Knotess

This library generates triangle meshes for all the prime knots in the Rolfsen table.

At run time, knotess consumes a compact binary file (centerlines.bin) containing bézier control points. It then generates triangle meshes by sweeping a polygon along the bézier curves.

• Interactive Demo using Filament and WebGL 2.0
• The demo source code is a single JS file.

Example

const SPINEDATA = 'centerlines.bin';
fetch(SPINEDATA).then(res => res.arrayBuffer()).then((data) => {
    const knots = new Knotess(data);
    const link = knots.tessellate('7.2.3');
    const mesh = link[0];
    const nverts = mesh.vertices.length / 6; // positions and normals
    console.info(`The first component has ${nverts} vertices.`);
});

Install

Install with NPM (npm install knotess) or Yarn (yarn add knotess), then:

import Knotess from 'knotess';

Or use one of the following two CDN builds.

<script src="//unpkg.com/knotess@1.1.2/knotess.min.js"></script> <!-- minified build -->
<script src="//unpkg.com/knotess@1.1.2/knotess.js"></script> <!-- dev build -->

API Reference

new Knotess(ArrayBuffer)

Constructs a tessellator given a flat array of floating-point XYZ coordinates for the knot centerlines.

knotess.tesselate(string, options)

Given an Alexander-Briggs-Rolfsen identifier and an optional configuration dictionary, returns an array of "meshes" where each mesh is a dictionary with three entries: a Float32Array vertex buffer, a Uint16Array triangle buffer, and aUint16Array wireframe buffer.

Knotess.LinksDb

Dictionary from Alexander-Briggs-Rolfsen number (e.g. "2.2.1") to arrays of two-tuples, where each two-tuple defines a range within the centerlines buffer. In knot theory parlance, each two-tuple corresponds to a component and each entry in the dictionary corresponds to a link.

Knotess.Rolfsen

Array of strings where each string corresponds to a row in the Rolfsen table. Each string is a space-delimited list of Alexander-Briggs-Rolfsen identifiers.