return aHeight;
}
+ //================================================================================
+ /*!
+ * \brief Standard quality of a tetrahedron but not normalized
+ */
+ //================================================================================
+
+ double tetQualityByHomardMethod( const gp_XYZ & p1,
+ const gp_XYZ & p2,
+ const gp_XYZ & p3,
+ const gp_XYZ & p4 )
+ {
+ gp_XYZ edgeVec[6];
+ edgeVec[0] = ( p1 - p2 );
+ edgeVec[1] = ( p2 - p3 );
+ edgeVec[2] = ( p3 - p1 );
+ edgeVec[3] = ( p4 - p1 );
+ edgeVec[4] = ( p4 - p2 );
+ edgeVec[5] = ( p4 - p3 );
+
+ double maxEdgeLen2 = edgeVec[0].SquareModulus();
+ maxEdgeLen2 = Max( maxEdgeLen2, edgeVec[1].SquareModulus() );
+ maxEdgeLen2 = Max( maxEdgeLen2, edgeVec[2].SquareModulus() );
+ maxEdgeLen2 = Max( maxEdgeLen2, edgeVec[3].SquareModulus() );
+ maxEdgeLen2 = Max( maxEdgeLen2, edgeVec[4].SquareModulus() );
+ maxEdgeLen2 = Max( maxEdgeLen2, edgeVec[5].SquareModulus() );
+ double maxEdgeLen = Sqrt( maxEdgeLen2 );
+
+ gp_XYZ cross01 = edgeVec[0] ^ edgeVec[1];
+ double sumArea = ( cross01 ).Modulus(); // actually double area
+ sumArea += ( edgeVec[0] ^ edgeVec[3] ).Modulus();
+ sumArea += ( edgeVec[1] ^ edgeVec[4] ).Modulus();
+ sumArea += ( edgeVec[2] ^ edgeVec[5] ).Modulus();
+
+ double sixVolume = Abs( cross01 * edgeVec[4] ); // 6 * volume
+ double quality = maxEdgeLen * sumArea / sixVolume; // not normalized!!!
+ return quality;
+ }
+
+ //================================================================================
+ /*!
+ * \brief HOMARD method of hexahedron quality
+ * 1. Decompose the hexa into 24 tetra: each face is splitted into 4 triangles by
+ * adding the diagonals and every triangle is connected to the center of the hexa.
+ * 2. Compute the quality of every tetra with the same formula as for the standard quality,
+ * except that the factor for the normalization is not the same because the final goal
+ * is to have a quality equal to 1 for a perfect cube. So the formula is:
+ * qual = max(lengthes of 6 edges) * (sum of surfaces of 4 faces) / (7.6569*6*volume)
+ * 3. The quality of the hexa is the highest value of the qualities of the 24 tetra
+ */
+ //================================================================================
+
+ double hexQualityByHomardMethod( const TSequenceOfXYZ& P )
+ {
+ gp_XYZ quadCenter[6];
+ quadCenter[0] = ( P(1) + P(2) + P(3) + P(4) ) / 4.;
+ quadCenter[1] = ( P(5) + P(6) + P(7) + P(8) ) / 4.;
+ quadCenter[2] = ( P(1) + P(2) + P(6) + P(5) ) / 4.;
+ quadCenter[3] = ( P(2) + P(3) + P(7) + P(6) ) / 4.;
+ quadCenter[4] = ( P(3) + P(4) + P(8) + P(7) ) / 4.;
+ quadCenter[5] = ( P(1) + P(4) + P(8) + P(5) ) / 4.;
+
+ gp_XYZ hexCenter = ( P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) ) / 8.;
+
+ // quad 1 ( 1 2 3 4 )
+ double quality = tetQualityByHomardMethod( P(1), P(2), quadCenter[0], hexCenter );
+ quality = Max( quality, tetQualityByHomardMethod( P(2), P(3), quadCenter[0], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(3), P(4), quadCenter[0], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(4), P(1), quadCenter[0], hexCenter ));
+ // quad 2 ( 5 6 7 8 )
+ quality = Max( quality, tetQualityByHomardMethod( P(5), P(6), quadCenter[1], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(6), P(7), quadCenter[1], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(7), P(8), quadCenter[1], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(8), P(5), quadCenter[1], hexCenter ));
+ // quad 3 ( 1 2 6 5 )
+ quality = Max( quality, tetQualityByHomardMethod( P(1), P(2), quadCenter[2], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(2), P(6), quadCenter[2], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(6), P(5), quadCenter[2], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(5), P(1), quadCenter[2], hexCenter ));
+ // quad 4 ( 2 3 7 6 )
+ quality = Max( quality, tetQualityByHomardMethod( P(2), P(3), quadCenter[3], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(3), P(7), quadCenter[3], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(7), P(6), quadCenter[3], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(6), P(2), quadCenter[3], hexCenter ));
+ // quad 5 ( 3 4 8 7 )
+ quality = Max( quality, tetQualityByHomardMethod( P(3), P(4), quadCenter[4], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(4), P(8), quadCenter[4], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(8), P(7), quadCenter[4], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(7), P(3), quadCenter[4], hexCenter ));
+ // quad 6 ( 1 4 8 5 )
+ quality = Max( quality, tetQualityByHomardMethod( P(1), P(4), quadCenter[5], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(4), P(8), quadCenter[5], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(8), P(5), quadCenter[5], hexCenter ));
+ quality = Max( quality, tetQualityByHomardMethod( P(5), P(1), quadCenter[5], hexCenter ));
+
+ return quality / 7.65685424949;
+ }
}
double AspectRatio3D::GetValue( long theId )
break;
}
case 8:{
+
+ return hexQualityByHomardMethod( P ); // bos #23982
+
+
{
gp_XYZ aXYZ[4] = {P( 1 ),P( 2 ),P( 5 ),P( 3 )};
aQuality = GetValue(TSequenceOfXYZ(&aXYZ[0],&aXYZ[4]));
