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2D Vector Field Simulation Walkthrough

We have successfully created a high-performance, interactive 2D Vector Field Simulator in Rust. The project leverages macroquad for hardware-accelerated rendering, egui-macroquad for a premium glassmorphic control panel, and glam for vectorized mathematics.

Project Architecture

The simulation is split into two core Rust modules and documented in a detailed README:

  1. Cargo.toml: Project configuration and dependencies.
  2. src/noise.rs: Custom-built 2D Perlin noise and Fractal Brownian Motion (FBM) generator.
  3. src/main.rs: Main simulation loop, particle physics models, boundary handlers, rendering engine, and the interactive egui user interface.
  4. README.md: Mathematical derivations, user manual, and operational guides.

Core Modules and Code Highlights

1. Perlin Curl & Gradient Noise

In src/noise.rs, we implement 2D Perlin noise using a pseudo-random hashing function that assigns gradients to grid corners:

// 2D Perlin Noise implementation
pub fn noise2d(p: Vec2) -> f32 {
    let i = p.floor();
    let f = p.fract();
    
    // Quintic interpolation curve: 6t^5 - 15t^4 + 10t^3
    let u = f * f * f * (f * (f * 6.0 - 15.0) + 10.0);
    // ... corner dot products & bilinear interpolation ...
}

In src/main.rs, we utilize this noise to compute a divergence-free Curl Noise field using central finite differences:

let fbm_y_plus  = noise::fbm2d(Vec2::new(pos.x * scale, (pos.y + eps) * scale) + Vec2::splat(t), octaves);
let fbm_y_minus = noise::fbm2d(Vec2::new(pos.x * scale, (pos.y - eps) * scale) + Vec2::splat(t), octaves);
let fbm_x_plus  = noise::fbm2d(Vec2::new((pos.x + eps) * scale, pos.y * scale) + Vec2::splat(t), octaves);
let fbm_x_minus = noise::fbm2d(Vec2::new((pos.x - eps) * scale, pos.y * scale) + Vec2::splat(t), octaves);

let dx = (fbm_x_plus - fbm_x_minus) / (2.0 * eps);
let dy = (fbm_y_plus - fbm_y_minus) / (2.0 * eps);

// Curl = (dPsi/dy, -dPsi/dx)
Vec2::new(dy, -dx)

Because the field is curl-based, particles loop and wrap endlessly in fluid-like channels without accumulating in clumps, creating a beautiful organic visual flow.

Premium Visual Elements

To guarantee a premium, wowed experience:

  1. Glow and Fading Trails: Particles render with a neon core and a soft outer aura. Their history trails are rendered with a dynamic width gradient (tapering at the tail) and an alpha gradient that smoothly fades into the dark obsidian background.
  2. Color Palettes: Predefined colormaps interpolate across multiple color nodes for spectacular gradients:
    • Electric Neon: Cyan $\rightarrow$ Deep Purple $\rightarrow$ Hot Pink $\rightarrow$ White.
    • Magma Fire: Charcoal $\rightarrow$ Deep Violet $\rightarrow$ Red $\rightarrow$ Yellow $\rightarrow$ White.
    • Deep Ocean: Navy $\rightarrow$ Teal $\rightarrow$ Mint $\rightarrow$ Ice White.
  3. Vector Arrow Grid: An optional grid of vector arrows that dynamically stretch, point, and change colors based on the localized field magnitude and direction.

Interactive Features

  • Dual Physics Models: Toggle between Velocity Flow (ideal for mapping stream lines) and Force Field (particles orbit, drift, and slingshot with physical inertia and adjustable air friction).
  • Warp Tools: Warp field lines under your mouse using Attractor, Repeller, or Vortex tools.
  • Gravity N-Body Sandbox: Select this mode to spawn heavy stars. You can:
    • Left-Click and drag stars to reposition them.
    • Right-Click to delete stars.
    • Select the "Add Gravity Body" mouse tool to create new wells on the fly.
    • Watch particles form Keplerian orbits, hyperbolic escapes, and chaotic three-body patterns.

Running the Project

Navigate to the project folder and run Cargo in release mode:

cd vector-field
cargo run --release