diff --git a/doc/salome/gui/SMESH/images/formula5.png b/doc/salome/gui/SMESH/images/formula5.png
new file mode 100644
index 000000000..823ba068d
Binary files /dev/null and b/doc/salome/gui/SMESH/images/formula5.png differ
diff --git a/doc/salome/gui/SMESH/input/aspect_ratio.doc b/doc/salome/gui/SMESH/input/aspect_ratio.doc
index 070d377cc..5e1f31673 100644
--- a/doc/salome/gui/SMESH/input/aspect_ratio.doc
+++ b/doc/salome/gui/SMESH/input/aspect_ratio.doc
@@ -13,10 +13,10 @@ nodes is calculated by the formula:
\image html formula4.png
-- The Aspect Ratio of a \b quadrangle 2D element consisting of
- 4 nodes is the worst (i.e. the greatest) value from all triangles
- which can be built taking three nodes of the quadrangle. There are
- four triangles to consider:
+- The Aspect Ratio of a \b quadrangle 2D element consisting of 4
+nodes is calculated by the formula:
+
+\image html formula5.png
\image html image138.gif
diff --git a/src/Controls/SMESH_Controls.cxx b/src/Controls/SMESH_Controls.cxx
index 4b370e61b..8f18f6605 100644
--- a/src/Controls/SMESH_Controls.cxx
+++ b/src/Controls/SMESH_Controls.cxx
@@ -465,46 +465,92 @@ double AspectRatio::GetValue( const TSequenceOfXYZ& P )
return alfa * maxLen * half_perimeter / anArea;
}
else if( nbNodes == 4 ) { // quadrangle
- // return aspect ratio of the worst triange which can be built
+ // Compute lengths of the sides
+ std::vector< double > aLen (4);
+ aLen[0] = getDistance( P(1), P(2) );
+ aLen[1] = getDistance( P(2), P(3) );
+ aLen[2] = getDistance( P(3), P(4) );
+ aLen[3] = getDistance( P(4), P(1) );
+ // Compute lengths of the diagonals
+ std::vector< double > aDia (2);
+ aDia[0] = getDistance( P(1), P(3) );
+ aDia[1] = getDistance( P(2), P(4) );
+ // Compute areas of all triangles which can be built
// taking three nodes of the quadrangle
- TSequenceOfXYZ triaPnts(3);
- // triangle on nodes 1 3 2
- triaPnts(1) = P(1);
- triaPnts(2) = P(3);
- triaPnts(3) = P(2);
- double ar = GetValue( triaPnts );
- // triangle on nodes 1 3 4
- triaPnts(3) = P(4);
- ar = Max ( ar, GetValue( triaPnts ));
- // triangle on nodes 1 2 4
- triaPnts(2) = P(2);
- ar = Max ( ar, GetValue( triaPnts ));
- // triangle on nodes 3 2 4
- triaPnts(1) = P(3);
- ar = Max ( ar, GetValue( triaPnts ));
-
- return ar;
+ std::vector< double > anArea (4);
+ anArea[0] = getArea( P(1), P(2), P(3) );
+ anArea[1] = getArea( P(1), P(2), P(4) );
+ anArea[2] = getArea( P(1), P(3), P(4) );
+ anArea[3] = getArea( P(2), P(3), P(4) );
+ // Q = alpha * L * C1 / C2, where
+ //
+ // alpha = sqrt( 1/32 )
+ // L = max( L1, L2, L3, L4, D1, D2 )
+ // C1 = sqrt( ( L1^2 + L1^2 + L1^2 + L1^2 ) / 4 )
+ // C2 = min( S1, S2, S3, S4 )
+ // Li - lengths of the edges
+ // Di - lengths of the diagonals
+ // Si - areas of the triangles
+ const double alpha = sqrt( 1 / 32. );
+ double L = Max( aLen[ 0 ],
+ Max( aLen[ 1 ],
+ Max( aLen[ 2 ],
+ Max( aLen[ 3 ],
+ Max( aDia[ 0 ], aDia[ 1 ] ) ) ) ) );
+ double C1 = sqrt( ( aLen[0] * aLen[0] +
+ aLen[1] * aLen[1] +
+ aLen[2] * aLen[2] +
+ aLen[3] * aLen[3] ) / 4. );
+ double C2 = Min( anArea[ 0 ],
+ Min( anArea[ 1 ],
+ Min( anArea[ 2 ], anArea[ 3 ] ) ) );
+ if ( C2 <= Precision::Confusion() )
+ return 0.;
+ return alpha * L * C1 / C2;
}
else if( nbNodes == 8 ){ // nbNodes==8 - quadratic quadrangle
- // return aspect ratio of the worst triange which can be built
+ // Compute lengths of the sides
+ std::vector< double > aLen (4);
+ aLen[0] = getDistance( P(1), P(3) );
+ aLen[1] = getDistance( P(3), P(5) );
+ aLen[2] = getDistance( P(5), P(7) );
+ aLen[3] = getDistance( P(7), P(1) );
+ // Compute lengths of the diagonals
+ std::vector< double > aDia (2);
+ aDia[0] = getDistance( P(1), P(5) );
+ aDia[1] = getDistance( P(3), P(7) );
+ // Compute areas of all triangles which can be built
// taking three nodes of the quadrangle
- TSequenceOfXYZ triaPnts(3);
- // triangle on nodes 1 3 2
- triaPnts(1) = P(1);
- triaPnts(2) = P(5);
- triaPnts(3) = P(3);
- double ar = GetValue( triaPnts );
- // triangle on nodes 1 3 4
- triaPnts(3) = P(7);
- ar = Max ( ar, GetValue( triaPnts ));
- // triangle on nodes 1 2 4
- triaPnts(2) = P(3);
- ar = Max ( ar, GetValue( triaPnts ));
- // triangle on nodes 3 2 4
- triaPnts(1) = P(5);
- ar = Max ( ar, GetValue( triaPnts ));
-
- return ar;
+ std::vector< double > anArea (4);
+ anArea[0] = getArea( P(1), P(3), P(5) );
+ anArea[1] = getArea( P(1), P(3), P(7) );
+ anArea[2] = getArea( P(1), P(5), P(7) );
+ anArea[3] = getArea( P(3), P(5), P(7) );
+ // Q = alpha * L * C1 / C2, where
+ //
+ // alpha = sqrt( 1/32 )
+ // L = max( L1, L2, L3, L4, D1, D2 )
+ // C1 = sqrt( ( L1^2 + L1^2 + L1^2 + L1^2 ) / 4 )
+ // C2 = min( S1, S2, S3, S4 )
+ // Li - lengths of the edges
+ // Di - lengths of the diagonals
+ // Si - areas of the triangles
+ const double alpha = sqrt( 1 / 32. );
+ double L = Max( aLen[ 0 ],
+ Max( aLen[ 1 ],
+ Max( aLen[ 2 ],
+ Max( aLen[ 3 ],
+ Max( aDia[ 0 ], aDia[ 1 ] ) ) ) ) );
+ double C1 = sqrt( ( aLen[0] * aLen[0] +
+ aLen[1] * aLen[1] +
+ aLen[2] * aLen[2] +
+ aLen[3] * aLen[3] ) / 4. );
+ double C2 = Min( anArea[ 0 ],
+ Min( anArea[ 1 ],
+ Min( anArea[ 2 ], anArea[ 3 ] ) ) );
+ if ( C2 <= Precision::Confusion() )
+ return 0.;
+ return alpha * L * C1 / C2;
}
return 0;
}