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Christophe Geuzaine authoredThis reverts commit 07cc55d9
Christophe Geuzaine authoredThis reverts commit 07cc55d9
pointsGenerators.cpp 25.14 KiB
// Gmsh - Copyright (C) 1997-2014 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
#include "pointsGenerators.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MTetrahedron.h"
#include "MHexahedron.h"
#include "MPrism.h"
#include "MPyramid.h"
// Points Generators
fullMatrix<double> gmshGeneratePointsLine(int order)
{
fullMatrix<double> points = gmshGenerateMonomialsLine(order);
if (order == 0) return points;
points.scale(2./order);
points.add(-1.);
return points;
}
fullMatrix<double> gmshGeneratePointsTriangle(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsTriangle(order, serendip);
if (order == 0) return points;
points.scale(1./order);
return points;
}
fullMatrix<double> gmshGeneratePointsQuadrangle(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsQuadrangle(order, serendip);
if (order == 0) return points;
points.scale(2./order);
points.add(-1.);
return points;
}
fullMatrix<double> gmshGeneratePointsTetrahedron(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsTetrahedron(order, serendip);
if (order == 0) return points;
points.scale(1./order);
return points;
}
fullMatrix<double> gmshGeneratePointsHexahedron(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsHexahedron(order, serendip);
if (order == 0) return points;
points.scale(2./order);
points.add(-1.);
return points;
}
fullMatrix<double> gmshGeneratePointsPrism(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsPrism(order, serendip);
if (order == 0) return points;
fullMatrix<double> tmp;
tmp.setAsProxy(points, 0, 2);
tmp.scale(1./order);
tmp.setAsProxy(points, 2, 1);
tmp.scale(2./order);
tmp.add(-1.);
return points;
}
fullMatrix<double> gmshGeneratePointsPyramid(int order, bool serendip)
{
fullMatrix<double> points = gmshGenerateMonomialsPyramid(order, serendip);
if (order == 0) return points;
for (int i = 0; i < points.size1(); ++i) {
points(i, 2) = 1 - points(i, 2) / order;
const double duv = -1. + points(i, 2);
points(i, 0) = duv + points(i, 0) * 2. / order;
points(i, 1) = duv + points(i, 1) * 2. / order;
}
return points;
}
fullMatrix<double> gmshGeneratePointsPyramidGeneral(bool pyr, int nij, int nk, bool forSerendipPoints)
{
fullMatrix<double> points =
gmshGenerateMonomialsPyramidGeneral(pyr, nij, nk, forSerendipPoints);
if (points.size1() == 1) return points;
for (int i = 0; i < points.size1(); ++i) {
int div = pyr ? nk+nij : std::max(nij, nk);
points(i, 2) = (nk - points(i, 2)) / div;
const double duv = -1. + points(i, 2);
points(i, 0) = duv + points(i, 0) * 2. / div;
points(i, 1) = duv + points(i, 1) * 2. / div;
}
return points;
}
// Monomials Generators
fullMatrix<double> gmshGenerateMonomialsLine(int order, bool serendip)
{
fullMatrix<double> monomials(order + 1, 1);
monomials(0,0) = 0;
if (order > 0) {
monomials(1, 0) = order;
for (int i = 2; i < order + 1; i++) monomials(i, 0) = i-1;
}
return monomials;
}
fullMatrix<double> gmshGenerateMonomialsTriangle(int order, bool serendip)
{
int nbMonomials = serendip ? 3 * order : (order + 1) * (order + 2) / 2;
if (serendip && !order) nbMonomials = 1;
fullMatrix<double> monomials(nbMonomials, 2);
monomials(0, 0) = 0;
monomials(0, 1) = 0;
if (order > 0) {
monomials(1, 0) = order; monomials(1, 1) = 0;
monomials(2, 0) = 0;
monomials(2, 1) = order;
if (order > 1) {
int index = 3;
for (int iedge = 0; iedge < 3; ++iedge) {
int i0 = MTriangle::edges_tri(iedge, 0);
int i1 = MTriangle::edges_tri(iedge, 1);
int u_0 = (monomials(i1,0)-monomials(i0,0)) / order;
int u_1 = (monomials(i1,1)-monomials(i0,1)) / 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;
}
}
if (!serendip && order > 2) {
fullMatrix<double> inner = gmshGenerateMonomialsTriangle(order-3);
inner.add(1);
monomials.copy(inner, 0, nbMonomials - index, 0, 2, index, 0);
}
}
}
return monomials;
}
fullMatrix<double> gmshGenerateMonomialsQuadrangle(int order, bool forSerendipPoints)
{
int nbMonomials = forSerendipPoints ? order*4 : (order+1)*(order+1);
if (forSerendipPoints && !order) nbMonomials = 1;
fullMatrix<double> monomials(nbMonomials, 2);
