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nodalBasis.cpp 51.41 KiB
// Gmsh - Copyright (C) 1997-2013 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 <limits>
#include "nodalBasis.h"
#include "BasisFactory.h"
//#include "pointsGenerators.h"
static int nbdoftriangle(int order) { return (order + 1) * (order + 2) / 2; }
//KH : caveat : node coordinates are not yet coherent with node numbering associated
// to numbering of principal vertices of face !!!!
// uv surface - orientation v0-v2-v1
static void nodepositionface0(int order, double *u, double *v, double *w)
{
int ndofT = nbdoftriangle(order);
if (order == 0) { u[0] = 0.; v[0] = 0.; w[0] = 0.; return; }
u[0]= 0.; v[0]= 0.; w[0] = 0.;
u[1]= 0.; v[1]= order; w[1] = 0.;
u[2]= order; v[2]= 0.; w[2] = 0.;
// edges
for (int k = 0; k < (order - 1); k++){
u[3 + k] = 0.;
v[3 + k] = k + 1;
w[3 + k] = 0.;
u[3 + order - 1 + k] = k + 1;
v[3 + order - 1 + k] = order - 1 - k ;
w[3 + order - 1 + k] = 0.;
u[3 + 2 * (order - 1) + k] = order - 1 - k;
v[3 + 2 * (order - 1) + k] = 0.;
w[3 + 2 * (order - 1) + k] = 0.;
}
if (order > 2){
int nbdoftemp = nbdoftriangle(order - 3);
nodepositionface0(order - 3, &u[3 + 3 * (order - 1)], &v[3 + 3 * (order - 1)],
&w[3 + 3* (order - 1)]);
for (int k = 0; k < nbdoftemp; k++){
u[3 + k + 3 * (order - 1)] = u[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
v[3 + k + 3 * (order - 1)] = v[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
w[3 + k + 3 * (order - 1)] = w[3 + k + 3 * (order - 1)] * (order - 3);
}
}
for (int k = 0; k < ndofT; k++){
u[k] = u[k] / order;
v[k] = v[k] / order;
w[k] = w[k] / order;
}
}
// uw surface - orientation v0-v1-v3
static void nodepositionface1(int order, double *u, double *v, double *w)
{
int ndofT = nbdoftriangle(order);
if (order == 0) { u[0] = 0.; v[0] = 0.; w[0] = 0.; return; }
u[0] = 0.; v[0]= 0.; w[0] = 0.;
u[1] = order; v[1]= 0.; w[1] = 0.;
u[2] = 0.; v[2]= 0.; w[2] = order;
// edges
for (int k = 0; k < (order - 1); k++){
u[3 + k] = k + 1;
v[3 + k] = 0.;
w[3 + k] = 0.;
u[3 + order - 1 + k] = order - 1 - k;
v[3 + order - 1 + k] = 0.;
w[3 + order - 1+ k ] = k + 1;
u[3 + 2 * (order - 1) + k] = 0. ;
v[3 + 2 * (order - 1) + k] = 0.;
w[3 + 2 * (order - 1) + k] = order - 1 - k;
}
if (order > 2){
int nbdoftemp = nbdoftriangle(order - 3);
nodepositionface1(order - 3, &u[3 + 3 * (order - 1)], &v[3 + 3 * (order -1 )],
&w[3 + 3 * (order - 1)]);
for (int k = 0; k < nbdoftemp; k++){
u[3 + k + 3 * (order - 1)] = u[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
v[3 + k + 3 * (order - 1)] = v[3 + k + 3 * (order - 1)] * (order - 3);
w[3 + k + 3 * (order - 1)] = w[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
}
}
for (int k = 0; k < ndofT; k++){
u[k] = u[k] / order;
