.. role:: blue
   :class: blue

Construction of a Regular Polygon
=================================
.. _Construction_of_a_Regular_Polygon_:

.. kernel version: 118058

The function

.. code-block:: cpp

   MbResultType RegularPolygon( const MbCartPoint3D &  centre,
                                const MbCartPoint3D &  point,
                                const MbVector3D &     axisZ,
                                      size_t           vertexCount,
                                      bool             describe,
                                      MbCurve3D *&     result )

constructs a regular polygon inscribed in a specified circle or
circumscribed about the circle.

The function parameters are:

- **centre** — the center of the circle circumscribed about the equilateral polygon or inscribed in the equilateral polygon;
- **point** — a point on the circle;
- **axisZ** — the vector perpendicular to the circle plane;
- **vertexCount** — the number of vertices of the polygon;
- **describe** — the flag indicating a circumscribed or an inscribed polygon (*true* — a circumscribed polygon, *false* — an inscribed polygon).

The output parameter of the function is the constructed polyline curve **result**.

If successful, the function returns :blue:`rt_Success`, otherwise
it returns an error code from the :ref:`MbResultType <MbResultType_>` enumeration.

The function is declared in the *action_curve3d.h* file.

The **centre**, **point** and **axisZ** parameters determine
the circle in which the polygon with **vertexCount** vertices is inscribed
(**describe** = *false*) or about which the polygon with
**vertexCount** vertices is circumscribed
(**describe** = *true*).
The center of the circle is located at point **centre**, the circle
passes through **point**, and the axis of the circle is parallel to
the **axisZ** vector.

The **vertexCount** parameter determines the number
of vertices of the regular polygon:

- if **vertexCount** == 0, a circle centered at **centre** and passing through **point** is constructed;
- if **vertexCount** == 1, a line segment with endpoints at **centre** and **point** is constructed;
- if **vertexCount** == 2, a rectangle with sides parallel to the global axes and with opposite vertices at **centre** and **point** is constructed;
- if **vertexCount** >= 3, a regular polygon with the specified number of sides is constructed, inscribed in the circle (**describe** == *false*) or circumscribed about the circle (**describe** == *true*) centered at **centre** and passing through **point**.

The constructed curve is a closed
polyline described in section :ref:`MbPolyline3D Polyline <MbPolyline3D_Polyline_>` (for **vertexCount** >= 3). Fig. 1 shows a regular polygon inscribed in a circle, and Fig. 2 shows a regular polygon circumscribed about a circle:

.. figure:: /MODELER/TWO-DIMENSIONAL_CURVE_CONSTRUCTION_METHODS/pictures/M.3.5.1.png
   :width: 12cm
   :align: center

   Fig. 1

.. figure:: /MODELER/TWO-DIMENSIONAL_CURVE_CONSTRUCTION_METHODS/pictures/M.3.5.2.png
   :width: 12cm
   :align: center

   Fig. 2