# 3D Gaussian ellipses constant probability curves

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Construct data points of ellipsoids depicting contour curves of 3-dimensional Gaussian distributions
Aggiornato 23 apr 2014

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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.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

### Cita come

Hugo (2024). 3D Gaussian ellipses constant probability curves (https://www.mathworks.com/matlabcentral/fileexchange/46333-3d-gaussian-ellipses-constant-probability-curves), MATLAB Central File Exchange. Recuperato .

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1.0.0.0