v[k] = v[k] / order;
w[k] = w[k] / order;
}
}
// vw surface - orientation v0-v3-v2
static void nodepositionface2(int order, double *u, double *v, double *w)
{
int ndofT = nbdoftriangle(order);
if (order == 0) { u[0] = 0.; v[0] = 0.; return; }
u[0]= 0.; v[0]= 0.; w[0] = 0.;
u[1]= 0.; v[1]= 0.; w[1] = order;
u[2]= 0.; v[2]= order; w[2] = 0.;
// edges
for (int k = 0; k < (order - 1); k++){
u[3 + k] = 0.;
v[3 + k] = 0.;
w[3 + k] = k + 1;
u[3 + order - 1 + k] = 0.;
v[3 + order - 1 + k] = k + 1;
w[3 + order - 1 + k] = order - 1 - k;
u[3 + 2 * (order - 1) + k] = 0.;
v[3 + 2 * (order - 1) + k] = order - 1 - k;
w[3 + 2 * (order - 1) + k] = 0.;
}
if (order > 2){
int nbdoftemp = nbdoftriangle(order - 3);
nodepositionface2(order - 3, &u[3 + 3 * (order - 1)], &v[3 + 3 * (order - 1)],
&w[3 + 3 * (order - 1)]);
for (int k = 0; k < nbdoftemp; k++){
u[3 + k + 3 * (order - 1)] = u[3 + k + 3 * (order - 1)] * (order - 3);
v[3 + k + 3 * (order - 1)] = v[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
w[3 + k + 3 * (order - 1)] = w[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
}
} for (int k = 0; k < ndofT; k++){
u[k] = u[k] / order;
v[k] = v[k] / order;
w[k] = w[k] / order;
}
}
// uvw surface - orientation v3-v1-v2
static void nodepositionface3(int order, double *u, double *v, double *w)
{
int ndofT = nbdoftriangle(order);
if (order == 0) { u[0] = 0.; v[0] = 0.; w[0] = 0.; return; }
u[0]= 0.; v[0]= 0.; w[0] = order;
u[1]= order; v[1]= 0.; w[1] = 0.;
u[2]= 0.; v[2]= order; w[2] = 0.;
// edges
for (int k = 0; k < (order - 1); k++){
u[3 + k] = k + 1;
v[3 + k] = 0.;
w[3 + k] = order - 1 - k;
u[3 + order - 1 + k] = order - 1 - k;
v[3 + order - 1 + k] = k + 1;
w[3 + order - 1 + k] = 0.;
u[3 + 2 * (order - 1) + k] = 0.;
v[3 + 2 * (order - 1) + k] = order - 1 - k;
w[3 + 2 * (order - 1) + k] = k + 1;
}
if (order > 2){
int nbdoftemp = nbdoftriangle(order - 3);
nodepositionface3(order - 3, &u[3 + 3 * (order - 1)], &v[3 + 3 * (order - 1)],
&w[3 + 3 * (order - 1)]);
for (int k = 0; k < nbdoftemp; k++){
u[3 + k + 3 * (order - 1)] = u[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
v[3 + k + 3 * (order - 1)] = v[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
w[3 + k + 3 * (order - 1)] = w[3 + k + 3 * (order - 1)] * (order - 3) + 1.;
}
}
for (int k = 0; k < ndofT; k++){
u[k] = u[k] / order;
v[k] = v[k] / order;
w[k] = w[k] / order;
}
}
static fullMatrix<double> generate1DPoints(int order)
{
fullMatrix<double> line(order + 1, 1);
line(0,0) = 0;
if (order > 0) {
line(0, 0) = -1.;
line(1, 0) = 1.;
double dd = 2. / order;
for (int i = 2; i < order + 1; i++) line(i, 0) = -1. + dd * (i - 1);
}
return line;
}
static fullMatrix<double> gmshGeneratePointsTetrahedron(int order, bool serendip)
{
int nbPoints = (serendip ?
