diff --git a/Numeric/pointsGenerators.cpp b/Numeric/pointsGenerators.cpp
index 40ac5f17a50b72aa56765283a4bbced84c88447f..d8e15c91f22cfe0c573ded445e1ea81098cd9eed 100644
--- a/Numeric/pointsGenerators.cpp
+++ b/Numeric/pointsGenerators.cpp
@@ -193,3 +193,570 @@ fullMatrix<double> gmshGenerateMonomialsQuadrangle(int order, bool forSerendipPo
}
return monomials;
}
+
+/*
+00 10 20 30 40 �..
+01 11 21 31 41 �..
+02 12
+03 13
+04 14
+�. �.
+*/
+
+fullMatrix<double> gmshGenerateMonomialsQuadSerendipity(int order)
+{
+ int nbMonomials = order ? order*4 : 1;
+ fullMatrix<double> monomials(nbMonomials, 2);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = 1;
+ monomials(1, 1) = 0;
+
+ monomials(2, 0) = 1;
+ monomials(2, 1) = 1;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = 1;
+
+ if (order > 1) {
+ int index = 3;
+ for (int p = 2; p <= order; ++p) {
+ monomials(++index, 0) = p;
+ monomials( index, 1) = 0;
+
+ monomials(++index, 0) = p;
+ monomials( index, 1) = 1;
+
+ monomials(++index, 0) = 1;
+ monomials( index, 1) = p;
+
+ monomials(++index, 0) = 0;
+ monomials( index, 1) = p;
+ }
+ }
+ }
+ return monomials;
+}
+
+//KH : caveat : node coordinates are not yet coherent with node numbering associated
+// to numbering of principal vertices of face !!!!
+fullMatrix<double> gmshGenerateMonomialsTetrahedron(int order, bool serendip)
+{
+ int nbMonomials = serendip ? 4 + (order - 1)*6 : (order + 1)*(order + 2)*(order + 3)/6;
+ if (serendip && !order) nbMonomials = 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = order;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = 0;
+ monomials(2, 1) = order;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = 0;
+ monomials(3, 2) = order;
+
+ // the template has been defined in table edges_tetra and faces_tetra (MElement.h)
+
+ if (order > 1) {
+ int index = 4;
+ for (int iedge = 0; iedge < 6; ++iedge) {
+ int i0 = MTetrahedron::edges_tetra(iedge, 0);
+ int i1 = MTetrahedron::edges_tetra(iedge, 1);
+
+ int u[3];
+ u[0] = (monomials(i1,0)-monomials(i0,0)) / order;
+ u[1] = (monomials(i1,1)-monomials(i0,1)) / order;
+ u[2] = (monomials(i1,2)-monomials(i0,2)) / order;
+
+ for (int i = 1; i < order; ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + u[0] * i;
+ monomials(index, 1) = monomials(i0, 1) + u[1] * i;
+ monomials(index, 2) = monomials(i0, 2) + u[2] * i;
+ }
+ }
+
+ if (!serendip && order > 2) {
+ fullMatrix<double> dudv = gmshGenerateMonomialsTriangle(order - 3);
+ dudv.add(1);
+
+ for (int iface = 0; iface < 4; ++iface) {
+ int i0 = MTetrahedron::faces_tetra(iface, 0);
+ int i1 = MTetrahedron::faces_tetra(iface, 1);
+ int i2 = MTetrahedron::faces_tetra(iface, 2);
+
+ int u[3];
+ u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
+ u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
+ u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
+ int v[3];
+ v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
+ v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
+ v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;
+
+ for (int i = 0; i < dudv.size1(); ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
+ monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
+ monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
+ }
+ }
+
+ if (order > 3) {
+ fullMatrix<double> inner = gmshGenerateMonomialsTetrahedron(order - 4);
+ inner.add(1);
+ monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
+ }
+ }
+ }
+ }
