CPSC 533D Assignment 3
Rigid Body Dynamics

What you need to do (and a recommended order)

• Compute and integrate the linear acceleration to get a moving (but not rotating) block which will simply cause to fall through the ground plane.
• Compute and integrate the angular motion of the object. The block should now spin (while still falling) due to the angular momentum assigned in the initial state. The block will spin in a fairly stable fashion with an initial spin around it's x-axis or z-axis, but will be unstable when spun around it's y-axis.
• Implement collision detection. Detect when a vertex first collides with the ground (z=0) and pause the simulation then by setting Simulation = false;
• Implement collision response. The code for this is already largely in place. You just need to compute j, the magnitude of the impulse.
• Submit a tarfile with your working code. Add a README.txt file that describes any issues you came across, any additional keybindings that you may have added, etc.

Template code

Key bindings for the template code

  space   start/pause simulation
  q       quit
  r       reset block to initial state
  >       increase eps, the coeff or restitution
  <       decrease eps, the coeff of restitution

Functions that you need to implement

• block.cpp: BLOCK::sim()
• block.cpp: BLOCK::collisionCheck()
• block.cpp: BLOCK::collisionImpulse()

Things that are useful to know

• Look at lib_math.h for the provided math functions.
• Don't expect your simulation to properly handle resting contact. This has not been discussed in class and so we will skip this.
• Use either L or omega as your state variable that drives changes in angular orientation. You will need to compute dL/dt or omega_dot to integrate these choices, respectively.
• VEC4 is a 4-vector, but it is also used liberally in the code to represent 3-vectors.
• The code should compile equally well under Linux and Windows. Let me (van@cs) know if you run into compilation problems. It relies on OpenGL and glut.
• The drawing code makes use of the current transformation matrix, TM, to draw the block. It is transposed before being passed on to OpenGL because OpenGL expects matrices in a column-major form.
• Use the functions I_inertial() and buildTM(), found in main.cpp to compute the inertia tensor in the inertial frame, and to build the object transformation matrix, respectively.
• See sim.pdf for a derivation of how to compute the collision response magnitude, j.