robust-predicates

Fast robust predicates for computational geometry in JavaScript. Provides reliable 2D and 3D point orientation tests (orient2d, orient3d, incircle, insphere) that are not susceptible to floating point errors (without sacrificing performance). A modern port of Jonathan R Shewchuk's C code, an industry standard since 1996.

_Figure: non-robust vs robust orient2d test for points within a tiny range (2^-42)._


Demo

API

Note: unlike J. Shewchuk's original code, all the functions in this library assume y axis is oriented _downwards_ ↓, so the semantics are different.

$3

- Returns a positive value if the points a, b, and c occur in _counterclockwise_ order (c lies to the left of the directed line defined by points a and b).
- Returns a negative value if they occur in _clockwise_ order (c lies to the right of the directed line ab).
- Returns zero if they are _collinear_.

The result is also an approximation of twice the signed area of the triangle defined by the three points.

$3

- Returns a _positive_ value if the point d lies _outside_ the circle passing through a, b, and c.
- Returns a _negative_ value if it lies _inside_.
- Returns _zero_ if the four points are _cocircular_.

The points a, b, and c must be in _counterclockwise_ order, or the sign of the result will be reversed.

$3

- Returns a _positive_ value if the point d lies _above_ the plane passing through a, b, and c, meaning that a, b, and c appear in counterclockwise order when viewed from d.
- Returns a _negative_ value if d lies _below_ the plane.
- Returns _zero_ if the points are _coplanar_.

The result is also an approximation of six times the signed volume of the tetrahedron defined by the four points.

$3

- Returns a _positive_ value if the point e lies _outside_ the sphere passing through a, b, c, and d.
- Returns a _negative_ value if it lies _inside_.
- Returns _zero_ if the five points are _cospherical_.

The points a, b, c, and d must be ordered so that they have a _positive orientation_
(as defined by orient3d), or the sign of the result will be reversed.

$3

Simple, approximate, non-robust versions of predicates above. Use when robustness isn't needed.

Example

``js
import {orient2d} from 'robust-predicates';

const ccw = orient2d(ax, ay, bx, by, cx, cy) > 0;
``

Install

Install with npm install robust-predicates or yarn add robust-predicates, or use one of the browser builds:

- predicates.min.js (all predicates)
- orient2d.min.js (orient2d, orient2dfast)
- orient3d.min.js (orient3d, orient3dfast)
- incircle.min.js (incircle, incirclefast)
- insphere.min.js (insphere, inspherefast`)

Thanks

This project is just a port — all the brilliant, hard work was done by Jonathan Richard Shewchuk.

The port was also inspired by Mikola Lysenko's excellent Robust Arithmetic Notes and related projects like robust-orientation and robust-in-sphere.

License

Since the original code is in the public domain, this project follows the same choice. See Unlicense.