+ return monomials;
+}
+
+fullMatrix<double> gmshGenerateMonomialsPrism(int order, bool forSerendipPoints)
+{
+ int nbMonomials = forSerendipPoints ? 6 + (order-1)*9 :
+ (order + 1)*(order + 1)*(order + 2)/2;
+ if (forSerendipPoints && !order) nbMonomials = 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = order;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = 0;
+ monomials(2, 1) = order;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = 0;
+ monomials(3, 2) = order;
+
+ monomials(4, 0) = order;
+ monomials(4, 1) = 0;
+ monomials(4, 2) = order;
+
+ monomials(5, 0) = 0;
+ monomials(5, 1) = order;
+ monomials(5, 2) = order;
+
+ if (order > 1) {
+ int index = 6;
+ for (int iedge = 0; iedge < 9; ++iedge) {
+ int i0 = MPrism::edges_prism(iedge, 0);
+ int i1 = MPrism::edges_prism(iedge, 1);
+
+ int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
+ int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
+ int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;
+
+ for (int i = 1; i < order; ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + i * u_1;
+ monomials(index, 1) = monomials(i0, 1) + i * u_2;
+ monomials(index, 2) = monomials(i0, 2) + i * u_3;
+ }
+ }
+
+ if (!forSerendipPoints) {
+ fullMatrix<double> dudvQ = gmshGenerateMonomialsQuadrangle(order - 2);
+ dudvQ.add(1);
+
+ fullMatrix<double> dudvT;
+ if (order > 2) {
+ dudvT = gmshGenerateMonomialsTriangle(order - 3);
+ dudvT.add(1);
+ }
+
+ for (int iface = 0; iface < 5; ++iface) {
+ int i0, i1, i2;
+ i0 = MPrism::faces_prism(iface, 0);
+ i1 = MPrism::faces_prism(iface, 1);
+ fullMatrix<double> dudv;
+ if (MPrism::faces_prism(iface, 3) != -1) {
+ i2 = MPrism::faces_prism(iface, 3);
+ dudv.setAsProxy(dudvQ);
+ }
+ else if (order > 2) {
+ i2 = MPrism::faces_prism(iface, 2);
+ dudv.setAsProxy(dudvT);
+ }
+ else continue;
+
+ int u[3];
+ u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
+ u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
+ u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
+ int v[3];
+ v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
+ v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
+ v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;
+
+ for (int i = 0; i < dudv.size1(); ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
+ monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
+ monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
+ }
+ }
+
+ if (order > 2) {
+ fullMatrix<double> triMonomials = gmshGenerateMonomialsTriangle(order - 3);
+ fullMatrix<double> lineMonomials = gmshGenerateMonomialsLine(order - 2);
+
+ for (int i = 0; i < triMonomials.size1(); ++i) {
+ for (int j = 0; j < lineMonomials.size1(); ++j, ++index) {
+ monomials(index, 0) = 1 + triMonomials(i, 0);
+ monomials(index, 1) = 1 + triMonomials(i, 1);
+ monomials(index, 2) = 1 + lineMonomials(j, 0);
+ }
+ }
+ }
+ }
+ }
+ }
+ return monomials;
+}
+
+fullMatrix<double> gmshGenerateMonomialsPrismSerendipity(int order)
+{
+ int nbMonomials = order ? 6 + (order-1) * 9 : 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = 1;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = 0;
+ monomials(2, 1) = 1;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = 0;
+ monomials(3, 2) = 1;
+
+ monomials(4, 0) = 1;
+ monomials(4, 1) = 0;
+ monomials(4, 2) = 1;
+
+ monomials(5, 0) = 0;
+ monomials(5, 1) = 1;
+ monomials(5, 2) = 1;
+
+ if (order > 1) {
+ const int ind[7][3] = {
+ {2, 0, 0},
+ {2, 0, 1},
+
