Precept 6: On assignment 3

Some stuff mentioned during precept:

• instead of writing a function which "draws a circle with a specific center and a specific radius", you may want to write a function which "draws a unit circle at the origin transformed by some matrix". This approach is more general, and will help you in the remainder of the assignment
• you're free to use an existing matrix/vector library, as long as you mention in your README where you got it from
• don't overdo it on the user I/O: there should just be a mechanism to put "shapes of generation 1" on the screen, with a certain velocity and direction. Also it should be possible to resize the window, i.e. to make the area the shapes bounce in larger (or smaller)
• a generation change after a collision may be up or down, but make it so that the trend is upwards. You can add a feature where a shape disappears when it reaches a certain generation. Feel free to implement your own additional rules here
• The formulas for (v` is the speed after a collision):
  • conservation of momentum:
    m_1 * v_1 + m_2 * v_2 = m_1 * v'_1 + m_2 * v'_2
  • conservation of kinetic energy:
    0.5 * m_1 * v_1^2 + 0.5 * m_2 * v_2^2 =
0.5 * m_1 * v'_1^2 + 0.5 * m_2 * v'_2^2
  It is easiest to use the formulas separately for the x- and y-direction. As has been said, if you want to keep it simple, you can assume all masses are the same, so all the "m's" cancel out in the above formulas