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August 30, 2021 06:17
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| import taichi as ti | |
| # import math | |
| ti.init(ti.gpu) | |
| # global control | |
| paused = ti.field(ti.i32, ()) | |
| # gravitational constant 6.67408e-11, using 1 for simplicity | |
| G = 1 | |
| # number of planets | |
| N = 8 | |
| # unit mass | |
| m = 100 | |
| # galaxy size | |
| galaxy_size = 0.2 | |
| # planet radius (for rendering) | |
| planet_radius = 10 | |
| # init vel | |
| init_vel = 40 | |
| # time-step size | |
| h = 1e-6 | |
| # substepping | |
| substepping = 10 | |
| PI = 3.141592653 | |
| # center of the screen | |
| center = ti.Vector.field(2, ti.f32, ()) | |
| # pos, vel and force of the planets | |
| # Nx2 vectors | |
| pos = ti.Vector.field(2, ti.f32, N) | |
| vel = ti.Vector.field(2, ti.f32, N) | |
| force = ti.Vector.field(2, ti.f32, N) | |
| @ti.kernel | |
| def initialize(): | |
| center[None]=[0.5,0.5] | |
| for i in range(N): | |
| theta = ti.random() * 4 * PI | |
| r = (ti.sqrt(ti.random()) * 0.7 + 0.3) * galaxy_size | |
| offset = r * ti.Vector([ti.cos(theta), ti.sin(theta)]) | |
| pos[i] = center[None]+offset | |
| vel[i] = [-offset.y, offset.x] | |
| vel[i] *= init_vel | |
| @ti.kernel | |
| def compute_force(): | |
| # clear force | |
| for i in range(N): | |
| force[i] = [0.0, 0.0] | |
| # compute gravitational force | |
| for i in range(N): | |
| p = pos[i] | |
| for j in range(N): | |
| #if i > j: # bad memory footprint and load balance | |
| # diff = p-pos[j] | |
| # r = diff.norm(1e-5) | |
| # # gravitational force -(GMm / r^2) * (diff/r) for i | |
| # f = -G * m * m * (1.0/r)**3 * diff | |
| # # assign to each particle | |
| # force[i] += f | |
| # force[j] += -f | |
| if i != j: # double the computation for a better memory footprint and load balance | |
| diff = p-pos[j] | |
| r = diff.norm(1e-5) | |
| # gravitational force -(GMm / r^2) * (diff/r) for i | |
| f = -G * m * m * (1.0/r)**3 * diff | |
| # assign to each particle | |
| force[i] += f | |
| @ti.kernel | |
| def update(): | |
| dt = h/substepping | |
| for i in range(N): | |
| #symplectic euler | |
| vel[i] += dt*force[i]/m | |
| pos[i] += dt*vel[i] | |
| gui = ti.GUI('N-body problem', (512, 512)) | |
| initialize() | |
| while gui.running: | |
| for i in range(substepping): | |
| compute_force() | |
| update() | |
| gui.clear(0x112F41) | |
| gui.circles(pos.to_numpy(), color=0xffffff, radius=planet_radius) | |
| gui.show() |
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