superellipse 0.1.0

Generalized superellipse (Lamé curve) geometry: discretization, curvature, arc-length, and export

superellipse

Generalized superellipse (Lamé curve) geometry for Python.

Overview

A superellipse (or Lamé curve) is defined by:

$$|x/a|^p + |y/b|^q = 1$$

This package provides tools for working with these curves:

• Geometry: Points, tangents, normals, curvature
• Discretization: Uniform, arc-length, or adaptive panel-based sampling
• Signed distance: Fast SDF evaluation for level-set methods
• Export: SVG paths, JSON, NumPy arrays
• Special cases: Squircle (p=q=4), rounded rectangles, stadium curves

Installation

pip install superellipse

# With plotting support
pip install superellipse[plot]

# With SVG export
pip install superellipse[export]

# Everything
pip install superellipse[all]

Quick Start

from superellipse import Superellipse

# Create a squircle (p=4, like iOS icons)
curve = Superellipse(a=1.0, b=1.0, p=4)

# Sample 100 points
points = curve.sample(n=100)

# Get curvature at each point
kappa = curve.curvature(points)

# Export to SVG path
path_data = curve.to_svg_path(n=100)

CLI

# Plot a superellipse
superellipse plot --a 1 --b 0.8 --p 4 --output squircle.png

# Export to SVG
superellipse export --a 1 --b 1 --p 6 --format svg --output curve.svg

# Compute arc length
superellipse info --a 1 --b 1 --p 4

Use Cases

• UI/UX Design: Squircles for app icons (iOS-style rounded rectangles)
• CAD/CAM: Smooth corner profiles for machining
• Graphics: Procedural shape generation
• Scientific Computing: Boundary geometry for PDEs
• Typography: Letterform design with smooth corners

API Reference

Superellipse(a, b, p, q=None)

Create a superellipse with semi-axes a, b and exponents p, q. If q is None, uses q=p (symmetric exponent).

Methods

Method	Description
sample(n, method='uniform')	Sample n points on the curve
curvature(points)	Signed curvature at given points
normal(points)	Outward unit normals
tangent(points)	Unit tangent vectors
arc_length(t0=0, t1=2π)	Arc length between parameter values
signed_distance(points)	Signed distance from points to curve
to_svg_path(n=100)	Export as SVG path data string
to_json()	Export curve parameters as JSON

Sampling Methods

• 'uniform': Uniform in parameter t ∈ [0, 2π]
• 'arclength': Uniform in arc length
• 'adaptive': Refine near high-curvature regions
• 'panels': Panel-based with Gauss-Legendre nodes (for BIE)

License

MIT License. See LICENSE for details.