + 1/2

   This question is to figure out how to make a rectangle from (0,0) to (2,3) fit into a square that is from (0,0) to (10,10). 

#. *(10 pts)* Consider a pinhole camera as discussed in slide 12 of ppt presentation 1_5.  Let d=2.  To where does the point (1,3,-3) project?  Use the equation on that slide.  x/z/d should be parenthesized as x/(z/d).

#. *(5)*   If your image has only 64 different colors across the whole image, how many bits per pixel do you need for the color buffer?

#. *(25)* Extend your program from last week that displays the Starship Enterprise as follows:

   #. Add 3 sliders that will rotate it around the X-axis, Y-axis, and Z-axis respectively.
   #. Do the rotations the simplest (and least efficient) way.  I.e., in your javascript program, have render rotate the matrix and resend it to the GPU.

*(Total: 50 points.)*