3D Gaussian ellipses constant probability curves

Constructs data points of ellipses representing contour curves of 3-dimensional Gaussian distributions with any covariance and mean value.
Example

In this example, the funcion ellipsedata constructs one ellipsoid (3-dimensional ellipse) of 400 points representing the contour curve corresponding to a standard deviation of 1.5 for a 3-dimensional Gaussian distribution with covariance matrix given by [4,1,1;1,2,1;1,1,1] and mean value given by [3,3,3].

[elv,elf]=ellipsedata3([4,1,1;1,2,1;1,1,1],[3,3,3],20,1.5);

The positions of the vertices are stored in elv, and can be plotted as follows

scatter3(elv(:,1),elv(:,2),elv(:,3));

The faces (vertices forming a patch) are stored in elf, and can be plotted as follows

patch('Faces',elf,'Vertices',elv,'FaceColor','white','EdgeColor','black');

Input arguments

covmat:
Covariance matrix of a 3-dimensional Gaussian distribution. Must be of size 3x3, symmetric and positive definite. If the format is not correct, an error is triggered. If the matrix is not symmetric, it is symmetrized by adding its transpose and dividing by 2.

center:
The center (mean value) of the 3-dimensional Gaussian distribution. If the format is not correct, it is set to [0,0,0].

numpoints:
Square root of the number of points that each ellipsoid will be composed of. Must be a positive integer number. If it is not numeric or positive, it is set to 20. If it is not integer, it is converted to integer using the function ceil.

sigmarule:
The proportion of standard deviation surrounded by each ellipsoid.

varargin (later assigned to "zeroprecision"):
A real number indicating the maximum difference after which two numbers are considered different. This value is used for assessing whether covmat is symmetric. If not specified, it is set to 1E-12

Output arguments

elv:
Matrix in which each row represents the positions of the points (vertices) that constitute the ellipsoid.

elf:
Matrix with the indices of the vertices that constitute each face (patch) of the ellipsoid.

Version control

V1.000: First version. Some points in elv are repeated. For simplicity, they are left as such.

Please, report any bugs to Hugo.Eyherabide@cs.helsinki.fi

Copyright (c) 2014, Hugo Gabriel Eyherabide, Department of Mathematics and Statistics, Department of Computer Science and Helsinki Institute for Information Technology, University of Helsinki, Finland.
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