## geometry-predicates

A Rust port of robust geometric predicates

### 6 releases

Uses old Rust 2015

 0.3.0 Feb 10, 2021 Jan 29, 2021 Aug 25, 2018 Sep 3, 2017

#281 in Algorithms

Used in 7 crates (3 directly)

1MB
20K SLoC

# geometry-predicates

This library provides a Rust solution to efficient exact geometry predicates used widely for computational geometry.

The following predicates are exposed at the root level:

• orient2d
• incircle
• orient3d
• insphere

Along with their approximate (inexact) counterparts:

• orient2d_fast
• incircle_fast
• orient3d_fast
• insphere_fast

In addition, the building blocks of these predicates, namely the adaptive precision floating-point arithmetic primitives are also exposed to allow for extensions to other predicates or exact geometric constructions.

This library supports `no-std` targets with standard IEEE 754 floats.

## Background

These predicates have been a staple in computational geometry for many years now and are widely used in industry. In the context of geometry algorithms, it is often essential to determine the orientation of a point with respect to a line (or a plane) and whether a point lies inside a circle (or a sphere) or not. The reason why these tests often need to be exact is because many geometry algorithms ask questions (to determine orientation or in-circle/sphere) about point configurations that require consistent answers. For instance, if `a`, `b`, and `c` are three points on a 2D plane, to ask where `b` with respect to the line through `a` and `c` (left-of, right-of, or coincident) is the same as asking where `a` lies with respect to the line through `c` and `b`. Formally this condition can be written as

``````sgn(orient2d(a,c,b)) == sgn(orient2d(c,b,a))
``````

Mathematically, predicates like `orient2d` are defined as

``````                                        ⎛⎡ax ay 1⎤⎞
orient2d([ax,ay],[bx,by],[cx,cy]) := det⎜⎢bx by 1⎥⎟
⎝⎣cx cy 1⎦⎠
``````

It's easy to see that these predicates solve the problem of computing the determinant of small matrices with the correct sign, regardless of how close the matrix is to being singular.

For instance to compute the determinant of a matrix `[a b; c d]` with the correct sign, we can invoke

``````orient2d([a,b], [c,d], [0,0])
``````

For more details please refer to Jonathan Shewchuk's original webpage for these predicates.

## Caveats

These predicates do NOT handle exponent overflow [1], which means inputs with floats smaller than `1e-142` or larger than `1e201` may not produce accurate results. This is true for the original predicates in `predicates.c` as well as other Rust ports and bindings for these predicates.

## Acknowledgements

This port was originally created by a C to Rust translator called Corrode. Without it, a full Rust port of this library would have been a daunting task. With that I would specifically like to thank the authors of Corrode for providing such a useful tool. Version 0.2 of this crate used the c2rust crate. The same gratitude goes towards the developers of C2Rust.