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58 lines
2.3 KiB
ReStructuredText
58 lines
2.3 KiB
ReStructuredText
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.. _quad_ijk_algo_page:
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*************************************
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Quadrangle: Mapping meshing algorithm
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*************************************
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**Quadrangle: Mapping** meshing algorithm is intended for creating
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all-quadrangle and quad-dominant meshes on faces without holes and
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bound by at least three edges.
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The algorithm can create mesh on any face but its quality and
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validity depend on two factors:
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* face shape (number of edges and boundary concavity);
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* discretization of edges.
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.. image:: ../images/quad_mesh_invalid.png
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:align: center
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.. centered::
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"Invalid mesh on quadrilateral concave faces"
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The algorithm uses **Transfinite Interpolation** technique in the
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parametric space of a face to locate nodes inside the face.
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The algorithm treats any face as quadrangle. If a face is bound by
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more than four edges, four most sharp vertices are considered as
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corners of the quadrangle and all edges between these vertices are
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treated as quadrangle sides. In the case of three edges, the vertex
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specified by the user is considered as a fourth degenerated side of the
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quadrangle.
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.. image:: ../images/quad_meshes.png
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:align: center
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.. centered::
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"Algorithm generates a structured mesh on complex faces provided that edges are properly discretized"
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To get an all-quadrangle mesh you have to carefully define 1D
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hypotheses on edges of a face. To get a **structured** mesh you have to provide
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equal number of segments on opposite sides of the quadrangle. If this
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condition is not respected, the algorithm by default (without a
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hypothesis) creates a **quad-dominant** mesh with triangles located near the
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side with the maximal number of segments. However, you can get an
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**all-quadrangle** mesh in this case by using
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:ref:`hypo_quad_params_anchor` hypothesis to specify how to make transition mesh between opposite
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sides with different number of segments, provided that certain
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conditions are respected. In any case the total number of segments must be
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even. To use *Reduced* transition method, there must be an equal number
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of segments on one pair of opposite sides.
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The following hypotheses help to create quadrangle meshes.
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* :ref:`propagation_anchor` additional 1D hypotheses help to get an equal number of segments on the opposite sides of a quadrilateral face.
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* :ref:`a1d_algos_anchor` algorithm is useful to discretize several C1 continuous edges as one quadrangle side.
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