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Add new capabilities
- module -T: added -ori odf, added -orisampling, improved -domain rodrigues, added -statcell scale and voxnb, fixed -morpho cube, fixed -transform rmsat, improved geo format, cleaned code, made minor fixes and improvements. - module -M: added -statelt vol_orispace, added -meshedge, -meshface and -meshpoly, made other minor improvements. - module -S: fixed -res... '\<result>` (result overwriting), made minor improvements to the simulation directory. - general: added tutorials "Generating and Meshing a Fundamental Region of Orientation Space" and "Specifying Orientation Information for Tessellation Cells", improved installation instructions, added developer documentation, added CMAKE_INSTALL_COMPLETION.
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‎VERSIONS‎

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New in 4.6.2-14 (08 Nov 2023):
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- module -T: fixed -transform rmsat and -transform cut, added -statcell scale,
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added -statcell voxnb, improved geo format, made minor fixes and
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improvements.
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- module -M: made minor improvements.
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- module -S: fixed -res... '\<result>` (result overwriting).
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- documentation: made minor improvements.
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- general: improved installation instructions.
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New in 4.7.0 (17 Nov 2023):
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- module -T: added -ori odf, added -orisampling, improved -domain rodrigues,
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added -statcell scale and voxnb, fixed -morpho cube, fixed -transform rmsat,
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improved geo format, cleaned code, made minor fixes and improvements.
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- module -M: added -statelt vol_orispace, added -meshedge, -meshface and
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-meshpoly, made other minor improvements.
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- module -S: fixed -res... '\<result>` (result overwriting), made minor
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improvements to the simulation directory.
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- general: added tutorials "Generating and Meshing a Fundamental Region of
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Orientation Space" and "Specifying Orientation Information for Tessellation
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Cells", improved installation instructions, added developer documentation,
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added CMAKE_INSTALL_COMPLETION.
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* Incompatible changes: In -T, now use `-orisampling uniform' in place of
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`-ori uniform'. Renamed CMAKE_INSTALL_PREFIX_COMPLETION into
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CMAKE_INSTALL_COMPLETION_PREFIX.
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New in 4.6.1 (12 Sep 2023):
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- module -T: fixed -domain cylinder and circle, fixed tesr reading, made minor

‎doc-dev/1dlaguerre.rst‎

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.. _1dmeshing:
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1-D Laguerre Tessellation
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=========================
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A Voronoi tessellation use an Euclidean distance, which in 1D is
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.. math::
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\begin{equation}
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{d_E(p_i,\,q)}^2 = (p_i - q)^2.
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\end{equation}
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In Laguerre geometry, the distance is
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.. math::
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\begin{equation}
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{d_L(p_i,\,q)}^2 = {d_E(p_i,\,q)}^2 - w_i.
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\end{equation}
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The interface between two points :math:`p_i` and :math:`p_j`, of coordinate :math:`q`, is such
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that
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.. math::
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\begin{equation}
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{d_L(p_i,\,q)}^2 = {d_L(p_j,\,q)}^2,
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\end{equation}
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which can be rewritten as
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.. math::
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\begin{equation}
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{d_E(p_i,\,q)}^2 - w_i = {d_E(p_j,\,q)}^2 - w_j,
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\end{equation}
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and so
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.. math::
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\begin{equation}
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{(p_i - q)}^2 - w_i = {(p_j - q)}^2 - w_j,
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\end{equation}
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.. math::
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\begin{equation}
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{p_i}^2 - 2\,p_i\,q + q^2 - w_i
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= {p_j}^2 - 2\,p_j\,q + q^2 - w_j,
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\end{equation}
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.. math::
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\begin{equation}
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-2\,(p_i-p_j)\,q
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= w_i - w_j
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- ({p_i}^2 - {p_j}^2),
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\end{equation}
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.. math::
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\begin{equation}
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q
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= \frac{1}{2}\,(p_i + p_j)
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- \frac{1}{2}\,\frac{w_i - w_j}
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{p_i-p_j}.
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\end{equation}
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It follows that
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.. math::
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\begin{equation}
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q - p_i
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= \frac{1}{2}\,(p_j - p_i)
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- \frac{1}{2}\,\frac{w_i - w_j}
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{p_i-p_j},
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\end{equation}
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or
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.. math::
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\begin{equation}
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q - p_i
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= \frac{1}{2}\,(p_j - p_i)
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- \frac{1}{2}\,\frac{w_j - w_i}
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{p_j-p_i}.
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\end{equation}
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‎doc-dev/1dmeshing.rst‎

