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==== Definition ====

An infinite elliptic cone is a ruled surface that resembles a cone except that its basis is an ellipse. As such, it is also ''a set of half-lines'' that start at the common point called ''apex'' and describe, in a plan perpendicular to the axis of the cone, an ellipse. It's equation is given hereunder :

<center><math>\mathcal{C} = \left\{ (x, y, z) \in {R}^3 \middle/ {x^2 \over \tan^2\alpha} + {y^2 \over \tan^2\beta} = 1 \right\}</math></center>

[[File:ellipticCone.PNG|center]]

==== Implementation ====
The InfiniteEllipticCone object in the SIRIUS library implements the [MAT_GEO_InfiniteConeInterface InfiniteCone Interface]. Please refer to the [{{JavaDoc3.4.1}}/org/apache/commons/math3/geometry/euclidean/threed/InfiniteEllipticCone.html Javadoc] for a complete list of public methods.

==== Instantiation ====

In order to instantiate an infinite elliptic cone object, the user must specify the cones' "center", its main axis, its axis along which aperture is <math>2*a</math> and both angles. For example :

<syntaxhighlight lang="java">
// Cones parameters
Vector3D position = new Vector3D(1, 2, 3);
Vector3D axis = new Vector3D(0, 1, 1);
Vector3D axisU = new Vector3D(2,-1, 0);
double alpha = Math.PI / 8;
double beta = Math.PI / 10;
// The cone itself
InfiniteEllipticCone myCone = new InfiniteEllipticCone(position, axis, axisU, alpha, beta);
</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 Infinite elliptic cone - Historique des versions

Admin : Page créée avec « ==== Definition ==== An infinite elliptic cone is a ruled surface that resembles a cone except that its basis is an ellipse. As such, it is also ''a set of half-lines'' t... »

Admin : Page créée avec « ==== Definition ==== An infinite elliptic cone is a ruled surface that resembles a cone except that its basis is an ellipse. As such, it is also ''a set of half-lines'' t... »