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 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,
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.
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_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.
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.
Last revised on 17 December 2022.