graphics/gravity_sim.cpp
/*******************************************************
* Copyright (c) 2014, ArrayFire
* All rights reserved.
*
* This file is distributed under 3-clause BSD license.
* The complete license agreement can be obtained at:
* http://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#include <arrayfire.h>
#include <iostream>
#include <cstdio>
#include <vector>
#include "gravity_sim_init.h"
using namespace af;
using namespace std;
static const bool is3D = true; const static int total_particles = 4000;
static const int reset = 3000;
static const float min_dist = 3;
static const int width = 768, height = 768, depth = 768;
static const float eps = 10.f;
static const int gravity_constant = 20000;
float mass_range = 0;
float min_mass = 0;
void initial_conditions_rand(af::array &mass, vector<af::array> &pos, vector<af::array> &vels, vector<af::array> &forces) {
for(int i=0; i< (int)pos.size(); ++i) {
pos[i] = af::randn(total_particles) * width + width;
vels[i] = 0 * af::randu(total_particles) - 0.5;
forces[i] = af::constant(0, total_particles);
}
mass = af::constant(gravity_constant, total_particles);
}
void initial_conditions_galaxy(af::array &mass, vector<af::array> &pos, vector<af::array> &vels, vector<af::array> &forces) {
af::array initial_cond_consts(af::dim4(7, total_particles), hbd);
initial_cond_consts = initial_cond_consts. T();
for(int i=0; i< (int)pos.size(); ++i) {
pos[i] = af::randn(total_particles) * width + width;
vels[i] = 0 * (af::randu(total_particles) - 0.5);
forces[i] = af::constant(0, total_particles);
}
mass = initial_cond_consts(span, 0);
pos[0] = (initial_cond_consts(span, 1)/32 + 0.6) * width;
pos[1] = (initial_cond_consts(span, 2)/32 + 0.3) * height;
pos[2] = (initial_cond_consts(span, 3)/32 + 0.5) * depth;
vels[0] = (initial_cond_consts(span, 4)/32) * width;
vels[1] = (initial_cond_consts(span, 5)/32) * height;
vels[2] = (initial_cond_consts(span, 6)/32) * depth;
pos[0](seq(0, pos[0].dims(0)-1, 2)) -= 0.4 * width;
pos[1](seq(0, pos[0].dims(0)-1, 2)) += 0.4 * height;
vels[0](seq(0, pos[0].dims(0)-1, 2)) += 4;
min_mass = min<float>(mass);
mass_range = max<float>(mass) - min<float>(mass);
}
af::array ids_from_pos(vector<af::array> &pos) {
return (pos[0].as(u32) * height) + pos[1].as(u32);
}
af::array ids_from_3D(vector<af::array> &pos, float Rx, float Ry, float Rz) {
af::array x0 = (pos[0] - width/2);
af::array y0 = (pos[1] - height/2) * cos(Rx) + (pos[2] - depth/2) * sin(Rx);
af::array z0 = (pos[2] - depth/2) * cos(Rx) - (pos[2] - depth/2) * sin(Rx);
af::array x1 = x0*cos(Ry) - z0*sin(Ry);
af::array y1 = y0;
af::array x2 = x1*cos(Rz) + y1*sin(Rz);
af::array y2 = y1*cos(Rz) - x1*sin(Rz);
x2 += width/2;
y2 += height/2;
return (x2.as(u32) * height) + y2.as(u32);
}
af::array ids_from_3D(vector<af::array> &pos, float Rx, float Ry, float Rz, af::array filter) {
af::array x0 = (pos[0](filter) - width/2);
af::array y0 = (pos[1](filter) - height/2) * cos(Rx) + (pos[2](filter) - depth/2) * sin(Rx);
af::array z0 = (pos[2](filter) - depth/2) * cos(Rx) - (pos[2](filter) - depth/2) * sin(Rx);
af::array x1 = x0*cos(Ry) - z0*sin(Ry);
af::array y1 = y0;
af::array x2 = x1*cos(Rz) + y1*sin(Rz);
af::array y2 = y1*cos(Rz) - x1*sin(Rz);
x2 += width/2;
y2 += height/2;
return (x2.as(u32) * height) + y2.as(u32);
}
void simulate(af::array &mass, vector<af::array> &pos, vector<af::array> &vels, vector<af::array> &forces, float dt) {
for(int i=0; i< (int)pos.size(); ++i) {
pos[i] += vels[i] * dt;
pos[i].eval();
}
//calculate forces to each particle
vector<af::array> diff(pos.size());
