robust-predicates

What is robust-predicates?

The robust-predicates package provides robust geometric predicates that are used to perform orientation and incircle tests on 2D and 3D points. These predicates are designed to return exact results, which is crucial in computational geometry to avoid errors due to floating-point arithmetic.

What are robust-predicates's main functionalities?

Orientation tests

This feature allows you to determine the orientation of three points in 2D space. The function returns a positive value if the points are in counterclockwise order, zero if they are collinear, and a negative value if they are in clockwise order.

const rp = require('robust-predicates');
const result = rp.orient2d([0, 0], [1, 1], [1, 0]);
console.log(result); // Outputs a positive or negative value indicating the orientation

Incircle tests

This feature checks whether a point is inside, on the edge, or outside the circle defined by three other points in 2D space. The function returns a positive value if the point is inside, zero if on the circle, and a negative value if outside.

const rp = require('robust-predicates');
const result = rp.incircle([0, 0], [1, 0], [0, 1], [1, 1]);
console.log(result); // Outputs a positive, zero, or negative value based on the point's position relative to the circle

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README

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.

orient2d(ax,ay, bx,by, cx,cy)

• 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.

incircle(ax,ay, bx,by, cx,cy, dx,dy)

• 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.

orient3d(ax,ay,az, bx,by,bz, cx,cy,cz, dx,dy,dz)

• 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.

insphere(ax,ay,az, bx,by,bz, cx,cy,cz, dx,dy,dz, ex,ey,ez)

• 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.

orient2dfast, orient3dfast, incirclefast, inspherefast

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

Example

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.