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.. |br| raw:: html

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Surfaces of translation
=================================================================================

See also: https://en.wikipedia.org/wiki/Translation_surface_(differential_geometry)

See also:http://www.3d-meier.de/tut3/Seite0.html

See also: https://en.wikipedia.org/wiki/Implicit_surface



Regular polygone as generator
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See also  Wikipedia :cite:p:`Wikipedia2D101`,  MathWorld :cite:p:`Wolfram3D101`.


|10a_Triangle_surface| `\quad` |10a_Square_surface| `\quad` |10a_Circle_surface|



.. |10a_Triangle_surface| image:: ../_static/TranslationSurfaces/Triangle/10a_Triangle_surface.3D.xml.jpg
   :width: 30 %


.. |10a_Square_surface| image:: ../_static/TranslationSurfaces/Square/10a_Square_surface.3D.xml.jpg
   :width: 30 %


.. |10a_Circle_surface| image:: ../_static/TranslationSurfaces/Circle/10a_Circle_surface.3D.xml.jpg
   :width: 30 %



**Left figure**: Triangle surface

**Middle figure**: Square surface

**Right figure**: Circle surface






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Hypocycloid as generator
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// see also: http://www.3d-meier.de/tut3/Seite152.html


See also  Wikipedia :cite:p:`Wikipedia2D101`,  MathWorld :cite:p:`Wolfram3D101`.




|10a_Hypocycloid_surface|



.. |10a_Hypocycloid_surface| image:: ../_static/TranslationSurfaces/Hypocycloid/10a_Hypocycloid_surface.3D.xml.jpg
   :width: 30 %


**Left figure**: Hypocycloid surface





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Archimedes spiral as generator
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// see http://www.3d-meier.de/tut3/Seite187.html
// see Krivoshapko, p. 498


See also  Wikipedia :cite:p:`Wikipedia2D101`,  MathWorld :cite:p:`Wolfram3D101`.




|01a_ArchimedesSpiral_surface| 

.. |01a_ArchimedesSpiral_surface| image:: ../_static/On2DCurves/GenCylinderOpen/01a_ArchimedesSpiral_surface.3D.xml.jpg
   :width: 30 %


**Left figure**: Archimedes spiral surface









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Fermat spiral as generator
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// see http://www.3d-meier.de/tut3/Seite189.html


See also  Wikipedia :cite:p:`Wikipedia2D101`,  MathWorld :cite:p:`Wolfram3D101`.




|02a_FermatSpiral_surface| 

.. |02a_FermatSpiral_surface| image:: ../_static/On2DCurves/GenCylinderOpen/02a_FermatSpiral_surface.3D.xml.jpg
   :width: 30 %



**Left figure**: Fermat spiral surface