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50 lines
2.2 KiB
Plaintext
50 lines
2.2 KiB
Plaintext
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/*!
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\page quad_ijk_algo_page Quadrangle (Mapping) meshing algorithm
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<b>Quadrangle (Mapping)</b> meshing algorithm is intended for creating
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all-quadrangle and quad-dominant meshes on faces with no 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 mesh quality and
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validity depends on two factors:
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- face shape (number of edges and concavity of boundary);
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- discretization of edges.
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\image html quad_mesh_invalid.png "Invalid mesh on quadrilateral concave faces"
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The algorithm uses <em>Transfinite Interpolation</em> technic in
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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 a 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 degenerated side of the
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quadrangle.
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\image html quad_meshes.png "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 \b structured mesh you have to assure
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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 (with no
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hypothesis) creates \b quad-dominant mesh with triangles located near a
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side with maximal number of segments. But you can get an
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\b all-quadrangle mesh in this case by using
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\ref hypo_quad_params_anchor "Quadrangle Parameters"
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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 total number of segments must be
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even. To use \a Reduced transition method there must be equal number
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of segments on one pair of opposite sides.
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The following hypotheses help in creation of quadrangle meshes.
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- \ref propagation_anchor "Propagation" additional 1D hypotheses
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help to get equal number of segments on opposite sides of the
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quadrilateral face.
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- \ref a1d_algos_anchor "Composite Side Discretization" algorithm is useful
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to discretize several C1 continues edges as one quadrangle side.
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*/
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