Merge from V6_main 15/03/2013

[tools/medcoupling.git] / doc / doxygen / interptheory.dox

diff --git a/doc/doxygen/interptheory.dox b/doc/doxygen/interptheory.dox
index f53984c828de6ea3ec885af3bd3c0ab32cab4f87..4fd32b8bbbe55e2681197b81f51d4c16628f1924 100644 (file)
--- a/doc/doxygen/interptheory.dox
+++ b/doc/doxygen/interptheory.dox
@@ -8,8 +8,8 @@ For fields with polynomial representation on each cell, the components of the di
 \f]
 
 \f$W\f$ is called the \anchor interpolationmatrix interpolation matrix.
-The objectives of interpolators is to compute the matrix W depending on their physical
-properties (\ref IntExtFields) and their mesh discretisation (P0, P1,...).
+The objective of interpolators is to compute the matrix W depending on their physical
+properties (\ref IntExtFields) and their mesh discretisation (on cells P0, on nodes P1,...).
 
 \section ConsInterp Conservative interpolation
 
@@ -42,9 +42,10 @@ fully overlapped by cells of S that is
 \sum_{S_j} Vol(T_i\cap S_j) = Vol(T_i),\hspace{1cm} and \hspace{1cm} \sum_{T_i} Vol(S_j\cap T_i) = Vol(S_j)
 \f]
 then the meshes S and T are said to be \b
-overlapping and all the algorithms will return the same results.
+overlapping. In this case the two formulas in a given column in the table below give the same
+result. All intensive formulas result in the same output, and all the extensive formulas give also the same output. 
 
-The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ in the formula one obtains an algorithm that respects either conservativity either the maximum principle (see the nature of field \ref TableNatureOfField "summary table").
+The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ one obtains an algorithm that respects either the conservativity or the maximum principle (see the nature of field \ref TableNatureOfField "summary table").
 
 
 \section InterpKerRemapInt Linear conservative remapping of P0 (cell based) fields
@@ -109,7 +110,7 @@ given by the formula :
 \f]
 
 \section TableNatureOfField Summary 
-In the case of fields with P0 representation, if the meshes do not overlap the scheme is either conservative or maximum preserving (not both) and depending on the prioritised property and the \ref NatureOfField the interpolation coefficients take the following value
+In the case of fields with a P0 representation (cell based) and when the meshes do not overlap, the scheme is either conservative or maximum preserving (not both). Depending on the \ref NatureOfField the interpolation coefficients take the following value:
 
  * <TABLE BORDER=1 >
  * <TR><TD> </TD><TD>Intensive</TD><TD> extensive </TD></TR>