Barnes hut simulation dating - Barnes–Hut simulation

For this assignment, you must use a version control system such as Git or SVN and submit the log file that...

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The Barnes—Hut simulation Josh Barnes and Piet Hut is an approximation algorithm for performing an n -body simulation.

The crucial idea in speeding up the brute force n-body algorithm is to group nearby bodies and approximate them as a single body. If the group is sufficiently far away, we can approximate its gravitational effects by using its center of mass.

The center of mass of a group of bodies is the average position of a body in that group, weighted by mass. Formally, if two bodies have positions x1 , y1 and x2 , y2 , and masses m1 and m2 , then their total mass and center of mass x , y are given by:.

The Barnes-Hut algorithm is a clever scheme for grouping together bodies that are sufficiently nearby. It recursively divides the set of bodies into groups by storing them in a quad-tree. A quad-tree is similar to a binary tree, except that each node has 4 children some of which may be empty.

Each node represents a region of the two dimensional space. The topmost node represents the whole space, and its four children represent the four quadrants of the space.

As shown in the diagram, the space is recursively subdivided into quadrants until each subdivision contains 0 or 1 bodies some regions do not have bodies in all of their quadrants.

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For each pair, compute a compatibility index , which is a float between 0. For this assignment, you must use a version control system such as Git or SVN and submit the log file that describes the activity on your repository. Finally , there is an Eclipse plug-in called Subclipse that provides nice integration with SVN repositories.

Rapid SVN may also work depending on your setup. To insert a body b into the tree rooted at node x , use the following recursive procedure:. Any other issues you feel are important to your solution. It recursively divides the set of bodies into groups by storing them in a quad-tree.

The Barnes-Hut Algorithm

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Barnes hut simulation dating

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for expressing data parallelism that have a long history, dating back to APL in . as All-Pairs algorithm, is N2 while the Barnes-Hut method is an. Simulation and Modeling. Integrated...