hyp-geom

A TypeScript library for working with hyperbolic geometry. This package provides geometric tools for the upper half plane model of the hyperbolic plane.

Installation

npm install hyp-geom

or with yarn:

yarn add hyp-geom

Features

• Distance and angle calculations
• Formulas and information for curves/shapes including geodesics (lines), circles, horocycles, and polygons
• Hyperbolic isometries as Möbius transformations, either by specifying the coordinates of the corresponding matrix or by choosing from one of the three types (hyperbolic, elliptic, or parabolic)

Planned Features

• Angle measure at intersection point of curves
• Support for additional models including the Poincare Disk model, the Bertrami-Klein model, and the Hyperboloid model
• Drawings and animations, e.g., the action of an isometry on a model
• Support for fundamental domains, ultimately leading to 3d interactions with hyperbolic surfaces

Quick Start

import { UhpIsometry } from "hyp-geom";

const uhp = new UpperHalfPlane();
const center = [0, 1];
const radius = 1;

const circle = uhp.circle(center, radius);

console.log(circle);
// {
//  center: { re: 0, im: 1 },
//  radius: 1,
//  eucCenter: { re: 0, im: cosh(1) },
//  eucRadius: sinh(1)
// }

See examples for more usage demonstrations.

Documentation

• API Reference: Method signatures and usage
• Mathematical Background (PDF): Derivations and theory

Examples

The examples folder contains runnable TypeScript snippets showing:

• Computing distances and angles
• Working with hyperbolic curves (geodesics, circles, etc.)
• Basic translations, rotations, and reflections
• Applying isometries to points
• Classifying isometries

Contributing

Contributions, issues, and feature requests are welcome! If you’d like to add functionality, improve docs, or suggest enhancements, please open an issue or submit a pull request.

See CONTRIBUTING.md for guidelines.

License

MIT © Nathan Lopez