\page quad_ijk_algo_page Quadrangle (Mapping) meshing algorithm
<b>Quadrangle (Mapping)</b> meshing algorithm is intended for creating
-all-quadrangle and quad-dominant meshes on faces with no holes and
+all-quadrangle and quad-dominant meshes on faces without holes and
bound by at least three edges.
-The algorithm can create mesh on any face but mesh quality and
-validity depends on two factors:
-- face shape (number of edges and concavity of boundary);
+The algorithm can create mesh on any face but its quality and
+validity depend on two factors:
+- face shape (number of edges and boundary concavity);
- discretization of edges.
\image html quad_mesh_invalid.png "Invalid mesh on quadrilateral concave faces"
-The algorithm uses <em>Transfinite Interpolation</em> technic in
+The algorithm uses <em>Transfinite Interpolation</em> technique in the
parametric space of a face to locate nodes inside the face.
-The algorithm treats any face as a quadrangle. If a face is bound by
+The algorithm treats any face as quadrangle. If a face is bound by
more than four edges, four most sharp vertices are considered as
corners of the quadrangle and all edges between these vertices are
treated as quadrangle sides. In the case of three edges, the vertex
\image html quad_meshes.png "Algorithm generates a structured mesh on complex faces provided that edges are properly discretized"
To get an all-quadrangle mesh you have to carefully define 1D
-hypotheses on edges of a face. To get a \b structured mesh you have to assure
+hypotheses on edges of a face. To get a \b structured mesh you have to provide
equal number of segments on opposite sides of the quadrangle. If this
-condition is not respected, the algorithm by default (with no
-hypothesis) creates \b quad-dominant mesh with triangles located near a
-side with maximal number of segments. But you can get an
+condition is not respected, the algorithm by default (without a
+hypothesis) creates a \b quad-dominant mesh with triangles located near the
+side with the maximal number of segments. However, you can get an
\b all-quadrangle mesh in this case by using
\ref hypo_quad_params_anchor "Quadrangle Parameters"
hypothesis to specify how to make transition mesh between opposite
sides with different number of segments, provided that certain
-conditions are respected. In any case total number of segments must be
-even. To use \a Reduced transition method there must be equal number
+conditions are respected. In any case the total number of segments must be
+even. To use \a Reduced transition method, there must be an equal number
of segments on one pair of opposite sides.
-The following hypotheses help in creation of quadrangle meshes.
+The following hypotheses help to create quadrangle meshes.
- \ref propagation_anchor "Propagation" additional 1D hypotheses
- help to get equal number of segments on opposite sides of the
+ help to get an equal number of segments on the opposite sides of a
quadrilateral face.
- \ref a1d_algos_anchor "Composite Side Discretization" algorithm is useful
- to discretize several C1 continues edges as one quadrangle side.
+ to discretize several C1 continuous edges as one quadrangle side.
*/
