POLYGON_PROPERTIES
Compute Properties of an Arbitrary Polygon

POLYGON_PROPERTIES, a MATLAB 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 estimates;
• 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:

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

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

POLYGON_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

polygon_properties_test

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

TRIANGLE_PROPERTIES, a MATLAB 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:

• angle_half.m finds half an angle.
• angle_rad.m returns the angle in radians swept out between two rays.
• i4_modp.m returns the nonnegative remainder of I4 division.
• i4_wrap.m forces an I4 to lie between given limits by wrapping.
• polygon_angles.m computes the interior angles of a polygon.
• polygon_area.m computes the area of a polygon.
• polygon_area_2.m computes the area of a polygon.
• polygon_centroid.m computes the centroid of a polygon.
• polygon_centroid_2.m computes the centroid of a polygon.
• polygon_contains_point.m finds if a point is inside a simple polygon.
• polygon_contains_point_2.m is a point inside a convex polygon.
• polygon_diameter.m computes the diameter of a polygon.
• polygon_expand.m expands a polygon.
• polygon_inrad_data.m determines polygonal data from its inner radius.
• polygon_integral_1.m integrates the function 1 over a polygon.
• polygon_integral_x.m integrates the function X over a polygon.
• polygon_integral_xx.m integrates the function X*X over a polygon.
• polygon_integral_xy.m integrates the function X*Y over a polygon.
• polygon_integral_y.m integrates the function Y over a polygon.
• polygon_integral_yy.m integrates the function Y*Y over a polygon.
• polygon_is_convex.m determines whether a polygon is convex.
• polygon_lattice_area.m computes the area of a lattice polygon.
• polygon_outrad_data.m determines polygonal data from its outer radius.
• polygon_perimeter.m determines the length of the perimeter of a polygon.
• polygon_perimeter_quad.m estimates the integral of a scalar function along the perimeter of a polygon.
• polygon_point_dist.m distance ( polygon, point ).
• polygon_point_near.m computes the nearest point on a polygon.
• polygon_sample.m returns sample points from a polygon.
• polygon_side_data.m determines polygonal data from its side length.
• polygon_triangulate.m triangulates a polygon.
• r8_degrees.m converts an angle from radian to degree measure.
• r8mat_solve.m uses Gauss-Jordan elimination to solve an N by N linear system.
• r8mat_transpose_print.m prints an R8MAT, transposed.
• r8mat_transpose_print_some.m prints some of an R8MAT, transposed.
• r8vec_print.m prints an R8VEC.
• segment_point_dist.m distance ( line segment, point ).
• segment_point_near.m nearest point on line segment to point.
• timestamp.m prints the current YMDHMS date as a time stamp.
• triangle_area.m computes the area of a triangle.
• triangle_barycentric.m finds the barycentric coordinates of a point.
• triangle_contains_point_1.m finds if a point is inside a triangle.