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;
• 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_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.
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:

• angle_half.py finds half an angle.
• angle_radian.py returns the angle in radians swept out between two rays.
• i4_ceiling.py returns the smallest I4 that is not smaller than an R8.
• i4_modp.py returns the nonnegative remainder of I4 division.
• i4_wrap.py forces an I4 to lie between given limits by wrapping.
• polygon_angles.py computes the interior angles of a polygon.
• polygon_area.py computes the area of a polygon.
• polygon_area_2.py computes the area of a polygon.
• polygon_centroid.py computes the centroid of a polygon.
• polygon_centroid_2.py computes the centroid of a polygon.
• polygon_contains_point.py finds if a point is inside a simple polygon.
• polygon_contains_point_2.py is a point inside a convex polygon.
• polygon_diameter.py computes the diameter of a polygon.
• polygon_expand.py expands a polygon.
• polygon_inrad_data.py determines polygonal data from its inner radius.
• polygon_integral_1.py integrates the function 1 over a polygon.
• polygon_integral_x.py integrates the function X over a polygon.
• polygon_integral_xx.py integrates the function X*X over a polygon.
• polygon_integral_xy.py integrates the function X*Y over a polygon.
• polygon_integral_y.py integrates the function Y over a polygon.
• polygon_integral_yy.py integrates the function Y*Y over a polygon.
• polygon_is_convex.py determines whether a polygon is convex.
• polygon_lattice_area.py computes the area of a lattice polygon.
• polygon_outrad_data.py determines polygonal data from its outer radius.
• polygon_perimeter.py determines the length of the perimeter of a polygon.
• polygon_perimeter_quad.py estimates the integral of a scalar function over the perimeter of a polygon.
• polygon_point_dist.py distance ( polygon, point ).
• polygon_point_near.py computes the nearest point on a polygon.
• polygon_sample.py returns sample points from a polygon.
• polygon_side_data.py determines polygonal data from its side length.
• polygon_triangulate.py triangulates a polygon.
• r8_atan2.py computes the arc-tangent of a ratio of R8 values.
• r8mat_solve.py uses Gauss-Jordan elimination to solve an N by N linear system.
• r8mat_transpose_print.py prints an R8MAT, transposed.
• r8mat_transpose_print_some.py prints some of an R8MAT, transposed.
• r8vec_print.py prints an R8VEC.
• segment_point_dist.py distance ( line segment, point ).
• segment_point_near.py nearest point on line segment to point.
• timestamp.py prints the current YMDHMS date as a time stamp.
• triangle_area.py computes the area of a triangle.
• triangle_barycentric.py finds the barycentric coordinates of a point.
• triangle_contains_point_1.py finds if a point is inside a triangle.

Examples and Tests:

• polygon_properties_test.py, calls all the tests.
• polygon_properties_test.sh, runs all the tests.
• polygon_properties_test.txt, the output file.

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