+ {0, 2, 0},
+ {0, 2, 1},
+
+ {0, 0, 2},
+ {1, 0, 2},
+ {0, 1, 2}
+ };
+ int val[3] = {0, 1, -1};
+ int index = 5;
+ for (int p = 2; p <= order; ++p) {
+ val[2] = p;
+ for (int i = 0; i < 7; ++i) {
+ monomials(++index, 0) = val[ind[i][0]];
+ monomials( index, 1) = val[ind[i][1]];
+ monomials( index, 2) = val[ind[i][2]];
+ }
+ }
+
+ int val0 = 1;
+ int val1 = order - 1;
+ for (int p = 2; p <= order; ++p) {
+ monomials(++index, 0) = val0;
+ monomials( index, 1) = val1;
+ monomials( index, 2) = 0;
+
+ monomials(++index, 0) = val0;
+ monomials( index, 1) = val1;
+ monomials( index, 2) = 1;
+
+ ++val0;
+ --val1;
+ }
+ }
+ }
+ return monomials;
+}
+
+fullMatrix<double> gmshGenerateMonomialsHexahedron(int order, bool forSerendipPoints)
+{
+ int nbMonomials = forSerendipPoints ? 8 + (order-1)*12 :
+ (order+1)*(order+1)*(order+1);
+ if (forSerendipPoints && !order) nbMonomials = 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = order;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = order;
+ monomials(2, 1) = order;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = order;
+ monomials(3, 2) = 0;
+
+ monomials(4, 0) = 0;
+ monomials(4, 1) = 0;
+ monomials(4, 2) = order;
+
+ monomials(5, 0) = order;
+ monomials(5, 1) = 0;
+ monomials(5, 2) = order;
+
+ monomials(6, 0) = order;
+ monomials(6, 1) = order;
+ monomials(6, 2) = order;
+
+ monomials(7, 0) = 0;
+ monomials(7, 1) = order;
+ monomials(7, 2) = order;
+
+ if (order > 1) {
+ int index = 8;
+ for (int iedge = 0; iedge < 12; ++iedge) {
+ int i0 = MHexahedron::edges_hexa(iedge, 0);
+ int i1 = MHexahedron::edges_hexa(iedge, 1);
+
+ int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
+ int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
+ int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;
+
+ for (int i = 1; i < order; ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + i * u_1;
+ monomials(index, 1) = monomials(i0, 1) + i * u_2;
+ monomials(index, 2) = monomials(i0, 2) + i * u_3;
+ }
+ }
+
+ if (!forSerendipPoints) {
+ fullMatrix<double> dudv = gmshGenerateMonomialsQuadrangle(order - 2);
+ dudv.add(1);
+
+ for (int iface = 0; iface < 6; ++iface) {
+ int i0 = MHexahedron::faces_hexa(iface, 0);
+ int i1 = MHexahedron::faces_hexa(iface, 1);
+ int i3 = MHexahedron::faces_hexa(iface, 3);
+
+ int u[3];
+ u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
+ u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
+ u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
+ int v[3];
+ v[0] = (monomials(i3, 0) - monomials(i0, 0)) / order;
+ v[1] = (monomials(i3, 1) - monomials(i0, 1)) / order;
+ v[2] = (monomials(i3, 2) - monomials(i0, 2)) / order;
+
+ for (int i = 0; i < dudv.size1(); ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
+ monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
+ monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
+ }
+ }
+
+ fullMatrix<double> inner = gmshGenerateMonomialsHexahedron(order - 2);
+ inner.add(1);
+ monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
+ }
+ }
+ }
+ return monomials;
+}
+
+fullMatrix<double> gmshGenerateMonomialsHexaSerendipity(int order)
+{
+ int nbMonomials = order ? 8 + (order-1) * 12 : 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = 1;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = 1;
+ monomials(2, 1) = 1;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = 1;
+ monomials(3, 2) = 0;
+
+ monomials(4, 0) = 0;
+ monomials(4, 1) = 0;
