# gerobust — Robust Geometry

Python extension of the C implementation of robust and quick incircles tests,
produced by Janathan Richard Shewchuk and explained in its paper *Robust Adaptive Floating-Point Geometric Predicates*.

## usage example

(see more in tests)

```
from gerobust.predicates import clockwise, counter_clockwise, incircle
triangle = (0, 0), (0, 1), (1, 0)
print(clockwise(*triangle)) # True
print(counter_clockwise.fast(*triangle)) # False
print(incircle(*triangle, (1, 1))) # False
print(incircle(*triangle, (1, 1), strict=False)) # True
```

## installation

```
pip install gerobust
```

### Tests

```
git clone git@github.com:Aluriak/gerobust.git
cd gerobust
make tests
```

## links

## Floating-point and compiler

The technics used in the C code needs the compiler to work with the IEEE 754 floating-point standard.

By looking about it in the web, i found the gcc wiki
that seems to get its full support (without micro optimization that could kill the C implementation)
with the `-frounding-math -fsignaling-nans`

options or the `#pragma STDC FENV ACCESS ON`

pragma.

The former is used. I however expect that only gcc is handled with this library. IEEE 754 compliancy through a standard way should be a short-term goal.

## Contributions

Patches as PR and ideas as issues are welcome.

Few ways to improve this lib :

- more geometric applications of the global method, for a more complete library
- compatibility with others compiler/OS
- unit test showing the (¬)robustness of functions
- general improvements over the python codebase (organization, style, efficiency, doc)

## Bibliography

Abstract and citation reproduced below.

```
Robust Adaptive Floating-Point Geometric Predicates
Jonathan Richard Shewchuk
School of Computer Science
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Fast C implementations of four geometric predicates, the 2D and 3D orientation
and incircle tests, are publicly available. Their inputs are ordinary single
or double precision floating-point numbers. They owe their speed to two
features. First, they employ new fast algorithms for arbitrary precision
arithmetic that have a strong advantage over other software techniques in
computations that manipulate values of extended but small precision. Second,
they are adaptive; their running time depends on the degree of uncertainty of
the result, and is usually small. These algorithms work on computers whose
floating-point arithmetic uses radix two and exact rounding, including machines
that comply with the IEEE 754 floating-point standard. Timings of the
predicates, in isolation and embedded in 2D and 3D Delaunay triangulation
programs, verify their effectiveness.
Proceedings of the Twelfth Annual Symposium on Computational Geometry
(Philadelphia, Pennsylvania), pages 141-150, ACM, May 1996. PostScript (310k).
Paper available through the URL
http://www.cs.berkeley.edu/~jrs/papers/robust-predicates.ps
For additional details and associated software, see the Web page
http://www.cs.cmu.edu/~quake/robust.html
```