4 + 6 * std::max(0, order - 1) + 4 * std::max(0, (order - 2) * (order - 1) / 2) :
(order + 1) * (order + 2) * (order + 3) / 6);
fullMatrix<double> point(nbPoints, 3);
double overOrder = (order == 0 ? 1. : 1. / order);
point(0, 0) = 0.;
point(0, 1) = 0.;
point(0, 2) = 0.;
if (order > 0) {
point(1, 0) = order;
point(1, 1) = 0;
point(1, 2) = 0;
point(2, 0) = 0.;
point(2, 1) = order;
point(2, 2) = 0.;
point(3, 0) = 0.;
point(3, 1) = 0.;
point(3, 2) = order;
// edges e5 and e6 switched in original version, opposite direction
// the template has been defined in table edges_tetra and faces_tetra (MElement.h)
if (order > 1) {
for (int k = 0; k < (order - 1); k++) {
point(4 + k, 0) = k + 1;
point(4 + order - 1 + k, 0) = order - 1 - k;
point(4 + 2 * (order - 1) + k, 0) = 0.;
point(4 + 3 * (order - 1) + k, 0) = 0.;
// point(4 + 4 * (order - 1) + k, 0) = order - 1 - k;
// point(4 + 5 * (order - 1) + k, 0) = 0.;
point(4 + 4 * (order - 1) + k, 0) = 0.;
point(4 + 5 * (order - 1) + k, 0) = k+1;
point(4 + k, 1) = 0.;
point(4 + order - 1 + k, 1) = k + 1;
point(4 + 2 * (order - 1) + k, 1) = order - 1 - k;
point(4 + 3 * (order - 1) + k, 1) = 0.;
// point(4 + 4 * (order - 1) + k, 1) = 0.;
// point(4 + 5 * (order - 1) + k, 1) = order - 1 - k;
point(4 + 4 * (order - 1) + k, 1) = k+1;
point(4 + 5 * (order - 1) + k, 1) = 0.;
point(4 + k, 2) = 0.;
point(4 + order - 1 + k, 2) = 0.;
point(4 + 2 * (order - 1) + k, 2) = 0.;
point(4 + 3 * (order - 1) + k, 2) = order - 1 - k;
point(4 + 4 * (order - 1) + k, 2) = order - 1 - k;
point(4 + 5 * (order - 1) + k, 2) = order - 1 - k;
}
if (order > 2) {
int ns = 4 + 6 * (order - 1);
int nbdofface = nbdoftriangle(order - 3);
double *u = new double[nbdofface];
double *v = new double[nbdofface];
double *w = new double[nbdofface];
nodepositionface0(order - 3, u, v, w);
// u-v plane
for (int i = 0; i < nbdofface; i++){
point(ns + i, 0) = u[i] * (order - 3) + 1.; point(ns + i, 1) = v[i] * (order - 3) + 1.;
point(ns + i, 2) = w[i] * (order - 3);
}
ns = ns + nbdofface;
// u-w plane
nodepositionface1(order - 3, u, v, w);
for (int i=0; i < nbdofface; i++){
point(ns + i, 0) = u[i] * (order - 3) + 1.;
point(ns + i, 1) = v[i] * (order - 3) ;
point(ns + i, 2) = w[i] * (order - 3) + 1.;
}
// v-w plane
ns = ns + nbdofface;
nodepositionface2(order - 3, u, v, w);
for (int i = 0; i < nbdofface; i++){
point(ns + i, 0) = u[i] * (order - 3);
point(ns + i, 1) = v[i] * (order - 3) + 1.;
point(ns + i, 2) = w[i] * (order - 3) + 1.;
}
// u-v-w plane
ns = ns + nbdofface;
nodepositionface3(order - 3, u, v, w);
for (int i = 0; i < nbdofface; i++){
point(ns + i, 0) = u[i] * (order - 3) + 1.;
point(ns + i, 1) = v[i] * (order - 3) + 1.;
point(ns + i, 2) = w[i] * (order - 3) + 1.;
}
ns = ns + nbdofface;
delete [] u;
delete [] v;
delete [] w;
if (!serendip && order > 3) {
fullMatrix<double> interior = gmshGeneratePointsTetrahedron(order - 4, false);
for (int k = 0; k < interior.size1(); k++) {
