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.


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Installation

``bash
npm install hyp-geom
`

or with yarn:

`bash
yarn add hyp-geom
`

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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)

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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

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Quick Start

`ts
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.

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Documentation

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

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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

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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.

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License

MIT © Nathan Lopez