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	A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal equatorial radii. Assuming the XYZ coordinate system is such that the spheroid is centered and axis-aligned, the spheroids equation is given by:		A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal equatorial radii. Assuming the XYZ coordinate system is such that the spheroid is centered and axis-aligned, the spheroids equation is given by:

	~~(% style="text-align:~~center~~;" %)~~		<center><math>\mathcal{S} = \left\{ (x, y, z) \in \mathbb{R}^3 \middle/ {x^2 + y^2 \over a^2} + {z^2 \over b^2} = 1\right\}</math></center>
	~~{{formula}}~~\mathcal{S} = \left\{ (x, y, z) \in \mathbb{R}^3 \middle/ {x^2 + y^2 \over a^2} + {z^2 \over b^2} = 1\right\}{{/~~formula}}~~

	~~(% style="text-align:center;" %)~~		[[File:spheroid.PNG\|center]]
	[[~~image~~:~~Images@~~spheroid.PNG]]

	The equatorial radius is called the transverse radius whereas the polar radius ~~{{formula}}~~b{{/~~formula}}~~ is the conjugate radius.		The equatorial radius is called the transverse radius whereas the polar radius <math>b</math> is the conjugate radius.

	==== Implementation ====		==== Implementation ====

	The Spheroid object in the SIRIUS library implements the [[Ellipsoid interface~~>>MAT_GEO_EllipsoidInterface]~~]. Please refer to the [{{~~JavaDoc4~~.0}}/org/apache/commons/math3/geometry/euclidean/threed/Spheroid.html Javadoc] for a complete list of public methods.		The Spheroid 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/Spheroid.html Javadoc] for a complete list of public methods.

	==== Instantiation ====		==== Instantiation ====

	In order to instantiate a spheroid object, the user must specify the spheroids' center, it's axis of revolution and both semi-axis (the transverse radius ~~{{formula}}~~a{{/~~formula}}~~ and the conjugate radius ~~{{formula}}~~b{{/~~formula}}~~). For example :		In order to instantiate a spheroid object, the user must specify the spheroids' center, it's axis of revolution and both semi-axis (the transverse radius <math>a</math> and the conjugate radius <math>b</math>). For example :

	~~{{code language~~="java"}}		<syntaxhighlight lang="java">
	// Spheroid parameters		// Spheroid parameters
	Vector3D position = new Vector3D(1, 2, 3);		Vector3D position = new Vector3D(1, 2, 3);
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	// The spheroid itself		// The spheroid itself
	Spheroid mySpheroid = new Spheroid(position, revAxis, a, b);		Spheroid mySpheroid = new Spheroid(position, revAxis, a, b);
	{{/~~code}}~~		</syntaxhighlight>

	==== Usage ====		==== Usage ====

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

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==== Definition ====

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal equatorial radii. Assuming the XYZ coordinate system is such that the spheroid is centered and axis-aligned, the spheroids equation is given by:

(% style="text-align:center;" %)
{{formula}}\mathcal{S} = \left\{ (x, y, z) \in \mathbb{R}^3 \middle/ {x^2 + y^2 \over a^2} + {z^2 \over b^2} = 1\right\}{{/formula}}

(% style="text-align:center;" %)
[[image:Images@spheroid.PNG]]

The equatorial radius is called the transverse radius whereas the polar radius {{formula}}b{{/formula}} is the conjugate radius.

==== Implementation ====

The Spheroid object in the SIRIUS library implements the [[Ellipsoid interface>>MAT_GEO_EllipsoidInterface]]. Please refer to the [{{JavaDoc4.0}}/org/apache/commons/math3/geometry/euclidean/threed/Spheroid.html Javadoc] for a complete list of public methods.

==== Instantiation ====

In order to instantiate a spheroid object, the user must specify the spheroids' center, it's axis of revolution and both semi-axis (the transverse radius {{formula}}a{{/formula}} and the conjugate radius {{formula}}b{{/formula}}). For example :

{{code language="java"}}
// Spheroid parameters
Vector3D position = new Vector3D(1, 2, 3);
Vector3D revAxis = new Vector3D(0, 1, 1);
double a = 2.0;
double b = 1.0;
// The spheroid itself
Spheroid mySpheroid = new Spheroid(position, revAxis, a, b);
{{/code}}

==== Usage ====

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

User Manual 3.4.1 Spheroids - Historique des versions

Admin le 4 avril 2018 à 13:16

Admin : Page créée avec « ==== Definition ==== A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellip... »

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