.. role:: blue
   :class: blue

MbPlane Plane
=============
.. _MbPlane_Plane_:

.. version: 

The :blue:`MbPlane` class is declared in the *surf_plane.h* file.

The :blue:`MbPlane` plane belongs to the group of elementary surfaces
:blue:`MbElementarySurface`. The plane is defined by the XY plane of the local
coordinate system :blue:`MbPlacement3D` **position**. The first
parameter of the plane is measured along the vector
**position.axisX**, and the second parameter of the plane
is measured along the vector **position.axisY**. The domain of the plane
is described by the boundary parameter values *umin*,
*umax* and *vmin*, *vmax*, Fig. 1:

.. figure:: /MODELER/SURFACES/pictures/O.5.2.1.png
   :width: 12cm
   :align: center

   Fig. 1

In the method :blue:`PointOn`\( double *u*, double *v*,
:blue:`MbCartPoint3D` \& **s** ), the radius vector **s** of the plane
is described by the vector function

.. math::

   \mathbf{s}(u, v) = \mathbf{position.origin} + u \cdot \mathbf{position.axisX} + v \cdot \mathbf{position.axisY}.

The plane behaves as an infinite object, although its data contains
the boundary parameter values *umin*, *umax* and
*vmin*, *vmax*. Note that, unlike other surfaces,
the plane does not adjust the parameters *u* and *v* when they go beyond
the domain defined by the values *umin*,
*umax* and *vmin*, *vmax* in the methods for computing the radius vector and its derivatives.

The local coordinate system **position** can be either right-handed or
left-handed. If the local coordinate system is left-handed, the normal of the plane
is directed opposite to the direction of the vector
**position.axisZ**.