gallery_particle_physics_sim.cpp

This gallery example demonstrates an advanced real-time physics simulation using Plotly.cpp. It simulates charged particles with electromagnetic interactions, collision detection, and realistic physics behavior in a bounded environment.

Features demonstrated:

• Real-time particle physics simulation with Coulomb force calculations
• Dynamic scatter plot animation using plot updates
• Multi-threaded simulation loop with controlled frame rate
• Interactive visualization with hover information showing particle properties
• Particle size mapping to mass and color mapping to electric charge
• Boundary collision detection with energy damping
• Scientific color scale for charge visualization with colorbar

Physics concepts implemented:

• Coulomb's law for electromagnetic force calculation (F = k·q₁·q₂/r²)
• Newton's laws of motion for particle dynamics (F = ma)
• Energy damping for realistic particle behavior
• Elastic collision with boundary walls
• Multi-particle interaction system with N-body calculations

The simulation creates a visually engaging demonstration of electrodynamics with particles that attract/repel based on their charges and exhibit realistic motion patterns within a confined space.

Interactive Particle Physics

Simulation"

 
#include "plotly/plotly.hpp"
#include <algorithm>
#include <chrono>
#include <cmath>
#include <iostream>
#include <random>
#include <string>
#include <thread>
#include <vector>
 
struct Particle {
  double x, y;
  double vx, vy;
  double mass;
  double charge;
  std::string color;
};
 
auto main() -> int {
  std::cout << "Starting particle physics simulation..." << '\n';
  plotly::Figure fig;
  fig.openBrowser();
 
  // Simulation parameters
  const int numParticles = 30;
  const double dt = 0.02;
  const double boxSize = 10.0;
  const double dampening = 0.999;
  const int animationFrames = 200;
  const int frameDelay = 50; // milliseconds
 
  // Initialize random particles
  std::random_device rd;
  std::mt19937 gen(rd());
  std::uniform_real_distribution<double> posDist(-boxSize / 2, boxSize / 2);
  std::uniform_real_distribution<double> velDist(-2.0, 2.0);
  std::uniform_real_distribution<double> massDist(0.5, 2.0);
  std::uniform_real_distribution<double> chargeDist(-1.0, 1.0);
 
  std::vector<std::string> colors = {"red",    "blue", "green",   "orange",
                                     "purple", "cyan", "magenta", "yellow",
                                     "brown",  "pink"};
 
  std::vector<Particle> particles(numParticles);
  for (int i = 0; i < numParticles; i++) {
    particles[i] = {
        .x = posDist(gen),
        .y = posDist(gen), // position
        .vx = velDist(gen),
        .vy = velDist(gen),                // velocity
        .mass = massDist(gen),             // mass
        .charge = chargeDist(gen),         // charge
        .color = colors[i % colors.size()] // color
    };
  }
 
  // Create initial particle positions
  std::vector<double> xPos, yPos, sizes, charges;
  std::vector<std::string> particleColors;
 
  for (const auto &p : particles) {
    xPos.push_back(p.x);
    yPos.push_back(p.y);
    sizes.push_back(p.mass * 20); // Scale size by mass
    charges.push_back(p.charge);
    particleColors.push_back(p.color);
  }
 
  // Create initial trace
  plotly::Object trace = {
      {"type", "scatter"},
      {"mode", "markers"},
      {"x", xPos},
      {"y", yPos},
      {"marker",
       {{"size", sizes},
        {"color", charges},
        {"colorscale", "RdBu"},
        {"showscale", true},
        {"colorbar", {{"title", "Electric Charge"}, {"titleside", "right"}}},
        {"line", {{"width", 2}, {"color", "black"}}}}},
      {"name", "Particles"},
      {"hovertemplate", "Position: (%{x:.2f}, %{y:.2f})<br>" +
                            std::string("Charge: %{marker.color:.2f}<br>") +
                            "Mass: %{marker.size:.0f}<extra></extra>"}};
 
  // Create layout
  plotly::Object layout = {
      {"title",
       {{"text", "Particle Physics Simulation<br>" +
                     std::string("<sub>Charged particles with electromagnetic "
                                 "interactions</sub>")},
        {"font", {{"size", 16}}}}},
      {"xaxis",
       {{"title", "X Position"},
        {"range", {-boxSize, boxSize}},
        {"showgrid", true},
        {"zeroline", true}}},
      {"yaxis",
       {{"title", "Y Position"},
        {"range", {-boxSize, boxSize}},
        {"showgrid", true},
        {"zeroline", true},
        {"scaleanchor", "x"}}},
      {"width", 800},
      {"height", 700},
      {"showlegend", false}};
 
  // Create initial plot
  std::vector<plotly::Object> data = {trace};
  fig.newPlot(data, layout);
 
  std::cout << "Starting animation with " << numParticles << " particles..."
            << '\n';
 
  // Physics simulation loop
  for (int frame = 0; frame < animationFrames && fig.isOpen(); frame++) {
    // Calculate forces and update particles
    for (int i = 0; i < numParticles; i++) {
      double fx = 0.0, fy = 0.0;
 
      // Calculate electromagnetic forces from other particles
      for (int j = 0; j < numParticles; j++) {
        if (i == j)
          continue;
 
        double dx = particles[j].x - particles[i].x;
        double dy = particles[j].y - particles[i].y;
        double r2 = dx * dx + dy * dy;
        double r = std::sqrt(r2);
 
        if (r > 0.1) { // Avoid division by zero
          // Coulomb force: F = k * q1 * q2 / r^2
          double forceMagnitude =
              particles[i].charge * particles[j].charge / r2;
          fx -= forceMagnitude * dx / r; // Repulsive if same charge
          fy -= forceMagnitude * dy / r;
        }
      }
 
      // Update velocity with force (F = ma, so a = F/m)
      particles[i].vx += fx / particles[i].mass * dt;
      particles[i].vy += fy / particles[i].mass * dt;
 
      // Apply dampening
      particles[i].vx *= dampening;
      particles[i].vy *= dampening;
 
      // Update position
      particles[i].x += particles[i].vx * dt;
      particles[i].y += particles[i].vy * dt;
 
      // Bounce off walls
      if (particles[i].x < -boxSize / 2 || particles[i].x > boxSize / 2) {
        particles[i].vx *= -0.8;
        particles[i].x =
            std::max(-boxSize / 2, std::min(boxSize / 2, particles[i].x));
      }
      if (particles[i].y < -boxSize / 2 || particles[i].y > boxSize / 2) {
        particles[i].vy *= -0.8;
        particles[i].y =
            std::max(-boxSize / 2, std::min(boxSize / 2, particles[i].y));
      }
    }
 
    // Update plot data
    xPos.clear();
    yPos.clear();
    for (const auto &p : particles) {
      xPos.push_back(p.x);
      yPos.push_back(p.y);
    }
 
    // Update the plot
    fig.restyle({{"x", {xPos}}, {"y", {yPos}}}, {0});
 
    std::this_thread::sleep_for(std::chrono::milliseconds(frameDelay));
 
    if (frame % 50 == 0) {
      std::cout << "Frame " << frame << "/" << animationFrames << '\n';
    }
  }
 
  std::cout << "Simulation completed. Close browser to exit." << '\n';
  fig.waitClose();
 
  return 0;
}