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.. _1dmeshing:
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1-D Meshing
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===========
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We consider the 1-D meshing of a unit length segment. The variables are
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- :math:`c_l`: the target element size,
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- :math:`{c_l}_1`: the characteristic length at vertex 1,
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- :math:`{c_l}_2`: the characteristic length at vertex 2,
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- :math:`p_l`: the element size progression factor.
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We have the following identities:
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.. math::
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\begin{equation}
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0 < {c_l}_1 \leq {c_l}\hbox{,} \qquad
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0 < {c_l}_2 \leq {c_l}\hbox{,} \qquad
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{c_l}_1 \leq {c_l}_2\hbox{,} \qquad
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{p_l} > 1
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\end{equation}
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The element size is increased following a geometric progression from the
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boundaries towards the body of the segment.
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..
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\begin{center}
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\begin{figure}[htp]
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\begin{center}
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%
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\includegraphics{fig/1dmesh-prog.pdf}
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\caption{1-D mesh.}
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\end{center}
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\end{figure}
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\end{center}
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.. image:: imgs/1dmesh-prog.png
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Transition to the target characteristic length at the boundaries
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----------------------------------------------------------------
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When considering mesh element size progression from one extremity, the characteristic length at node :math:`i` (:math:`i=1,\dots,n`), :math:`c_l(i)`, is given by,
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.. math::
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:label: cl
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\begin{equation}
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c_l (i) = {c_l}_1 \, {p_l}^{i-1}
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\end{equation}
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Let :math:`x(i)` be the coordinate of point :math:`i`, :math:`c_l(x)` be the characteristic length at coordinate :math:`x`, :math:`n` be the number of nodes necessary to reach :math:`c_l/p_l` (i.e. the
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value necessary to enable an element size of :math:`c_l` in the rest of the edge), and :math:`l` be the length necessary to reach :math:`c_l/p_l`. It follows from Equation :eq:`cl` that
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.. math::
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:label: x
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\begin{equation}
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x(i) = {c_l}_1 \, \frac{{p_l}^{i-1} - 1}{p_l - 1} \qquad
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\left(\Leftrightarrow i = 1 + \lfloor\frac{\ln{\left(1 + \left(p_l-1\right) \, \frac{x}{{c_l}_1}\right)}}
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{\ln{p_l}}\rfloor \right)
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\end{equation}
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.. math::
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:label: clx
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\begin{equation}
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c_l (x) = {c_l}_1 + \left(p_l-1\right) \, x
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\end{equation}
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.. math::
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:label: n
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\begin{equation}
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n = 1 + \lceil\frac{\ln\left(c_l/{c_l}_1\right)}
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{\ln{p_l} }\rceil
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\end{equation}
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.. math::
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:label: l
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\begin{equation}
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l = {c_l}_1\,\frac{p_l^{n-1} - 1}{p_l - 1}
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\qquad \left( = \frac{c_l - {c_l}_1}{p_l - 1}\hbox{ if }n\hbox{ was real}\right)
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\end{equation}
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where :math:`\lfloor\bullet\rfloor` is the largest previous integer of :math:`\bullet`.
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Meshing
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-------
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The segment mesh is subdivided into 3 parts: the :math:`c_l`-progression parts
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at both extremities and the body of the segment. The number of
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nodes/elements in each parts must be determined, as well as their
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coordinates.
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The coordinate where the characteristic lengths progressed from the two
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extremities are equal, called :math:`I`, is given by,
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.. math::
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\begin{equation}
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I = \frac{1}{2} \, \left[
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1 + \frac{p_l}{p_l - 1} \left({c_l}_2 - {c_l}_1\right)
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\right]
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\qquad
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\left(I \geq \frac{1}{2}\right)
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\end{equation}
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- :math:`I>1`: 1 segment only
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If :math:`I > 1`, :math:`{c_l}_2` cannot be reached using the progression
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factor :math:`p_l`. A greater value must be used. It follows from
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Equation :eq:`clx` that,
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.. math::
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\begin{equation}
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{p_l}^\prime = 1 + {c_l}_2 - {c_l}_1
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\end{equation}
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- :math:`I \leq 1`
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The characteristic length at :math:`I`, :math:`{c_l}_I`, can be obtained from
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Equation :eq:`cl` and is equal to,
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.. math::
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\begin{equation}
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{c_l}_I = {c_l}\left(I\right)
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= \frac{1}{2} \, \left( {c_l}_1 + {c_l}_2 + \frac{p_l - 1}{p_l} \right)
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\end{equation}
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If :math:`{c_l}_I < c_l / p_l`, then the edge will be divided into two :math:`c_l`-progression parts.
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The number of nodes in the progression parts are
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.. math::
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\begin{equation}
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n_1 = f\left(\frac{\ln{\left({c_l}_I / {c_l}_1\right)}}
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{\ln{\left(p_l\right)}}
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\right)
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\qquad
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n_2 = f\left( \frac{\ln{\left({c_l}_I / {c_l}_2\right)}}
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{\ln{\left(p_l\right)}}
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\right)
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\end{equation}
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The lengths of the progression parts can be obtained from Equation :eq:`l` and are denoted :math:`l_1` and :math:`l_2`. They are such that
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.. math::
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\begin{equation}
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0 \leq \Delta l = 1 - \left(l_1 + l_2\right) \leq 2\,{c_l}_I
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\end{equation}

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