# POLYGON_PROPERTIES Compute Properties of an Arbitrary Polygon

POLYGON_PROPERTIES is a Python library 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;
• integral over polygon of 1, x, x^2, xy, y, y^2;
• is polygon convex?;
• lattice area;
• perimeter;
• perimeter integral;
• point to polygon distance;
• point to nearest point on polygon;
• sampling uniformly;
• triangulation (decomposition into N-3 triangles).

### Languages:

POLYGON_PROPERTIES 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 library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

POLYGON_MONTE_CARLO, a Python library 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 library 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 library 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.
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.

### Examples and Tests:

You can go up one level to the Python source codes.

Last revised on 18 October 2015.