.. role:: blue
   :class: blue

MbExtrusionSurface Extrusion Surface
======================================
.. _MbExtrusionSurface_Extrusion_Surface_:

.. версия ядра: 1180ХХ

The :blue:`MbExtrusionSurface` class is declared in the *surf\_extrusion\_surface.h* file.

The :blue:`MbExtrusionSurface` extrusion surface belongs to the group of
swept surfaces :blue:`MbSweptSurface`. The extrusion surface is a special case
of a swept surface with a rectilinear spine curve. The extrusion surface is described
by the generatrix curve :ref:`MbCurve3D <MbCurve3D_Curve_>` **curve**, the extrusion
direction vector :blue:`MbVector3D` **direction**, and the extrusion length *distance*.

The first surface parameter *u* coincides with the parameter of the generatrix
curve. The first surface parameter takes values on the interval
*umin* ≤ *u* ≤ *umax*, which corresponds to the domain
of the generatrix curve. The surface can be periodic with respect to
the first parameter if the generatrix curve is periodic.

The second surface parameter *v* takes values on the interval:
*vmin* ≤ *v* ≤ *vmax*. The value *v* = 0 corresponds
to a point on the generatrix curve; the value *v* = 1 corresponds to a point
of the generatrix curve displaced by the vector
**direction** \* *distance*. The surface cannot be
periodic with respect to the second parameter.

In the :blue:`PointOn`\( double *u*, double *v*,
:ref:`MbCartPoint3D <MbCartPoint3D_Radius_Vector_of_Point_in_3D_Space_>` & **s** ) method, the position vector of the surface **s**
is described by the vector function

.. math::
   :nowrap:

   \begin{equation}
   \mathbf{s}(u, v) = \mathbf{curve}(u) + \mathbf{direction} \cdot \mathit{distance} \cdot v
   \end{equation}

Figure shows the extrusion surface:

.. figure:: /MODELER/SURFACES/pictures/O.5.7.1.png
   :width: 12cm
   :align: center

The following inequality must hold for the boundary values of the second surface parameter: *vmin* < *vmax*.