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47 lines
1.9 KiB
ReStructuredText
47 lines
1.9 KiB
ReStructuredText
.. _quad_from_ma_algo_page:
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***************************************************
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Medial Axis Projection Quadrangle meshing algorithm
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***************************************************
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Medial Axis Projection algorithm can be used for meshing faces with
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sinuous borders and a channel-like shape, for which it can be
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difficult to define 1D hypotheses such that to obtain a good shape of
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resulting quadrangles. The algorithm can be also applied to faces with ring
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topology, which can be viewed as a closed 'channel'. In the latter
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case radial discretization of a ring can be specified by
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using *Number of Layers* or *Distribution of Layers*
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hypothesis.
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.. image:: ../images/quad_from_ma_mesh.png
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:align: center
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.. centered::
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A mesh of a river model (to the left) and of a ring-face (to the right)
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The algorithm provides proper shape of quadrangles by constructing Medial
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Axis between sinuous borders of the face and using it to
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discretize the borders. (Shape of quadrangles can be not perfect at
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locations where opposite sides of a 'channel' are far from being parallel.)
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.. image:: ../images/quad_from_ma_medial_axis.png
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:align: center
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.. centered::
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Medial Axis between two blue sinuous borders
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The Medial Axis is used in two ways:
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#. If there is a sub-mesh on a sinuous border, then the nodes of this border are mapped to the opposite border via the Medial Axis.
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#. If there are no sub-meshes on sinuous borders, then the part of the Medial Axis that can be mapped to both borders is discretized using a 1D hypothesis assigned to the face or its ancestor shapes, and the division points are mapped from the Medial Axis to both borders to find positions of nodes.
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.. image:: ../images/quad_from_ma_ring_mesh.png
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:align: center
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.. centered::
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Mesh depends on defined sub-meshes: to the left - sub-meshes on both wires, to the right - a sub-mesh on internal wire only
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**See Also** a sample TUI Script of a :ref:`tui_quad_ma_proj_algo`.
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