point(ns + k, 0) = 1. + interior(k, 0) * (order - 4);
point(ns + k, 1) = 1. + interior(k, 1) * (order - 4);
point(ns + k, 2) = 1. + interior(k, 2) * (order - 4);
}
}
}
}
}
point.scale(overOrder);
return point;
}
static fullMatrix<double> gmshGeneratePointsTriangle(int order, bool serendip)
{
int nbPoints = serendip ? 3 * order : (order + 1) * (order + 2) / 2;
fullMatrix<double> point(nbPoints, 2);
point(0, 0) = 0;
point(0, 1) = 0;
if (order > 0) {
double dd = 1. / order;
point(1, 0) = 1;
point(1, 1) = 0;
point(2, 0) = 0;
point(2, 1) = 1;
int index = 3;
if (order > 1) {
double ksi = 0;
double eta = 0;
for (int i = 0; i < order - 1; i++, index++) {
ksi += dd;
point(index, 0) = ksi;
point(index, 1) = eta;
}
ksi = 1.;
for (int i = 0; i < order - 1; i++, index++) {
ksi -= dd;
eta += dd;
point(index, 0) = ksi;
point(index, 1) = eta;
}
eta = 1.;
ksi = 0.;
for (int i = 0; i < order - 1; i++, index++) {
eta -= dd;
point(index, 0) = ksi;
point(index, 1) = eta;
}
if (order > 2 && !serendip) {
fullMatrix<double> inner = gmshGeneratePointsTriangle(order - 3, serendip);
inner.scale(1. - 3. * dd);
inner.add(dd);
point.copy(inner, 0, nbPoints - index, 0, 2, index, 0);
}
}
}
return point;
}
static fullMatrix<double> gmshGeneratePointsPrism(int order, bool serendip)
{
const double prism18Pts[18][3] = {
{0, 0, -1}, // 0
{1, 0, -1}, // 1
{0, 1, -1}, // 2
{0, 0, 1}, // 3
{1, 0, 1}, // 4
{0, 1, 1}, // 5
{0.5, 0, -1}, // 6
{0, 0.5, -1}, // 7
{0, 0, 0}, // 8
{0.5, 0.5, -1}, // 9
{1, 0, 0}, // 10
{0, 1, 0}, // 11 {0.5, 0, 1}, // 12
{0, 0.5, 1}, // 13
{0.5, 0.5, 1}, // 14
{0.5, 0, 0}, // 15
{0, 0.5, 0}, // 16
{0.5, 0.5, 0}, // 17
};
int nbPoints = (order + 1)*(order + 1)*(order + 2)/2;
fullMatrix<double> point(nbPoints, 3);
int index = 0;
fullMatrix<double> triPoints = gmshGeneratePointsTriangle(order,false);
fullMatrix<double> linePoints = generate1DPoints(order);
if (order == 2)
for (int i =0; i<18; i++)
for (int j=0; j<3;j++)
point(i,j) = prism18Pts[i][j];
else
for (int j = 0; j <linePoints.size1() ; j++) {
for (int i = 0; i < triPoints.size1(); i++) {
point(index,0) = triPoints(i,0);
point(index,1) = triPoints(i,1);
point(index,2) = linePoints(j,0);
index ++;
}
}
return point;
}
static fullMatrix<double> gmshGeneratePointsQuad(int order, bool serendip)
{
int nbPoints = serendip ? order*4 : (order+1)*(order+1);
fullMatrix<double> point(nbPoints, 2);
if (order > 0) {
point(0, 0) = -1;
point(0, 1) = -1;
point(1, 0) = 1;
point(1, 1) = -1;
point(2, 0) = 1;
point(2, 1) = 1;
point(3, 0) = -1;
point(3, 1) = 1;
if (order > 1) {
int index = 4;
const static int edges[4][2]={{0,1},{1,2},{2,3},{3,0}};
for (int iedge=0; iedge<4; iedge++) {
int p0 = edges[iedge][0];
int p1 = edges[iedge][1];
for (int i = 1; i < order; i++, index++) {
point(index, 0) = point(p0, 0) + i*(point(p1,0)-point(p0,0))/order;
point(index, 1) = point(p0, 1) + i*(point(p1,1)-point(p0,1))/order;
}
}
// FIXIT it was > 2 and I beleive it is >= 2 !!
