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==== Definition ====

An ellipsoid is a closed quadric surface that is the three dimensional analogue of an ellipse. Assuming the XYZ coordinate system is such that the ellipsoid is centered and axis-aligned, the ellipsoids equation is given by:

<center><math>\mathcal{S} = \left\{ (x, y, z) \in \mathbb{R}^3 \middle/ {x^2 \over a^2} + {y^2 \over b^2} + {z^2 \over c^2} = 1\right\}</math></center>

[[File:ellipsoid.PNG|center]]

'''a''','''b''' and '''c''' are called the semi axes of the ellipsoid.

==== Implementation ====

The Ellipsoid object in the SIRIUS library implements the [MAT_GEO_EllipsoidInterface Ellipsoid interface]. Please refer to the [{{JavaDoc3.4.1}}/org/apache/commons/math3/geometry/euclidean/threed/Ellipsoid.html Javadoc] for a complete list of public methods.

==== Instantiation ====

In order to instantiate an ellipsoid, the user must specify the ellipsoids' center, it's axis of revolution, X-axis, and all three semi-axis <math>a, b</math> and <math>c</math>. For example :

<syntaxhighlight lang="java">
// Spheroid parameters
Vector3D position = new Vector3D(0, 0, 0);
Vector3D revAxis = new Vector3D(0, 0, 1);
Vector3D xAxis = new Vector3D(1, 0, 0);
double a = 2.0;
double c = 1.5;
double c = 1.0;
// The ellipsoid itself
Ellipsoid myEllipsoid = new Ellipsoid(position, revAxis, xAxis, a, b, c);
</syntaxhighlight>

==== Usage ====

Please refer to the [MAT_GEO_Home#HInteractions Interactions with other geometrical objects section] for methods inherited from the Shape interface.

User Manual 3.4.1 Ellipsoids - Historique des versions

Admin : Page créée avec « ==== Definition ==== An ellipsoid is a closed quadric surface that is the three dimensional analogue of an ellipse. Assuming the XYZ coordinate system is such that the el... »

Admin : Page créée avec « ==== Definition ==== An ellipsoid is a closed quadric surface that is the three dimensional analogue of an ellipse. Assuming the XYZ coordinate system is such that the el... »