The assignment is due Monday at midnight, although you can turn it in without penality until Tuesday at midnight. Please note that any assignment turned in after 12 midnight on Tuesday (Dean's Date) will receive zero credit by University rule. No exceptions.
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The bodies seem to move in straight lines. Is this correct? Yes, most of the bodies do end up moving in fairly straight lines. Use planets.txt to see planets orbiting or halo.txt to see some interesting effects.
Why does the update formula use dt/2 instead of dt? That's a mistake. It should be dt, although the only effect of dt/2 will be to make the time step half as big.
How should I call the static add method in class Body? Use something like c = Body.add(a, b). It's legal and equivalent to write c = b.add(a, b), but this is bad style.
What's the quad for the initial universe? It's between (-R, -R) and (+R, +R) where R is the radius of the universe. Don't forget to check that each body is in the universe before inserting it into the tree.
I get a stack overflow error? Most likely you have an infinite recursive loop in your insert method. Also, be sure that when you insert a body that it will only end up in one of the four quads, e.g., use if-else-if-else-if-else or ensure that your contains method will only place a point in at most one of the four sub-quadrants of a quad.
How do I tell if a tree node is internal or external? Check if all four children are null. Consider writing a helper method isExternal() to check this.
How do I calculate center-of-mass of a body with an aggregate body? Just treat the aggregate body like any other body - the center of mass formula works even if one body is already the center of mass of several other bodies.
None of the particles appear on the screen. What could I be doing wrong? Make sure that your particles are not being drawn in the same color as your background. Don't forget to call Turtle.pause. Make sure that the x and y coordinates that you plot are between 0 and SIZE.
When computing the net force acting on body b, do I need a special case to prevent calculating the force between b and an aggregate body that happens to contain b? No. If an aggregate body representing a quad of size s contains b, then the distance d from b to the center of mass will be at most sqrt(2) × s. But in this case θ = s / d > 1/2, so the algorithm would need to expand the aggregate body anyway.
Who discovered the first subquadratic algorithm for N-Body simulation? Andrew Appel discovered his algorithm while at Princeton University working on his senior thesis in the Department of Physics.
When was the Barnes-Hut algorithm discovered? It was developed in 1986 by two astrophysicists at Princeton's Institute for Advanced Study.
Can the Barnes-Hut algorithm be extended to three dimensions? Yes. You can use an oct-tree instead of a quad-tree, although there are more wasted links.
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Input. Copy the files from the directory barnes-hut into your working directory. The file test2.txt is the 5 node example from the assignment.
Compilation and execution. The main function must be in the file NBody.java. We will compile your program with:
and execute withjavac NBody.java
java NBody < input.txt
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readme.txt. Use the following readme file template and answer any questions.
Submission. Submit NBody.java and all of the files needed to run your program. Don't forget to hit the "Run Script" button on the submission system to test that it compiles cleanly.
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These are purely suggestions for how you might make progress. You do not have to follow these steps.
BHTree object whose
body field is set to null.
This way, you can recursively call the BHTree methods
on this external node without getting a null pointer exception.
This will also simplify the methods insert and updateForce.
BHTree.java. Mark internal nodes with an asterisk.
If you implement null branches as suggested above, this code would look
something like this:
public String toString() {
if(NE != null) return "*" + body + "\n" + NW + NE + SW + SE;
else return " " + body + "\n";
}
For testing, modify NBody.java to print
only the first iteration of the simulation, then stop.
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