.. role:: blue
   :class: blue

Constructing a Regular Polygon
==============================
.. _Constructing_Regular_Polygon_:

.. kernel version: 118047

The function

.. code-block:: cpp

   MbResultType RegularPolygon( const MbCartPoint &   centre,
                                const MbCartPoint &   point,
                                      size_t          vertexCount,
                                      bool            describe,
                                      MbCurve *&      result );

constructs a closed two-dimensional polyline representing a regular polygon inscribed in or circumscribed about a specified circle.

Input parameters of the function are:

- **centre** - the center of the circle circumscribed about or inscribed in the regular polygon;
- **point** - a point on the circle;
- **vertexCount** - the number of polygon vertices;
- **describe** - a flag determining the polygon's position relative to the circle.

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

The function returns an operation result code from the enumeration :ref:`MbResultType <MbResultType_>` (see *mb_operation_result.h*).

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

Parameters **centre** and **point** define the circle in which the polygon with *vertexCount* vertices will be inscribed (**describe** = *false*) or about which the polygon with **vertexCount** vertices will be circumscribed (**describe** = *true*).

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

- when **vertexCount** == 0, a circle with center **centre** passing through **point** is constructed;
- when **vertexCount** == 1, a line segment with endpoints at **centre** and **point** is constructed;
- when **vertexCount** == 2, a rectangle with sides parallel to the global axes and opposite vertices at **centre** and **point** is constructed, Fig. 1:

.. figure:: /MODELER/TWO-DIMENSIONAL_CURVE_CONSTRUCTION_METHODS/pictures/M.3.5.3.png
   :width: 9cm
   :align: center

   Fig. 1

- when **vertexCount** >= 3, a regular polygon with the specified number of sides is constructed.

The constructed curve is a closed polyline described in the paragraph :ref:`Two-dimensional polyline MbPolyline <MbPolyline_Two-Dimensional_Polyline_>`. Figure 2 shows a regular polygon inscribed in a circle, and Fig. 3 shows a regular polygon circumscribed about a circle:

.. figure:: /MODELER/TWO-DIMENSIONAL_CURVE_CONSTRUCTION_METHODS/pictures/M.3.5.1.png
   :width: 9cm
   :align: center

   Fig. 2

.. figure:: /MODELER/TWO-DIMENSIONAL_CURVE_CONSTRUCTION_METHODS/pictures/M.3.5.2.png
   :width: 9cm
   :align: center

   Fig. 3

In the test application *test.exe*, construction of a regular polygon is performed via the menu command "Create→Curve on plane→By points→Polygon".