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robust-predicates\n\nFast 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](https://www.cs.cmu.edu/~quake/robust.html), an industry standard since 1996.\n\n![](\"predicates.png\")
\n\n_Figure: non-robust vs robust `orient2d` test for points within a tiny range (2-42)._\n\n[](https://github.com/mourner/robust-predicates/actions/workflows/node.yml)\n[](https://github.com/mourner/projects)\n[](https://unpkg.com/robust-predicates)\n\n## [Demo](https://observablehq.com/@mourner/non-robust-arithmetic-as-art)\n\n## API\n\nNote: unlike J. Shewchuk's original code, all the functions in this library assume `y` axis is oriented _downwards_ ↓, so the semantics are different.\n\n### `orient2d(ax,ay, bx,by, cx,cy)`\n\n- 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`).\n- Returns a *negative* value if they occur in _clockwise_ order (`c` lies to the right of the directed line `ab`).\n- Returns *zero* if they are _collinear_.\n\nThe result is also an approximation of twice the signed area of the triangle defined by the three points.\n\n### `incircle(ax,ay, bx,by, cx,cy, dx,dy)`\n\n- Returns a _positive_ value if the point `d` lies _outside_ the circle passing through `a`, `b`, and `c`.\n- Returns a _negative_ value if it lies _inside_.\n- Returns _zero_ if the four points are _cocircular_.\n\nThe points `a`, `b`, and `c` must be in _counterclockwise_ order, or the sign of the result will be reversed.\n\n### `orient3d(ax,ay,az, bx,by,bz, cx,cy,cz, dx,dy,dz)`\n\n- 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`.\n- Returns a _negative_ value if `d` lies _below_ the plane.\n- Returns _zero_ if the points are _coplanar_.\n\nThe result is also an approximation of six times the signed volume of the tetrahedron defined by the four points.\n\n### `insphere(ax,ay,az, bx,by,bz, cx,cy,cz, dx,dy,dz, ex,ey,ez)`\n\n- Returns a _positive_ value if the point `e` lies _outside_ the sphere passing through `a`, `b`, `c`, and `d`.\n- Returns a _negative_ value if it lies _inside_.\n- Returns _zero_ if the five points are _cospherical_.\n\nThe points `a`, `b`, `c`, and `d` must be ordered so that they have a _positive orientation_\n(as defined by `orient3d`), or the sign of the result will be reversed.\n\n### `orient2dfast`, `orient3dfast`, `incirclefast`, `inspherefast`\n\nSimple, approximate, non-robust versions of predicates above. Use when robustness isn't needed.\n\n## Example\n\n```js\nimport {orient2d} from 'robust-predicates';\n\nconst ccw = orient2d(ax, ay, bx, by, cx, cy) > 0;\n````\n\n## Install\n\nInstall with `npm install robust-predicates` or `yarn add robust-predicates`, or use one of the browser builds:\n\n- [predicates.min.js](https://unpkg.com/robust-predicates/umd/predicates.min.js) (all predicates)\n- [orient2d.min.js](https://unpkg.com/robust-predicates/umd/orient2d.min.js) (`orient2d`, `orient2dfast`)\n- [orient3d.min.js](https://unpkg.com/robust-predicates/umd/orient3d.min.js) (`orient3d`, `orient3dfast`)\n- [incircle.min.js](https://unpkg.com/robust-predicates/umd/incircle.min.js) (`incircle`, `incirclefast`)\n- [insphere.min.js](https://unpkg.com/robust-predicates/umd/insphere.min.js) (`insphere`, `inspherefast`)\n\n## Thanks\n\nThis project is just a port — all the brilliant, hard work was done by [Jonathan Richard Shewchuk](https://people.eecs.berkeley.edu/~jrs/).\n\nThe port was also inspired by [Mikola Lysenko](https://twitter.com/MikolaLysenko)'s excellent [Robust Arithmetic Notes](https://github.com/mikolalysenko/robust-arithmetic-notes) and related projects like [robust-orientation](https://github.com/mikolalysenko/robust-orientation) and [robust-in-sphere](https://github.com/mikolalysenko/robust-in-sphere).\n\n## License\n\nSince the original code is in the public domain, this project follows the same choice. See [Unlicense](https://unlicense.org).\n","_attachments":{},"homepage":"https://github.com/mourner/robust-predicates#readme","bugs":{"url":"https://github.com/mourner/robust-predicates/issues"},"license":"Unlicense"}