.. role:: blue
   :class: blue

MbPlaneCurve Plane Curve
========================
.. _MbPlaneCurve_Plane_Curve_:

.. версия ядра: 

The :blue:`MbPlaneCurve` class is declared in the *cur_plane_curve.h* file.

The :blue:`MbPlaneCurve` plane curve is defined by a local coordinate system :ref:`MbPlacement3D <MbPlacement3D_Local_Coordinate_System_>` **position** and a two-dimensional curve :ref:`MbCurve <MbCurve_Two-Dimensional_Curve_>` **curve** lying in the XY plane of the local coordinate system. 

A plane curve represents a mapping of a curve in the two-dimensional space of the XY plane of the local coordinate system into three-dimensional space. 

In the :blue:`PointOn`\(double & *t*, :ref:`MbCartPoint3D <MbCartPoint3D_Radius_Vector_of_Point_in_3D_Space_>` & **r**) method, the radius vector **r** of the curve is described by the vector function

.. math::

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

where **point** is a point of the two-dimensional curve computed by the **curve**\-\> :blue:`PointOn`\(*t*, **point**) method. 

A plane curve as part of a two-dimensional ellipse and a local coordinate system is shown in the figure:

.. figure:: /MODELER/CURVES/pictures/O.4.19.1.png
   :width: 12cm
   :align: center

The domain of the parameters and the periodicity of the plane curve coincide with the parameter domain and periodicity of the two-dimensional **curve**.