# polygon

polygon, a Fortran90 code which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including interior angles, area, centroid, containment of a point, convexity, counter clockwise ordering, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling, and triangulation.

### Languages:

polygon is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

ellipse, a Fortran90 code which carries out geometric calculations for ellipses and ellipsoids, including area, distance to a point, eccentricity, perimeter, points along the perimeter, random sampling, conversion between standard and quadratic forms.

geometry, a FORTRAN90 code which performs geometric calculations in 2, 3 and N dimensional space.

hypersphere, a FORTRAN90 code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

polygon_integrals, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

polygon_monte_carlo, a FORTRAN90 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 FORTRAN90 code which triangulates a possibly nonconvex polygon, and which can use gnuplot to display the external edges and internal diagonals of the triangulation.

tetrahedron, a FORTRAN90 code which computes properties of a given tetrahedron.

triangle, a FORTRAN90 code which computes properties of a triangle.

### 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.

### Source Code:

Last revised on 18 August 2020.