polygon

polygon, an Octave 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 information on this web page is distributed under the MIT license.

Languages:

polygon is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Programs:

polygon_test

ellipse, an Octave 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.

hypersphere, an Octave code which carries out various operations for a D-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_average, an Octave code which demonstrates a process of repeatedly averaging and normalizing the vertices of a polygon, illustrating a property of the power method.

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

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

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

polygon_minkowski, an Octave code which converts polygons between the vertex representation and the Minkowski representation, which uses a sequence of (non-unit) normal vectors.

polygon_monte_carlo, an Octave code which applies a monte carlo method to estimate the integral of a function over the interior of a polygon in 2d.

polygon_triangulate, an Octave code which triangulates a (possibly nonconvex) polygon, based on a C function by Joseph Orourke.

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

tetrahedron, an Octave 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.

triangle, an Octave code which computes properties, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality, of a triangle in 2D.

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.m, finds if a point is inside a polygon;
• polygon_convex_contains_point.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.