if (order >= 2 && !serendip) {
fullMatrix<double> inner = gmshGeneratePointsQuad(order - 2, false);
inner.scale(1. - 2./order);
point.copy(inner, 0, nbPoints - index, 0, 2, index, 0);
}
}
}
else {
point(0, 0) = 0; point(0, 1) = 0;
}
return point;
}
static fullMatrix<double> gmshGeneratePointsHex(int order, bool serendip)
{
int nbPoints = (order+1)*(order+1)*(order+1);
if (serendip) nbPoints -= (order-1)*(order-1)*(order-1);
fullMatrix<double> point(nbPoints, 3);
// should be a public member of MHexahedron, just copied
static const int edges[12][2] = {
{0, 1},
{0, 3},
{0, 4},
{1, 2},
{1, 5},
{2, 3},
{2, 6},
{3, 7},
{4, 5},
{4, 7},
{5, 6},
{6, 7}
};
static const int faces[6][4] = {
{0, 3, 2, 1},
{0, 1, 5, 4},
{0, 4, 7, 3},
{1, 2, 6, 5},
{2, 3, 7, 6},
{4, 5, 6, 7}
};
if (order > 0) {
point(0, 0) = -1;
point(0, 1) = -1;
point(0, 2) = -1;
point(1, 0) = 1;
point(1, 1) = -1;
point(1, 2) = -1;
point(2, 0) = 1;
point(2, 1) = 1;
point(2, 2) = -1;
point(3, 0) = -1;
point(3, 1) = 1;
point(3, 2) = -1;
point(4, 0) = -1;
point(4, 1) = -1;
point(4, 2) = 1;
point(5, 0) = 1;
point(5, 1) = -1;
point(5, 2) = 1;
point(6, 0) = 1;
point(6, 1) = 1;
point(6, 2) = 1;
point(7, 0) = -1;
point(7, 1) = 1;
point(7, 2) = 1;
if (order > 1) {
int index = 8;
for (int iedge=0; iedge<12; iedge++) {
int p0 = edges[iedge][0];
int p1 = edges[iedge][1];
for (int i = 1; i < order; i++, index++) { point(index, 0) = point(p0, 0) + i*(point(p1,0)-point(p0,0))/order;
point(index, 1) = point(p0, 1) + i*(point(p1,1)-point(p0,1))/order;
point(index, 2) = point(p0, 2) + i*(point(p1,2)-point(p0,2))/order;
}
}
fullMatrix<double> fp = gmshGeneratePointsQuad(order - 2, false);
fp.scale(1. - 2./order);
for (int iface=0; iface<6; iface++) {
int p0 = faces[iface][0];
int p1 = faces[iface][1];
int p2 = faces[iface][2];
int p3 = faces[iface][3];
for (int i=0;i<fp.size1();i++, index++){
const double u = fp(i,0);
const double v = fp(i,1);
const double newU =
0.25*(1.-u)*(1.-v)*point(p0,0) +
0.25*(1.+u)*(1.-v)*point(p1,0) +
0.25*(1.+u)*(1.+v)*point(p2,0) +
0.25*(1.-u)*(1.+v)*point(p3,0) ;
const double newV =
0.25*(1.-u)*(1.-v)*point(p0,1) +
0.25*(1.+u)*(1.-v)*point(p1,1) +
0.25*(1.+u)*(1.+v)*point(p2,1) +
0.25*(1.-u)*(1.+v)*point(p3,1) ;
const double newW =
0.25*(1.-u)*(1.-v)*point(p0,2) +
0.25*(1.+u)*(1.-v)*point(p1,2) +
0.25*(1.+u)*(1.+v)*point(p2,2) +
0.25*(1.-u)*(1.+v)*point(p3,2) ;
point(index, 0) = newU;
point(index, 1) = newV;
