Interactive Vector Field Sandbox

A real-time, high-performance, and visually stunning interactive vector field simulator built in Rust using Macroquad, Egui, and Glam.

This sandbox allows you to visualize and interact with complex 2D vector fields. It simulates thousands of colorful particles flowing through dynamic, time-varying mathematical fields.

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Core Features

• 7 Mathematical Field Presets:
  • Perlin Curl Noise: Generates divergence-free fluid-like currents (vortices and laminar streams).
  • Perlin Gradient Noise: Organic topographic field where particles settle in local extrema.
  • Vortex / Hurricane: A classic rotational flow spiraling outward or inward.
  • Electric Dipole: Visualizes field lines between a positive source and a negative sink.
  • Saddle Point: A hyperbolic flow demonstrating saddle point deflection.
  • Trig Flow (Parametric): Fully customizable combinations of sine and cosine waves.
  • Gravity N-Body Sandbox: Place, drag, and delete heavy stars to simulate orbital gravitational wells.
• Dual Physics Models:
  • Velocity Flow (First-order): Particle velocities are directly mapped to the vector field ($v = F$). Particles follow field lines exactly.
  • Force Field (Second-order / Inertia): The vector field acts as an acceleration force ($a = F / m$). Particles possess inertia, enabling orbits, chaotic loops, and slingshots.
• Aesthetics & Visuals:
  • Smooth, tapered, alpha-faded particle trails that taper off into the obsidian background.
  • Optional Neon Glow Core flare around particle heads.
  • High-fidelity color mappings (Spectral Rainbow, Magma Fire, Deep Ocean, Neon Electric, and Viridis).
  • Optional arrow grid overlay reflecting field directions and strengths in real-time.
• Direct Viewport Interaction:
  • Attract & Repel: Warps the field under your cursor.
  • Clockwise & Counter-Clockwise Vortex: Twists the field locally.
  • Gravity Sandboxing: Place stars with Left-Click, drag them around, or delete them with Right-Click.

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Mathematical Fields

1. Perlin Curl Noise (Divergence-Free)

To simulate fluid-like currents that don't aggregate into sinks, we compute the curl of a 2D scalar Fractal Brownian Motion field $\psi(x, y, t)$: $$\mathbf{V}(x, y) = \left( \frac{\partial \psi}{\partial y}, -\frac{\partial \psi}{\partial x} \right)$$ We approximate these partial derivatives numerically via central differences: $$\frac{\partial \psi}{\partial x} \approx \frac{\psi(x + \epsilon, y) - \psi(x - \epsilon, y)}{2\epsilon}$$

2. Electric Dipole

Calculates forces acting from a source at $\mathbf{p}{\text{src}}$ and a sink at $\mathbf{p}{\text{snk}}$: $$\mathbf{V}(\mathbf{x}) = \frac{\mathbf{x} - \mathbf{p}{\text{src}}}{|\mathbf{x} - \mathbf{p}{\text{src}}|^3 + \delta} - \frac{\mathbf{x} - \mathbf{p}{\text{snk}}}{|\mathbf{x} - \mathbf{p}{\text{snk}}|^3 + \delta}$$ (where $\delta$ is a softening factor to prevent singularities).

3. Custom Trig Flow

Controlled via 8 independent coefficient sliders in the GUI: $$V_x = A \sin(B \cdot y + t) + C \cos(D \cdot x - t)$$ $$V_y = E \sin(F \cdot x - t) + G \cos(H \cdot y + t)$$

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Installation & Running

Ensure you have Rust and Cargo installed.

1. Navigate to the project directory:

   cd vector-field

2. Build and run the project:

   cargo run --release

Note: Running with the --release flag is highly recommended to compile code optimizations, allowing you to run 10,000+ particles with trails smoothly at 60+ FPS.

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Controls & Sandbox Usage

• Interactive Panel (egui): Tweak presets, particle counts (from 100 to 9,000), trail lengths, neon glows, particle sizes, damping rates, and color palettes.
• Viewport Interaction:
  • Left-Click + Drag: Apply the active mouse tool (Attract, Repel, Vortex) to distort the field lines.
  • Gravity Mode (Sandbox):
    • Place Star: Select "Add Gravity Body" mouse tool and Left-Click.
    • Move Star: Left-Click and drag any existing star.
    • Delete Star: Right-Click on a star to remove it.
    • Clear: Use the "Clear Stars" button in the menu.

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