monomials(0, 0) = 0;
monomials(0, 1) = 0;
if (order > 0) {
monomials(1, 0) = order;
monomials(1, 1) = 0;
monomials(2, 0) = order;
monomials(2, 1) = order;
monomials(3, 0) = 0;
monomials(3, 1) = order;
if (order > 1) {
int index = 4;
for (int iedge = 0; iedge < 4; ++iedge) {
int i0 = MQuadrangle::edges_quad(iedge, 0);
int i1 = MQuadrangle::edges_quad(iedge, 1);
int u_0 = (monomials(i1,0)-monomials(i0,0)) / order;
int u_1 = (monomials(i1,1)-monomials(i0,1)) / 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;
}
}
if (!forSerendipPoints) {
fullMatrix<double> inner = gmshGenerateMonomialsQuadrangle(order-2);
inner.add(1);
monomials.copy(inner, 0, nbMonomials - index, 0, 2, index, 0);
}
}
} 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) = order;
if (order > 0) {
monomials(1, 0) = order;
monomials(1, 1) = 0;
monomials(1, 2) = order;
monomials(2, 0) = order; monomials(2, 1) = order;
monomials(2, 2) = order;
monomials(3, 0) = 0;
monomials(3, 1) = order;
monomials(3, 2) = order;
monomials(4, 0) = 0;
monomials(4, 1) = 0;
monomials(4, 2) = 0;
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);
fullMatrix<double> prox;
prox.setAsProxy(inner, 0, 2);
prox.add(1);
prox.setAsProxy(inner, 2, 1);
prox.add(2);
monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
}
}
}
}
return monomials;
}
fullMatrix<double> gmshGenerateMonomialsPyramidGeneral(
bool pyr, int nij, int nk, bool forSerendipPoints)
{
if (nij < 0 || nk < 0) {
Msg::Fatal("Wrong arguments for pyramid's monomials generation !");
}
if (!pyr && nk > 0 && nij == 0) {
Msg::Error("Wrong argument association for pyramid's monomials generation ! Setting nij to 1");
nij = 1;
}
// If monomials for pyramidal space, generate them in gmsh convention.
if (forSerendipPoints || (pyr && nij == 0))
return gmshGenerateMonomialsPyramid(nk, forSerendipPoints);
// Otherwise, just put corners at first places,
// order of others having no importance.
int nbMonomials;
if (pyr) {
nbMonomials = 0;
for (int k = 0; k <= nk; ++k) {
nbMonomials += (k+nij+1) * (k+nij+1);
}
}
else nbMonomials = (nij+1) * (nij+1) * (nk+1);
fullMatrix<double> monomials(nbMonomials, 3);
monomials(0, 0) = 0;
monomials(0, 1) = 0;
monomials(0, 2) = nk;
if (nk == 0 && nij == 0) return monomials;
// Here, nij > 0
int nijBase = pyr ? nk+nij : nij;
// Corners
monomials(1, 0) = nijBase;
monomials(1, 1) = 0;
monomials(1, 2) = nk;
monomials(2, 0) = nijBase;
monomials(2, 1) = nijBase;
monomials(2, 2) = nk;
monomials(3, 0) = 0;
monomials(3, 1) = nijBase;
monomials(3, 2) = nk;
if (nk > 0) {
monomials(4, 0) = 0;
monomials(4, 1) = 0;
monomials(4, 2) = 0;
monomials(5, 0) = nij;
monomials(5, 1) = 0;
monomials(5, 2) = 0;
monomials(6, 0) = nij;
monomials(6, 1) = nij;
monomials(6, 2) = 0;
monomials(7, 0) = 0;
monomials(7, 1) = nij;
monomials(7, 2) = 0;
}
int index = 8;
// Base
if (nijBase > 1) {
for (int iedge = 0; iedge < 4; ++iedge) {
int i0 = iedge;
int i1 = (iedge+1) % 4;
int u0 = (monomials(i1,0)-monomials(i0,0)) / nijBase;
int u1 = (monomials(i1,1)-monomials(i0,1)) / nijBase;
for (int i = 1; i < nijBase; ++i, ++index) {
monomials(index, 0) = monomials(i0, 0) + i * u0;
monomials(index, 1) = monomials(i0, 1) + i * u1;
monomials(index, 2) = nk;
}
}
for (int i = 1; i < nijBase; ++i) {
for (int j = 1; j < nijBase; ++j, ++index) {
monomials(index, 0) = i;
monomials(index, 1) = j;
monomials(index, 2) = nk;
}
}
}
// Above base
if (nk > 0) {
// Top
if (nij > 1) {
for (int iedge = 0; iedge < 4; ++iedge) {
int i0 = 4 + iedge;
int i1 = 4 + (iedge+1)%4;
int u0 = (monomials(i1,0)-monomials(i0,0)) / nijBase;
int u1 = (monomials(i1,1)-monomials(i0,1)) / nijBase;
for (int i = 1; i < nijBase; ++i, ++index) {
monomials(index, 0) = monomials(i0, 0) + i * u0;
monomials(index, 1) = monomials(i0, 1) + i * u1;
monomials(index, 2) = 0;
}
}
for (int i = 1; i < nijBase; ++i) {
for (int j = 1; j < nijBase; ++j, ++index) {
monomials(index, 0) = i;
monomials(index, 1) = j;
monomials(index, 2) = 0;
}
}
}
// Between bottom & top
for (int k = nk-1; k > 0; --k) {
int currentnij = pyr ? k+nij : nij; for (int i = 0; i <= currentnij; ++i) {
for (int j = 0; j <= currentnij; ++j, ++index) {
monomials(index, 0) = i;
monomials(index, 1) = j;
monomials(index, 2) = k;
}
}
}
}
return monomials;
}