.. role:: blue  
   :class: blue

MbArc3D Elliptical Arc
======================
.. _MbArc3D_Elliptical_Arc_:

.. kernel version: 

The :blue:`MbArc3D` class is declared in the *cur_arc_3d.h* file.

The elliptical arc is a inheritor of the :blue:`MbCurve3D` curve. The :blue:`MbArc3D` elliptical arc is defined by two radii *a* and *b* and two angles *trim1* and *trim2* specified in the local coordinate system :ref:`MbPlacement3D <MbPlacement3D_Local_Coordinate_System_>` **position**.

The angles *trim1* and *trim2* are measured along the arc in the direction of motion from the **position.axisX** vector to the **position.axisY** vector. The angles *trim1* and *trim2* will be called trimming parameters. The trimming parameter values equal to zero and 2π correspond to the point on the coordinate axis **position.axisX**.
The curve parameter *t* takes values on the interval 0 ≤ *t* ≤ *trim2* – *trim1*. The curve may be periodic. For a periodic curve, *trim2* – *trim1* = 2π.

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

.. math::

   \mathbf{r}(t) = \mathbf{position.origin} +
   a \cos(\mathit{trim1} + t)\,\mathbf{position.axisX} +
   b \sin(\mathit{trim1} + t)\,\mathbf{position.axisY}.

The elliptical arc is shown in the figure: 

.. figure:: /MODELER/CURVES/pictures/O.4.4.1.png
   :width: 15cm
   :align: center

The radii of the curve must be greater than zero: *a* > 0, *b* > 0. The trimming parameters must satisfy the inequalities *trim1* < *trim2*. 

The local coordinate system **position** may be either right-handed or left-handed.