point(index, 2) = newW;
}
}
if (!serendip) {
fullMatrix<double> inner = gmshGeneratePointsHex(order - 2, false);
inner.scale(1. - 2./order);
point.copy(inner, 0, nbPoints - index, 0, 3, index, 0);
}
}
}
else if (order == 0){
point(0, 0) = 0;
point(0, 1) = 0;
point(0, 2) = 0;
}
return point;
}
static fullMatrix<double> gmshGeneratePointsPyramid(int order, bool serendip)
{
int nbPoints = (order+1)*((order+1)+1)*(2*(order+1)+1)/6;
// Remove volume points if incomplete basis
if (serendip && order > 2) nbPoints -= (order-2)*((order-2)+1)*(2*(order-2)+1)/6;
fullMatrix<double> points(nbPoints, 3);
static const int edges[8][2] = {
{0, 1},
{0, 3},
{0, 4},
{1, 2},
{1, 4},
{2, 3},
{2, 4}, {3, 4},
};
static const int faces[5][4] = {
{0, 1, 4, -1},
{3, 0, 4, -1},
{1, 2, 4, -1},
{2, 3, 4, -1},
{0, 3, 2, 1}
};
if (order == 0) {
points(0,0) = 0.0;
points(0,1) = 0.0;
points(0,2) = 0.0;
return points;
}
// Principal vertices of the pyramid
points(0,0) = -1.0; points(0,1) = -1.0; points(0,2) = 0.0;
points(1,0) = 1.0; points(1,1) = -1.0; points(1,2) = 0.0;
points(2,0) = 1.0; points(2,1) = 1.0; points(2,2) = 0.0;
points(3,0) = -1.0; points(3,1) = 1.0; points(3,2) = 0.0;
points(4,0) = 0.0; points(4,1) = 0.0; points(4,2) = 1.0;
if (order > 1) {
int p = 5;
// Edges
for (int e = 0; e < 8; e++) {
double vec[3];
vec[0] = points(edges[e][1],0) - points(edges[e][0],0);
vec[1] = points(edges[e][1],1) - points(edges[e][0],1);
vec[2] = points(edges[e][1],2) - points(edges[e][0],2);
for (int i = 0; i < order - 1; i++) {
points(p,0) = points(edges[e][0],0) + vec[0]/order * (i+1);
points(p,1) = points(edges[e][0],1) + vec[1]/order * (i+1);
points(p,2) = points(edges[e][0],2) + vec[2]/order * (i+1);
p++;
}
}
// Faces
for (int f = 0; f < 4; f++) {
fullMatrix<double> fp = gmshGeneratePointsTriangle(order, false);
fullVector<double> u(4);
fullVector<double> v(4);
fullVector<double> w(4);
fullVector<double> y(4);
fullVector<double> up(4);
fullVector<double> vp(4);
fullVector<double> wp(4);
fullVector<double> yp(4);
for (int c = 0; c < 3; c++) {
u(c) = fp(0,c);
v(c) = fp(1,c);
w(c) = fp(2,c);
up(c) = points(faces[f][0],c);
vp(c) = points(faces[f][1],c);
wp(c) = points(faces[f][2],c);
}
u(2) = 0.0;
v(2) = 0.0;
w(2) = 0.0;
u(3) = 1.0;
v(3) = 1.0;
w(3) = 1.0;
y(0) = u(0) + ((v(1)-u(1))*(w(2)-u(2)) - (v(2)-u(2))*(w(1)-u(1)));
y(1) = u(1) + ((v(2)-u(2))*(w(0)-u(0)) - (v(0)-u(0))*(w(2)-u(2)));
