ellipsoid

ellipsoid, a MATLAB code which carries out geometric calculations for ellipsoids, including area, random sampling, and volume.

Licensing:

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

Languages:

ellipsoid 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:

ellipse, a MATLAB code which carries out geometric calculations for ellipses, including area, distance to a point, eccentricity, perimeter, points along the perimeter, random sampling, conversion between standard and quadratic forms.

geometry, a MATLAB code which performs geometric calculations in 2, 3 and M dimensional space, including the computation of angles, areas, containment, distances, intersections, lengths, and volumes.

hypersphere, a MATLAB 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, a MATLAB code which carries out geometric calculations on polygons, including angles, area, centroid, containment of a point, diameter, integrals of monomials, convexity, distance to a point.

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

random_data, a MATLAB code which uses a random number generator (RNG) to sample points corresponding to various probability density functions (PDF), spatial dimensions, and geometries, including the annulus, circle, ellipse, ellipsoid, hypercube, hypersphere, simplex, tetrahedron and triangle.

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:

• ellipsoid_area.m, returns the surface area of an ellipsoid.
• ellipsoid_volume.m, returns the volume of an ellipsoid.
• elliptic_inc_em.m evaluates the incomplete elliptic integral E(PHI,M).
• elliptic_inc_fm.m evaluates the incomplete elliptic integral F(PHI,M).
• rd.m computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• rf.m computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).

Last revised on 06 January 2022.