:class:`TorusEvaluation`
========================

.. py:class:: ansys.geometry.core.shapes.surfaces.torus.TorusEvaluation(torus: Torus, parameter: ansys.geometry.core.shapes.parameterization.ParamUV)

   Bases: :py:obj:`ansys.geometry.core.shapes.surfaces.surface_evaluation.SurfaceEvaluation`


   
   Evaluate the torus`` at given parameters.


   :Parameters:

       **Torus: ~ansys.geometry.core.shapes.surfaces.torus.Torus**
           Torust to evaluate.

       **parameter: ParamUV**
           Parameters (u, v) to evaluate the torus at.














   ..
       !! processed by numpydoc !!


.. py:currentmodule:: TorusEvaluation

Overview
--------

.. tab-set::




   .. tab-item:: Properties

      .. list-table::
          :header-rows: 0
          :widths: auto

          * - :py:attr:`~torus`
            - Torus being evaluated.
          * - :py:attr:`~parameter`
            - Parameter that the evaluation is based upon.
          * - :py:attr:`~position`
            - Position of the evaluation.
          * - :py:attr:`~normal`
            - Normal to the surface.
          * - :py:attr:`~u_derivative`
            - First derivative with respect to the U parameter.
          * - :py:attr:`~v_derivative`
            - First derivative with respect to the V parameter.
          * - :py:attr:`~uu_derivative`
            - Second derivative with respect to the U parameter.
          * - :py:attr:`~uv_derivative`
            - Second derivative with respect to the U and V parameters.
          * - :py:attr:`~vv_derivative`
            - Second derivative with respect to the V parameter.
          * - :py:attr:`~curvature`
            - Curvature of the torus.
          * - :py:attr:`~min_curvature`
            - Minimum curvature of the torus.
          * - :py:attr:`~min_curvature_direction`
            - Minimum curvature direction.
          * - :py:attr:`~max_curvature`
            - Maximum curvature of the torus.
          * - :py:attr:`~max_curvature_direction`
            - Maximum curvature direction.


   .. tab-item:: Attributes

      .. list-table::
          :header-rows: 0
          :widths: auto

          * - :py:attr:`~cache`
            - 






Import detail
-------------

.. code-block:: python

    from ansys.geometry.core.shapes.surfaces.torus import TorusEvaluation

Property detail
---------------
.. py:property:: torus
   :type: Torus

   
   Torus being evaluated.
















   ..
       !! processed by numpydoc !!

.. py:property:: parameter
   :type: ansys.geometry.core.shapes.parameterization.ParamUV

   
   Parameter that the evaluation is based upon.
















   ..
       !! processed by numpydoc !!

.. py:property:: position
   :type: ansys.geometry.core.math.point.Point3D

   
   Position of the evaluation.





   :Returns:

       :obj:`Point3D`
           Point that lies on the torus at this evaluation.











   ..
       !! processed by numpydoc !!

.. py:property:: normal
   :type: ansys.geometry.core.math.vector.UnitVector3D

   
   Normal to the surface.





   :Returns:

       :obj:`UnitVector3D`
           Normal unit vector to the torus at this evaluation.











   ..
       !! processed by numpydoc !!

.. py:property:: u_derivative
   :type: ansys.geometry.core.math.vector.Vector3D

   
   First derivative with respect to the U parameter.





   :Returns:

       :obj:`Vector3D`
           First derivative with respect to the U parameter.











   ..
       !! processed by numpydoc !!

.. py:property:: v_derivative
   :type: ansys.geometry.core.math.vector.Vector3D

   
   First derivative with respect to the V parameter.





   :Returns:

       :obj:`Vector3D`
           First derivative with respect to the V parameter.











   ..
       !! processed by numpydoc !!

.. py:property:: uu_derivative
   :type: ansys.geometry.core.math.vector.Vector3D

   
   Second derivative with respect to the U parameter.





   :Returns:

       :obj:`Vector3D`
           Second derivative with respect to the U parameter.











   ..
       !! processed by numpydoc !!

.. py:property:: uv_derivative
   :type: ansys.geometry.core.math.vector.Vector3D

   
   Second derivative with respect to the U and V parameters.





   :Returns:

       :obj:`Vector3D`
           Second derivative with respect to the U and V parameters.











   ..
       !! processed by numpydoc !!

.. py:property:: vv_derivative
   :type: ansys.geometry.core.math.vector.Vector3D

   
   Second derivative with respect to the V parameter.





   :Returns:

       :obj:`Vector3D`
           Second derivative with respect to the V parameter.











   ..
       !! processed by numpydoc !!

.. py:property:: curvature
   :type: tuple[ansys.geometry.core.typing.Real, ansys.geometry.core.math.vector.Vector3D, ansys.geometry.core.typing.Real, ansys.geometry.core.math.vector.Vector3D]

   
   Curvature of the torus.





   :Returns:

       :class:`python:tuple`\[:obj:`Real`, :obj:`Vector3D`, :obj:`Real`, :obj:`Vector3D`]
           Minimum and maximum curvature value and direction, respectively.











   ..
       !! processed by numpydoc !!

.. py:property:: min_curvature
   :type: ansys.geometry.core.typing.Real

   
   Minimum curvature of the torus.





   :Returns:

       :obj:`Real`
           Minimum curvature of the torus.











   ..
       !! processed by numpydoc !!

.. py:property:: min_curvature_direction
   :type: ansys.geometry.core.math.vector.UnitVector3D

   
   Minimum curvature direction.





   :Returns:

       :obj:`UnitVector3D`
           Minimum curvature direction.











   ..
       !! processed by numpydoc !!

.. py:property:: max_curvature
   :type: ansys.geometry.core.typing.Real

   
   Maximum curvature of the torus.





   :Returns:

       :obj:`Real`
           Maximum curvature of the torus.











   ..
       !! processed by numpydoc !!

.. py:property:: max_curvature_direction
   :type: ansys.geometry.core.math.vector.UnitVector3D

   
   Maximum curvature direction.





   :Returns:

       :obj:`UnitVector3D`
           Maximum curvature direction.











   ..
       !! processed by numpydoc !!



Attribute detail
----------------
.. py:attribute:: cache