[−][src]Crate geometry_predicates
geometry-predicates
A safe Rust port of "Adaptive Precision Floating-Point Arithmetic and Fast Robust Predicates for Computational Geometry"
This crate 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 in predicates
to allow for extensions
to other predicates or exact geometric constructions.
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.
Re-exports
pub use predicates::incircle; |
pub use predicates::incircle_fast; |
pub use predicates::insphere; |
pub use predicates::insphere_fast; |
pub use predicates::orient2d; |
pub use predicates::orient2d_fast; |
pub use predicates::orient3d; |
pub use predicates::orient3d_fast; |
Modules
predicates |