User Manual 3.4.1 Spheroids : Différence entre versions

Version du 4 avril 2018 à 13:14

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;" %) Modèle: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\}Modèle:/formula

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

The equatorial radius is called the transverse radius whereas the polar radius Modèle:FormulabModèle:/formula is the conjugate radius.

Implementation

The Spheroid object in the SIRIUS library implements the [[Ellipsoid interface>>MAT_GEO_EllipsoidInterface]]. Please refer to the 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 Modèle:FormulaaModèle:/formula and the conjugate radius Modèle:FormulabModèle:/formula). For example :

Modèle: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); Modèle:/code

Usage

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