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====Definition====
The parallelepipeds are rectangles defined in a 3D space by their centre and a local orthogonal frame (U, V, W).

* The normalized U vector defines the "length" direction
* The normalized V vector defines the "width" direction
* The normalized W vector defines the "height" direction

The four corners and faces can be retrieved in the following orders :

[[File:parallelepipede2.png|center]]

====Implementation====
The Parallelepiped object implements the [{{JavaDoc3.3}}/org/apache/commons/math3/geometry/euclidean/threed/SolidShape.html SolidShape interface]. Please refer to the [{{JavaDoc3.3}}/org/apache/commons/math3/geometry/euclidean/threed/Parallelepiped.html Parallelepiped javadoc] for a complete list of public methods.

====Instantiation====
The parallelepiped object is built from a centre (Vector3D), two vectors (Vector3D) to describe its orientation, and three dimensions :

<syntaxhighlight lang="java">
Vector3D center = new Vector3D(1.0, 1.0, 1.0);
Vector3D uVector = new Vector3D(1.0, 1.0, 0.0);
Vector3D inputvVector = new Vector3D(-5.0, 1.0, 0.0);
Parallelepipedparallelepiped= new Parallelepiped(center, uVector, inputvVector, 4.0, 6.0, 2.0);
</syntaxhighlight>

The local frame of the plate is build from the two orientation vector :

* U is the first once normalized (uVector)
* V is the vector computed to be orthogonal to U in the plane define by the two given vectors, in the direction of inputvVector.
* W is computed by cross product of U and V

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

User Manual 3.3 Parallelepipeds - Historique des versions

Admin : Page créée avec « ====Definition==== The parallelepipeds are rectangles defined in a 3D space by their centre and a local orthogonal frame (U, V, W). * The normalized U vector defines the... »

Admin : Page créée avec « ====Definition==== The parallelepipeds are rectangles defined in a 3D space by their centre and a local orthogonal frame (U, V, W). * The normalized U vector defines the... »