--- /dev/null
+.. _quad_ijk_algo_page:
+
+*************************************
+Quadrangle: Mapping meshing algorithm
+*************************************
+
+**Quadrangle: Mapping** meshing algorithm is intended for creating
+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 its quality and
+validity depend on two factors:
+
+* face shape (number of edges and boundary concavity);
+* discretization of edges.
+
+.. image:: ../images/quad_mesh_invalid.png
+ :align: center
+
+.. centered::
+ "Invalid mesh on quadrilateral concave faces"
+
+The algorithm uses *Transfinite Interpolation* technique in the
+parametric space of a face to locate nodes inside the face.
+
+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
+specified by the user is considered as a fourth degenerated side of the
+quadrangle.
+
+.. image:: ../images/quad_meshes.png
+ :align: center
+
+.. centered::
+ 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 **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 (without a
+hypothesis) creates a **quad-dominant** mesh with triangles located near the
+side with the maximal number of segments. However, you can get an
+**all-quadrangle** mesh in this case by using
+:ref:`hypo_quad_params_anchor` 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 the total number of segments must be
+even. To use *Reduced* transition method, there must be an equal number
+of segments on one pair of opposite sides.
+
+The following hypotheses help to create quadrangle meshes.
+
+* :ref:`Propagation <propagation_anchor>` additional 1D hypotheses help to get an equal number of segments on the opposite sides of a quadrilateral face.
+* :ref:`Composite Side Discretization <a1d_algos_anchor>` algorithm is useful to discretize several C1 continuous edges as one quadrangle side.
