ellipse

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.

Licensing:

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

Languages:

ellipse 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_test

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.

Source code:

• ellipse_area1.m, returns the area of an ellipse x'*A*x=r^2;
• ellipse_area2.m, returns the area of an ellipse ax^2+bxy+cy^2=d;
• ellipse_area3.m, returns the area of an ellipse (x/r1)^2+(y/r2)^2=1;
• ellipse_aspect_ratio.m, returns the aspect ratio of an ellipse (x/a)^2+(y/b)^2=1;
• ellipse_ecentricity.m, returns the eccentricity of an ellipse (x/a)^2+(y/b)^2=1;
• ellipse_flattening.m, returns the flattening of an ellipse (x/a)^2+(y/b)^2=1;
• ellipse_perimeter.m, returns the perimeter of an ellipse (x/a)^2+(y/b)^2=1;
• ellipse_point_dist_2d.m, returns the distance to an ellipse in 2D;
• ellipse_point_near_2d.m, returns the nearest point on an ellipse in 2D;
• ellipse_points_2d.m, returns points on an ellipse in 2D;
• ellipse_points_arc_2d.m, returns points on an elliptical arc;
• ellipse_quadratic_to_standard.m, converts the formula for an ellipse from quadratic to standard form.
• ellipse_standard_to_quadratic.m, converts the formula for an ellipse from standard to quadratic form.
• ellipsoid_area.m, returns the surface area 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).
• r8_modp.m, returns the positive remainder of R8 division;
• r8_sign.m, returns the sign of an R8;
• 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).