af::array dist = af::constant(0, pos[0].dims(0),pos[0].dims(0));
for(int i=0; i< (int)pos.size(); ++i) {
diff[i] = tile(pos[i], 1, pos[i].dims(0)) - transpose(tile(pos[i], 1, pos[i].dims(0)));
dist += (diff[i]*diff[i]);
}
dist = sqrt(dist);
dist = af::max(min_dist, dist);
dist *= dist * dist;
for(int i=0; i< (int)pos.size(); ++i) {
//calculate force vectors
forces[i] = diff[i] / dist;
forces[i].eval();
//af::array idx = af::where(af::isNaN(forces[i]));
//if(idx.elements() > 0)
// forces[i](idx) = 0;
//forces[i] = sum(forces[i]).T();
forces[i] = matmul(forces[i].T(), mass);
//update force scaled to time, magnitude constant
forces[i] *= (gravity_constant);
forces[i].eval();
//update velocities from forces
vels[i] += forces[i] * dt;
vels[i].eval();
//noise
//forces[i] += 0.1 * af::randn(forces[i].dims(0));
//dampening
//vels[i] *= 1 - (0.005*dt);
}
}
void collisions(vector<af::array> &pos, vector<af::array> &vels, bool is3D) {
//clamp particles inside screen border
af::array invalid_x = -2 * (pos[0] > width-1 || pos[0] < 0) + 1;
af::array invalid_y = -2 * (pos[1] > height-1 || pos[1] < 0) + 1;
//af::array invalid_x = (pos[0] < width-1 || pos[0] > 0);
//af::array invalid_y = (pos[1] < height-1 || pos[1] > 0);
vels[0]= invalid_x * vels[0] ;
vels[1]= invalid_y * vels[1] ;
af::array projected_px = min(width-1, max(0, pos[0]));
af::array projected_py = min(height - 1, max(0, pos[1]));
pos[0] = projected_px;
pos[1] = projected_py;
if(is3D){
af::array invalid_z = -2 * (pos[2] > depth-1 || pos[2] < 0) + 1;
vels[2]= invalid_z * vels[2] ;
af::array projected_pz = min(depth - 1, max(0, pos[2]));
pos[2] = projected_pz;
}
}
int main(int argc, char *argv[])
{
try {
af::info();
af::Window myWindow(width, height, "Gravity Simulation using ArrayFire");
myWindow. setColorMap(AF_COLORMAP_HEAT);
int frame_count = 0;
// Initialize the kernel array just once
const af::array draw_kernel = gaussianKernel(7, 7);
const int dims = (is3D)? 3 : 2;
vector<af::array> pos(dims);
vector<af::array> vels(dims);
vector<af::array> forces(dims);
af::array mass;
// Generate a random starting state
initial_conditions_galaxy(mass, pos, vels, forces);
af::array image = af::constant(0, width, height);
af::array ids(total_particles, u32);
af::timer timer = af::timer::start();
while(!myWindow. close()) {
float dt = af::timer::stop(timer);
timer = af::timer::start();
af::array mid = mass(span) > (min_mass + mass_range/3);
ids = (is3D)? ids_from_3D(pos, 0, 0+frame_count/150.f, 0, mid) : ids_from_pos(pos);
//ids = (is3D)? ids_from_3D(pos, 0, 0, 0, mid) : ids_from_pos(pos); //uncomment for no 3d rotation
image(ids) += 4.f;
mid = mass(span) > (min_mass + 2*mass_range/3);
ids = (is3D)? ids_from_3D(pos, 0, 0+frame_count/150.f, 0, mid) : ids_from_pos(pos);
//ids = (is3D)? ids_from_3D(pos, 0, 0, 0, mid) : ids_from_pos(pos); //uncomment for no 3d rotation
image(ids) += 4.f;
ids = (is3D)? ids_from_3D(pos, 0, 0+frame_count/150.f, 0) : ids_from_pos(pos);
//ids = (is3D)? ids_from_3D(pos, 0, 0, 0) : ids_from_pos(pos); //uncomment for no 3d rotation
image(ids) += 4.f;
image = convolve(image, draw_kernel);
myWindow. image(image);
image = af::constant(0, image. dims());
frame_count++;
// Generate a random starting state
if(frame_count % reset == 0) {
initial_conditions_galaxy(mass, pos, vels, forces);
}
//simulate
simulate(mass, pos, vels, forces, dt);
//check for collisions and adjust positions/velocities accordingly
collisions(pos, vels, is3D);
}
} catch (af::exception& e) {
fprintf(stderr, "%s\n", e. what());
throw;
}
return 0;
}