knotess

Knotess

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

Knotess consumes a compact binary file that provides XYZ positions for bézier control points, then produces tube shapes by sweeping a polygon along the bézier curve.

• Interactive Demo

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 a browser build directly as follows. Note the external dependency on glMatrix.

<script src="//unpkg.com/gl-matrix@2.8.1/dist/gl-matrix-min.js"></script>
<script src="//unpkg.com/knotess@1.0.0/knotess.js"></script>

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.