.. role:: blue
   :class: blue

MbContourOnPlane Contour on Plane
=================================
.. _MbContourOnPlane_Contour_on_Plane_:

.. kernel version:

The :blue:`MbContourOnPlane` class is declared in the *cur_contour_on_plane.h* file.

A contour on a plane MbContourOnPlane is a derived class of
:ref:`MbContourOnSurface <MbContourOnSurface_Contour_on_Surface_>`. A contour
on a plane is defined by a plane
:ref:`MbSurface <MbSurface_Surface_>` **surface** and a two-dimensional contour
:ref:`MbContour <MbContour_Two-Dimensional_Contour_>` **contour** in the plane parameter
space. The curve also contains some additional data that is not mandatory and
is used to speed up the work of the curve methods.

A contour on a plane is a composite curve, therefore it may
have breaks at the junction points of the segments of the two-dimensional contour. A contour on
a plane represents a mapping of a contour from the two-dimensional plane
parameter space into three-dimensional space. The two-dimensional contour
**contour** may lie outside the domain
of the plane parameters. The parameter domain of the contour
on a plane coincides with the parameter domain of the two-dimensional
contour **contour**.

In the :blue:`PointOn`\( double & *t*,
:blue:`MbCartPoint3D` & *r* ) method, the radius vector of the curve *r* is described by the vector function

.. math::

   \mathbf{r}(t) = \mathbf{position.origin} +
   (\mathbf{point}.x \, \mathbf{position.axisX}) +
   (\mathbf{point}.y \, \mathbf{position.axisY}),

where **position** is the local coordinate system of the plane
**surface**, and **point** is a point of the two-dimensional contour
that is calculated by the *contour* → :blue:`PointOn`\( *t*, *point* ) method.

A contour on a plane is shown in the figure:

.. figure:: /MODELER/CURVES/pictures/O.4.23.1.png
   :width: 12cm
   :align: center

A contour on a plane can be periodic if the two-dimensional contour
**contour** is periodic or if the plane **surface** is periodic and
the end points of the contour
**contour** are shifted by the corresponding period
of the plane that is periodic in the first or second parameter
**surface**.

A periodic contour on a plane is usually used to describe
the boundary of this plane.

A contour on a plane is similar to a contour on a surface but has higher
computation speed.