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diff --git a/design.txt b/design.txt deleted file mode 100644 index 9d1495a..0000000 --- a/design.txt +++ /dev/null @@ -1,84 +0,0 @@ -= Multithreaded 2D Bouncing Balls Simulation = - -The goal is to simulate and render multiple balls bouncing in a rectangular -container (the window). The number of balls is confurable by a command line -argument at runtime. - -# Collisions - -When a collision occurs, there are two steps: 1) detect the collision, and 2) -respond to the collision. - -1) Collision detection - -Collision between two balls is detected by comparing the distance between -them to the sum of their radii. Calculating the distance involves a square -root operation, but the compution can be simplified by comparing the square -of both sides of the equation. I.e. rather than checking - -sqrt((x2-x1)^2 + (y2-y1)^2) < (r1+r2) - -the formula is simplified using the identity - -(a < b) <=> (a^2 < b^2) - -to avoid the square root: - -(x2-x1)^2 + (y2-y1) < (r1+r2)^2 - - -2) Collision response - -Once a collision is detected, the reaction of the ball should be calculated. -Each ball has a position, a velocity, a radius and a mass. The first step is -to correct the position so that the two balls don't overlap. This is done -by first finding the vector from ball 2 to ball 1, and then normalizing it. -Then multiply the normal vector by the sum of the radii of the two balls---this -will be the final distance between the two. Calculate the final position -of ball 1 as the endpoint of the aforementioned vector beginning at ball -2's position. - -Once the corrected position of the ball is known, then next step is to -calculate its velocity after the collision. Collisions are assumed to -be perfectly elastic: kinetic energy is conserved. The final velocity is -calculated by a sequence of vector operations outlined at the following link: - -https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional_collision_with_two_moving_objects - -The "angle-free representation" is used. - -# Implementation - -The simulation is implemented using the Plan 9 thread and graphics libraries: - -https://man.cat-v.org/plan_9/2/thread -https://man.cat-v.org/plan_9/2/graphics - -Each ball is simulated in its own computation thread. With each frame, -the thread updates the ball's velocity and position, checks for collisions -with other balls and the edges of the screen, and redraws the ball on the -screen. Threads communicate the positions, velocities, etc. of their ball -via "Channels" provided by the thread library. "A Channel is a buffered or -unbuffered queue for fixed-size messages." In this case, buffered channels -are used to send Ball data structures between threads. Before calculating -collisions, each ball thread broadcasts its Ball to other threads. Then, for -each ball, it receives a Ball from the channel it shares with another thread -and checks for a collision between its own ball and the ball it just received. - -Not only does this provide race-free communication, it also enforces a -"soft synchronization." If one thread runs faster than the others, it will -be forced to synchronize with the others when either its outgoing channel -fills up or its incoming channel runs dry. - -There is also a frame-timing mechanism that keeps the whole simulation -running at a steady pace. This is implemented as a "frametick" thread that -broadcasts "tick" messages to all computation threads at a fixed interval -(approximately every 16666667 ns.) Each thread waits for this message before -redrawing its ball on the screen. - -There is a single control thread that initializes all of the necessary data -structures, starts the computation threads, and listens for system events. - -The control thread creates the specified number of balls as well as the -n*(n-1) channels used to communicate between the worker threads. It then -enters a loop waiting for window resize and keyboard input events. |