A safe 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.
The following predicates are exposed at the root level: - orient2d - incircle - orient3d - insphere
Along with their approximate (inexact) counterparts: - orient2dfast - incirclefast - orient3dfast - inspherefast
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.
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.