+ monomials(4, 2) = 1;
+
+ monomials(5, 0) = 1;
+ monomials(5, 1) = 0;
+ monomials(5, 2) = 1;
+
+ monomials(6, 0) = 1;
+ monomials(6, 1) = 1;
+ monomials(6, 2) = 1;
+
+ monomials(7, 0) = 0;
+ monomials(7, 1) = 1;
+ monomials(7, 2) = 1;
+
+ if (order > 1) {
+ const int ind[12][3] = {
+ {2, 0, 0},
+ {2, 0, 1},
+ {2, 1, 1},
+ {2, 1, 0},
+
+ {0, 2, 0},
+ {0, 2, 1},
+ {1, 2, 1},
+ {1, 2, 0},
+
+ {0, 0, 2},
+ {0, 1, 2},
+ {1, 1, 2},
+ {1, 0, 2}
+ };
+ int val[3] = {0, 1, -1};
+ int index = 7;
+ for (int p = 2; p <= order; ++p) {
+ val[2] = p;
+ for (int i = 0; i < 12; ++i) {
+ monomials(++index, 0) = val[ind[i][0]];
+ monomials( index, 1) = val[ind[i][1]];
+ monomials( index, 2) = val[ind[i][2]];
+ }
+ }
+ }
+ }
+ return monomials;
+}
+
+fullMatrix<double> gmshGenerateMonomialsPyramid(int order, bool forSerendipPoints)
+{
+ int nbMonomials = forSerendipPoints ? 5 + (order-1)*8 :
+ (order+1)*((order+1)+1)*(2*(order+1)+1)/6;
+ if (forSerendipPoints && !order) nbMonomials = 1;
+ fullMatrix<double> monomials(nbMonomials, 3);
+
+ monomials(0, 0) = 0;
+ monomials(0, 1) = 0;
+ monomials(0, 2) = 0;
+
+ if (order > 0) {
+ monomials(1, 0) = order;
+ monomials(1, 1) = 0;
+ monomials(1, 2) = 0;
+
+ monomials(2, 0) = order;
+ monomials(2, 1) = order;
+ monomials(2, 2) = 0;
+
+ monomials(3, 0) = 0;
+ monomials(3, 1) = order;
+ monomials(3, 2) = 0;
+
+ monomials(4, 0) = 0;
+ monomials(4, 1) = 0;
+ monomials(4, 2) = order;
+
+ if (order > 1) {
+ int index = 5;
+ for (int iedge = 0; iedge < 8; ++iedge) {
+ int i0 = MPyramid::edges_pyramid(iedge, 0);
+ int i1 = MPyramid::edges_pyramid(iedge, 1);
+
+ int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
+ int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
+ int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;
+
+ for (int i = 1; i < order; ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + i * u_1;
+ monomials(index, 1) = monomials(i0, 1) + i * u_2;
+ monomials(index, 2) = monomials(i0, 2) + i * u_3;
+ }
+ }
+
+ if (!forSerendipPoints) {
+ fullMatrix<double> dudvQ = gmshGenerateMonomialsQuadrangle(order - 2);
+ dudvQ.add(1);
+
+ fullMatrix<double> dudvT;
+ if (order > 2) {
+ dudvT = gmshGenerateMonomialsTriangle(order - 3);
+ dudvT.add(1);
+ }
+
+ for (int iface = 0; iface < 5; ++iface) {
+ int i0, i1, i2;
+ i0 = MPyramid::faces_pyramid(iface, 0);
+ i1 = MPyramid::faces_pyramid(iface, 1);
+ fullMatrix<double> dudv;
+ if (MPyramid::faces_pyramid(iface, 3) != -1) {
+ i2 = MPyramid::faces_pyramid(iface, 3);
+ dudv.setAsProxy(dudvQ);
+ }
+ else if (order > 2) {
+ i2 = MPyramid::faces_pyramid(iface, 2);
+ dudv.setAsProxy(dudvT);
+ }
+ else continue;
+
+ int u[3];
+ u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
+ u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
+ u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
+ int v[3];
+ v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
+ v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
+ v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;
+
+ for (int i = 0; i < dudv.size1(); ++i, ++index) {
+ monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
+ monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
+ monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
+ }
+ }
+
+ if (order > 2) {
+ fullMatrix<double> inner = gmshGenerateMonomialsPyramid(order - 3);
+ inner.add(1);
+ monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
+ }
+ }
+ }
+ }
+ return monomials;
+}
+