polygon

polygon, a FORTRAN77 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;
• 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 an Octave version and a Python version.

Related Data and Programs:

polygon_test

GEOMETRY, a FORTRAN77 library which performs geometric calculations in 2, 3 and N dimensional space.

HYPERSPHERE, a FORTRAN77 library 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 FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

POLYGON_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 library which triangulates a possibly nonconvex polygon, and which can use gnuplot to display the external edges and internal diagonals of the triangulation.

TETRAHEDRON, a FORTRAN77 program which computes properties of a tetrahedron in 3D, including the centroid, circumsphere, dihedral angles, edge lengths, face angles, face areas, insphere, quality, solid angles, and volume.

TRIANGLE, a FORTRAN77 program which computes properties of a triangle whose vertex coordinates are read from a file.

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:

• polygon.f, the source code.
• polygon.sh, compiles the source code.