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 information on this web page is 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, an Octave 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, 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.

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:

• 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_xy_from_t.m, converts ellipse points from angular to Cartesian coordinates.
• 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).