# polygon

polygon, a Python code which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including

• angles;
• area;
• centroid;
• containment of a point;
• diameter;
• expand polygon outward by H;
• inradius of regular polygon to area, outradius side length;
• integral over polygon of 1, x, x^2, xy, y, y^2;
• is polygon convex?;
• lattice area;
• outradius of regular polygon to area, inradius, side length;
• perimeter;
• perimeter integral;
• point to polygon distance;
• point to nearest point on polygon;
• sampling uniformly;
• side length of regular polygon to area, inradius, outradius;
• triangulation (decomposition into N-3 triangles).

### Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

### Languages:

polygon is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

polygon_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

polygon_monte_carlo, a Python code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

polygon_triangulate, a Python code which triangulates a possibly nonconvex polygon, and which can use gnuplot to display the external edges and internal diagonals of the triangulation.

toms112, a Python code which determines whether a point is contained in a polygon, by Moshe Shimrat. This is a version of ACM TOMS algorithm 112.

### Reference:

1. Gerard Bashein, Paul Detmer,
Centroid of a Polygon,
in Graphics Gems IV,
edited by Paul Heckbert,
AP Professional, 1994,
ISBN: 0123361559,
LC: T385.G6974.
2. SF Bockman,
Generalizing the Formula for Areas of Polygons to Moments,
American Mathematical Society Monthly,
Volume 96, Number 2, February 1989, pages 131-132.
3. Adrian Bowyer, John Woodwark,
A Programmer's Geometry,
Butterworths, 1983,
ISBN: 0408012420.
4. Peter Schorn, Frederick Fisher,
Testing the Convexity of a Polygon,
in Graphics Gems IV,
edited by Paul Heckbert,
AP Professional, 1994,
ISBN: 0123361559,
LC: T385.G6974.
5. Moshe Shimrat,
Algorithm 112: Position of Point Relative to Polygon,
Communications of the ACM,
Volume 5, Number 8, August 1962, page 434.
6. Allen VanGelder,
Efficient Computation of Polygon Area and Polyhedron Volume,
in Graphics Gems V,
edited by Alan Paeth,
AP Professional, 1995,
ISBN: 0125434553,
LC: T385.G6975.

### Source Code:

Last revised on 29 January 2020.