polygon

polygon, a MATLAB 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT 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 Programs:

polygon_test

ellipse, a MATLAB 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.

polygon_average, a MATLAB code which demonstrates a process of repeatedly averaging and normalizing the vertices of a polygon, illustrating a property of the power method.

polygon_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from a polygon in 2D.

polygon_grid, a MATLAB code which generates a grid of points over the interior of a polygon in 2D.

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

polygon_monte_carlo, a MATLAB 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 MATLAB code which triangulates a (possibly nonconvex) polygon, based on a C function by Joseph Orourke.

quadrilateral, a MATLAB code which carries out geometric calculations on quadrilaterals, including angles, area, distances, nearest point, point containment, perimeter, and random generation.

tetrahedron, a MATLAB code which carries out geometric calculations involving a general tetrahedron, including solid and facial angles, face areas, point containment, distances to a point, circumsphere and insphere, measures of shape quality, centroid, barycentric coordinates, edges and edge lengths, random sampling, and volumes.

Source code:

• angle_half.m, returns a ray defining half the angle between two rays;
• angle_rad.m, returns the angle between two rays;
• boolean_to_string.m, returns "True" or "False", given a boolean value.
• i4_wrap.m, forces an integer to lie in a given range;
• polygon_angles.m, computes the angles of a polygon;
• polygon_area.m, computes the area of a polygon;
• polygon_area_2.m, computes the area of a polygon;
• polygon_area_3.m, computes the area of a polygon;
• polygon_area_3d.m, computes the area of a polygon in 3D;
• polygon_area_3d_2.m, computes the area of a polygon in 3D;
• polygon_area_lattice.m, finds the area of a lattice polygon;
• polygon_centroid.m, computes the centroid of a polygon;
• polygon_centroid_2.m, computes the centroid of a polygon;
• polygon_centroid_3d.m, computes the centroid of a polygon in 3D;
• polygon_contains_point_1.m, finds if a point is inside a polygon;
• polygon_contains_point_2.m, finds if a point is inside a convex polygon;
• polygon_contains_point_3.m, finds if a point is inside a simple polygon;
• polygon_data_inrad.m, uses the inradius to compute other data for a regular polygon;
• polygon_data_outrad.m, uses the outradius to compute other data for a regular polygon;
• polygon_data_side.m, uses the side length to compute other data for a regular polygon;
• polygon_diameter.m, computes the diameter of a polygon;
• polygon_expand.m, "expands" a polygon;
• 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^2 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 the convexity of a polygon;
• polygon_normal_3d.m, finds the normal vector for a (planar) polygon in 3D;
• 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, finds the distance to a polygon;
• polygon_point_near.m, finds the nearest point on a polygon;
• polygon_sample.m returns sample points from a polygon.
• polygon_solid_angle_3d.m, determines the solid angle subtended by a polygon with respect to a unit sphere around a given point in 3D;
• polygon_triangulate.m triangulates a polygon.
• r8vec_cross_product_3d.m, computes the cross product of two R8VEC's in 3D;
• r8vec_scalar_triple_product.m, computes the scalar triple product;
• segment_point_dist.m, computes the distance between a point and a line segment;
• triangle_area.m, returns the area of a triangle;
• triangle_area_3d.m, returns the area of a triangle in 3D;
• triangle_area_vector_3d.m, returns the area vector of a triangle in 3D;
• triangle_barycentric.m finds the barycentric coordinates of a point.
• triangle_contains_point_1.m finds if a point is inside a triangle.