divergence02

Interactive 2D vector-field explorer for building intuition for divergence and curl. AI Generated finetuned for the visualisation and not code quality.

divergence_curl.mov

This repository is a small C + Raylib application that lets you pan around synthetic flow fields, flip between divergence and curl, drop probes into the scene, and inspect the finite-difference stencil used to estimate each quantity. It also includes a second explainer page focused on the sign convention in the curl formula.

What This Repo Does

• Renders a live 2D vector field with arrow glyphs and animated particles
• Colors the field by the currently selected derived quantity: div F or curl F
• Shows a hover inspector with the local vector value and numerical estimate
• Draws a finite-difference stencil and step-by-step derivative breakdown at the cursor
• Lets you place persistent probes to compare multiple locations
• Includes several presets built from sources, sinks, vortices, and base flows
• Includes a second page that visually explains why curl ~= dFy/dx - dFx/dy

Presets

The field page cycles through five built-in scenes:

• Mixed Playground: waves, sources, sinks, and vortices combined
• Source And Sink: strong positive and negative divergence
• Counter Rotations: mostly rotational structure with strong curl
• Expansion Vs Spin: a side-by-side contrast between spreading and spinning
• Shear With Eddy: a background shear flow with a localized vortex

Controls

Global

• q: quit
• 1: open the interactive field page
• 2: open the curl-sign explainer page
• v or tab: toggle between divergence and curl
• p: cycle to the next field preset
• space: pause or resume particle advection on the field page
• r: reset camera, probes, particles, and animation time

Field Page

• left drag: pan the camera
• mouse wheel: zoom toward the cursor
• left click: place a probe at the clicked world position
• hover: inspect the local vector, numerical quantity, and derivative stencil

Build

Dependencies

• raylib
• pkg-config
• a C compiler such as cc or clang

Commands

make
make run

To remove the built binary:

make clean

How To Read The Visualization

• Arrow field: the base vector field F(x, y)
• Heatmap: the numerically sampled divergence or curl at each grid cell
• Particles: flow direction and speed over time
• Hover stencil: the local centered-difference samples used for the derivative estimate
• Probe labels: persistent sampled locations for comparing values across the scene

Notes

• The app window is resizable.
• The numerical estimates are centered finite differences sampled around the cursor or probe position.
• Page 2 is not another simulation scene; it is a visual explainer for the curl minus sign.