15-462 Programming Lab 4: Physics Simulation

Due Tuesday, December 6th, 11:59 PM

Overview

In this assignment, you will be implementing a simple physics simulation. You will implement physically-correct motion of simple geometrical objects in an environment. For this, you will need to know how to handle physical object properties that cannot be directly observed, such as mass and momentum. Your code will be required to model sphere/plane and sphere/sphere collisions, but you can do more if you wish. As with the previous starter codes, the code you are provided with will extend the ray tracer starter code so that you will be able to combine any part(s) of the previous three labs if you wish.

Briefing of Tasks

• Applying Forces - First, you will need to implement basic forces acting on your objects, such as gravity and initial velocity, as your world evolves in time. In order to do this, you will need to update your world by a realistic timestep. This will make your objects look like they have some mass.
• Collision Detection - Finding a collision in a physics world will be similar in some ways to your ray tracer implementation. You will need to use mathematical representation of your objects to solve for intersections. Keep efficiency in mind since your simulation is supposed to run in real time.
• Collision Response - Your objects need to react realistically when they hit each other. Depending on the contact points between objects, you will determine the exchange of momentum between them.
• Test! - The final step will be to make sure that there are no bugs in your simulation that break it severely. Some minor errors should be expected as your simulation updates are at descrete timesteps and if some objects are moving too quickly or the timestep is too large, your object may fail to collide. There are ways to compensate for this but are not required.

Basic Physics

Rigid body movements rely on mainly on a few formulas

Force: F = ma

Momentum: p = mv

Conservation of Momentum: p1 = -p2 (remember that this is per-axis)

Implementation

Starter Code

The starter code [1] has been set up to be able to built in both Visual Studio 2005 and with the Makefile in Linux. As mentioned before, the starter code should be familiar to you from the previous projects, and so objects are loaded in the same way that they are in the ray tracer with modifications to load in other attributes such as mass and initial velocity.

A good starting point will be to understand how the various objects work in the normal renderer. The Scene loads a Gravity Vector and each SceneObject loads with a mass, initialVelocity, and initialTransform. The two parts you will need to update on the Scene will be the Matrix currentTransform and Vector currentVelocity in the SceneObject classes. The currentVelocity variable is there only as a placeholder for you to use to be able to update the objects' transformation matrix. As a side note, a mass of 0.0 or less should mean infinite-mass or one that is not affected by forces such as gravity.

The transformation matrices are ordered such that the member variables are accessed as _RowColumn. e.g. matrix._14 gives the element at row-1, column-4. There are a couple of additional functions that have been added in Utils.h for your convenience also: BuildTranslation, BuildRotationX, BuildRotationY, BuildRotationZ, BuildScale, and finally BuildTransform which combines all together.

Grading Criteria

Your program must:

• (20%) have objects move realistically with forces and updates
• (20%) detect Sphere-Sphere Collision
• (20%) detect Sphere-Plane Collision
• (25%) handle Collision Response
• (10%) be reasonably commented and written in an understandable manner-- we will read your code.
• (5%) be summitted along with at least 1 good test scene file to demonstrate your simulation features. You must also submit a movie of 99 frames maximum in JPEG named (00.jpg - 99.jpg). Put XML scene files and corresponding .3ds or .obj files in a sub-directory called scenes and JPEG files in a sub-directory called images.
• (required) Be submitted along with a readme file documenting your program's features and describing the approaches you took to each of the open-ended problems we posed here. This is especially crucial if you have done something spectacular for which you wish to receive extra credit!
• (required) Be submitted to your turnin directory as documented in the submission section.

Submission

Please submit your project to /afs/andrew/scs/cs/15-462/turnin/your_andrew_id/. Copy your modified src directory into that directory. When we run "make" in the src directory it should compile your program successfully. Also within asst4, make a sub-directory called scenes and images, and place your representative XML scene files and JPEG snapshots into the respectively sub-directory.

Tips

• Start this assignment as soon as you can. This project may not be as tough and long as the ray tracer but can still take a long time to get right.
• Review the ray tracer write-up to understand the scene format and getting a general idea of how things should work.
• Again, think before you hack! There are several cases that need consideration. To give one, the conservation of momentum may end up giving you extra velocity each time and might need damping.
• Leave time to work on your representative screenshots. You'll want to show off your work! Especially if you integrate it with the ray tracer.

Extras

Here are some suggestions for extra credit ideas:

• Angular Momentum - implement angular momentum.
• Warped-Sphere - allow ellipsoidal sphere to work.
• Convex Hulls - allow your simulation to handle more than just round-objects.
• Spatial Partitioning: put your model objects in an octtree, BSP tree, or spatial hash data structure to accelerate your collision detection.
• Ray-traced Simulation - (WARNING: THIS MAY TAKE A WHILE TO RENDER!)

Please note that the amount of extra credit awarded will not exceed 10% of this assignment's total value.

Links