geometry-predicates

A Rust port of "Adaptive Precision Floating-Point Arithmetic and Fast Robust Predicates for Computational Geometry"

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

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.o

So far, the following predicates are supported:

• orient2d
• orient3d

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 (using MATLAB-style notation), predicates like orient2d are defined as

orient2d([ax,ay],[bx by],[cx cy]) := det([ax ay 1; 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 the original webpage for these predicates.

Acknowledgements

This port was 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.