Geometric Calculations

GEOMETRY, a MATLAB library which carries out geometric calculations in 2, 3 and N space.

These calculations include angles, areas, containment, distances, intersections, lengths, and volumes.

Some geometric objects can be described in a variety of ways. For instance, a line has implicit, explicit and parametric representations. The names of routines often will specify the representation used, and there are routines to convert from one representation to another.

Another useful task is the delineation of a standard geometric object. For instance, there is a routine that will return the location of the vertices of an octahedron, and others to produce a series of "equally spaced" points on a circle, ellipse, sphere, or within the interior of a triangle.

Note that I much prefer vectors to be expressed as column vectors; MATLAB, on the other hand, seems to make it easier to work with row vectors. In my original codes, I primarily used row vectors, but I have determined to convert to column vectors; the code is in the middle of this transition, so in some cases there may be be some inconsistencies in style, and accidental inconsistencies in use. On the other hand, I am willing to put up with the practice of declaring a column vector's entries as though they were in a matrix of dimension n by 1, since this guarantees me that, for instance, a dot product is written as (u' * v), and everything finally makes sense to me.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


GEOMETRY is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Programs:


POLYGON_MOMENTS, a MATLAB library which computes arbitrary moments of a polygon.

SIMPLEX_COORDINATES, a MATLAB library which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.

SPHERE_GRID, a MATLAB library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, over the unit sphere.

SPHERE_STEREOGRAPH, a MATLAB library which computes the stereographic mapping between points on the unit sphere and points on the plane Z = 1.

TETRAHEDRON_PROPERTIES, a MATLAB program which computes properties of a given tetrahedron.

TETRAHEDRONS, a dataset directory which contains examples of tetrahedrons;

TRIANGLES, a dataset directory which contains examples of triangles;

TRIANGULATE, a MATLAB program which triangulates a (possibly nonconvex) polygon.

TRIANGULATION, a MATLAB library which defines and analyzes triangulations.


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Source code:

Last revised on 08 April 2019.