Interactive Curl Visualization

An interactive 3D tool for visualizing and understanding curl in vector fields, built with Python and Matplotlib. It uses an animated paddlewheel metaphor to intuitively demonstrate the difference between conservative and non-conservative vector fields.

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Overview

The curl of a vector field measures how much the field "rotates" or "circulates" around a point. This tool makes that concept tangible: a 3D paddlewheel placed in the field will spin only when curl is non-zero — just like a physical paddle wheel placed in a swirling fluid.

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Features

• 3D interactive vector field rendered using Matplotlib's quiver plot
• Animated paddlewheel that spins in response to the field's curl
• Switch between field types using radio buttons:
  • Conservative — zero curl; the paddlewheel stays still
  • Non-Conservative — non-zero curl; the paddlewheel spins
• Adjustable field strength via a live slider
• Mouse-rotatable 3D view for exploring the field from any angle

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Requirements

• Python 3.7+
• NumPy
• Matplotlib (with mpl_toolkits for 3D support in Ubuntu's linux distribution.)

Install dependencies with:

pip install numpy matplotlib

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Usage

Run the script directly:

python field_visualizer.py

Controls

Control	Action
Radio Buttons	Switch between Conservative and Non-Conservative fields
Strength Slider	Adjust the magnitude of the field
Mouse Drag	Rotate the 3D view

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Field Types

Conservative Field

• Uniform downward field: F = (0, 0, -strength)
• Curl is zero everywhere
• The paddlewheel does not spin
• Rendered in cyan

Non-Conservative Field

• Rotational field: F = (-strength·y, strength·x, 0)
• Curl is non-zero (points in the Z direction)
• The paddlewheel spins, with speed proportional to field strength
• Rendered in magenta

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Code Structure

Class / Method	Description
FieldVisualizer	Main class — owns the figure, state, and animation loop
setup_plot()	Initializes axes, labels, and draws initial elements
_create_paddlewheel()	Builds 4-bladed paddle geometry using Poly3DCollection
setup_widgets()	Creates the radio button and slider UI
update_vector_field()	Recalculates and redraws the quiver plot
_update(frame)	Animation callback — rotates the paddlewheel each frame

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How It Works

1. A 3D grid of points is created using np.meshgrid.
2. Vector field arrows are drawn at each grid point with ax.quiver.
3. The paddlewheel consists of four rectangular paddles (Poly3DCollection) rotated 90° apart around the Z-axis.
4. Each animation frame applies a rotation matrix to the paddle vertices. In the non-conservative field, the rotation angle increments each frame; in the conservative field, the angle stays fixed.

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License

This project is provided for educational purposes. Feel free to modify and extend it.