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Special techniques for height surfaces, real and complex functions
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The 3D Viewer 
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The formatting of 3D bitmap graphics is done with the following app:


.. image:: ../_static/BuiltIn/Intro/App3D.png
   :width: 50 %
   :align: center

More info to follow.


General Background
---------------------------------------


Rod Stephens: 

WPF 3d: Three-Dimensional Graphics with WPF and C

Herausgeber: CreateSpace Independent Publishing Platform

Erscheinungstermin: 8. Februar 2018

ISBN-10: 1983905968

ISBN-13: 978-1983905964 

Github: https://github.com/WriterRod/WPF-3d-source





3D Bitmaps: Export to JPG and PNG
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These formats are natively supported.






Axes in 3D
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Some text




Positioning 3D objects
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Some text



Resizing 3D objects
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Some text






Rotating 3D objects
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Some text






Translating 3D objects
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Some text




Solid colors
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Some text



Wireframes
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Some text




Textures
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Some text




Transparency
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Some text



.. _rst_wpf_complex_function: 

Wpf figures as standard display of complex functions
-------------------------------------------------------------

This is a description of the standard display of complex functions, using the square function as an example:


The figures below are showing the real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex function `z = \mathrm{sqr}(x + iy)` with  `-2 \le x \le 2` (blue axis), `-2 \le y \le 2` (red axis), `-10 \le z \le 10` (green axis).



|01a_TestSquare_re1| `\quad` |01b_TestSquare_im1| `\quad` |01c_TestSquare_abs1|

.. |01a_TestSquare_re1| image:: ../_static/ExplicitSurfaces/CplxRoots/01a_TestSquare_re.3D.xml.jpg
   :width: 30 %

.. |01b_TestSquare_im1| image:: ../_static/ExplicitSurfaces/CplxRoots/01b_TestSquare_im.3D.xml.jpg
   :width: 30 %

.. |01c_TestSquare_abs1| image:: ../_static/ExplicitSurfaces/CplxRoots/01c_TestSquare_abs.3D.xml.jpg
   :width: 30 %



.. note::
    Although the range of the green axis is stated in the form `z_{\text{min}} \le z \le z_{\text{max}}`, with `z_{\text{min}} \ne 0` in general, this applies only for the figures showing the real and imaginary part. For the figure showing the absolute value we have always `z_{\text{min}} = 0`. This note is omitted from the standard text describing complex functions in this manual for better readability.






.. _rst_mpm_loglog_transformation: 

Truncation vs loglog transformation
---------------------------------------------------



|TestTruncated| `\quad` |TestLogLog|

.. |TestTruncated| image:: ../_static/ExplicitSurfaces/Intro/01a_TestLogLogErf_abs.3D.xml.jpg
   :width: 30 %

.. |TestLogLog| image:: ../_static/ExplicitSurfaces/Intro/01b_TestLogLogErf_abs.3D.xml.jpg
   :width: 30 %


**Left figure**: Surface plot without cutting of the branch cut. Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.


**Right figure**: Surface plot with cutting of the branch cut. Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.





Displaying branch cuts
-----------------------------------------------------



|TestWithoutCut| `\quad` |TestWithCut|

.. |TestWithoutCut| image:: ../_static/ExplicitSurfaces/Intro/02a_TestBranchCutsLog_im.3D.xml.jpg
   :width: 30 %

.. |TestWithCut| image:: ../_static/ExplicitSurfaces/Intro/02b_TestBranchCutsLog_im.3D.xml.jpg
   :width: 30 %

**Left figure**: Surface plot without cutting of the branch cut. Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.


**Right figure**: Surface plot with cutting of the branch cut. Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.