y(2) = u(2) + ((v(0)-u(0))*(w(1)-u(1)) - (v(1)-u(1))*(w(0)-u(0)));
y(3) = 1.0;
up(3) = 1.0;
vp(3) = 1.0;
wp(3) = 1.0;
yp(0) = up(0) + ((vp(1)-up(1))*(wp(2)-up(2)) - (vp(2)-up(2))*(wp(1)-up(1)));
yp(1) = up(1) + ((vp(2)-up(2))*(wp(0)-up(0)) - (vp(0)-up(0))*(wp(2)-up(2)));
yp(2) = up(2) + ((vp(0)-up(0))*(wp(1)-up(1)) - (vp(1)-up(1))*(wp(0)-up(0)));
yp(3) = 1.0;
fullMatrix<double> M(4,4);
fullMatrix<double> Mp(4,4);
M(0,0) = u(0); M(0,1) = v(0); M(0,2) = w(0); M(0,3) = y(0);
M(1,0) = u(1); M(1,1) = v(1); M(1,2) = w(1); M(1,3) = y(1);
M(2,0) = u(2); M(2,1) = v(2); M(2,2) = w(2); M(2,3) = y(2);
M(3,0) = u(3); M(3,1) = v(3); M(3,2) = w(3); M(3,3) = y(3);
Mp(0,0) = up(0); Mp(0,1) = vp(0); Mp(0,2) = wp(0); Mp(0,3) = yp(0);
Mp(1,0) = up(1); Mp(1,1) = vp(1); Mp(1,2) = wp(1); Mp(1,3) = yp(1);
Mp(2,0) = up(2); Mp(2,1) = vp(2); Mp(2,2) = wp(2); Mp(2,3) = yp(2);
Mp(3,0) = up(3); Mp(3,1) = vp(3); Mp(3,2) = wp(3); Mp(3,3) = yp(3);
M.invertInPlace();
fullMatrix<double> T(4,4);
Mp.mult(M, T);
for(int k = 3*order; k < fp.size1(); k++) {
fullVector<double> pnt(4);
pnt(0) = fp(k,0);
pnt(1) = fp(k,1);
pnt(2) = 0.0;
pnt(3) = 1.0;
fullVector<double> res(4);
T.mult(pnt, res);
points(p, 0) = res(0);
points(p, 1) = res(1);
points(p, 2) = res(2);
p++;
}
}
fullMatrix<double> fpq = gmshGeneratePointsQuad(order-2, false);
fullMatrix<double> transform(2,2);
fullMatrix<double> scaled(fpq.size1(), fpq.size2());
transform(0,0) = (order-2)/(double)order; transform(0,1) = 0.0;
transform(1,0) = 0.0; transform(1,1) = (order-2)/(double)order;
fpq.mult(transform, scaled);
for (int i = 0; i < scaled.size1(); i++) {
points(p, 0) = scaled(i, 1);
points(p, 1) = scaled(i, 0);
points(p, 2) = 0.0;
p++;
}
// Volume
if ((!serendip) && (order > 2)) {
fullMatrix<double> volume_points = gmshGeneratePointsPyramid(order - 3, false);
// scale to order-3/order fullMatrix<double> T(3,3);
T(0,0) = (order - 3.0) / order; T(0,1) = 0.0; T(0,2) = 0.0;
T(1,0) = 0.0; T(1,1) = (order - 3.0) / order; T(1,2) = 0.0;
T(2,0) = 0.0; T(2,1) = 0.0; T(2,2) = (order - 3.0) / order;
fullMatrix<double> scaled(volume_points.size1(), volume_points.size2());
volume_points.mult(T, scaled);
// translate 1/order
for (int i = 0; i < scaled.size1(); i++) {
points(p, 0) = scaled(i,0);
points(p, 1) = scaled(i,1);
points(p, 2) = scaled(i,2) + 1.0/order;
p++;
}
}
}
return points;
}
static void generate1dVertexClosure(nodalBasis::clCont &closure, int order)
{
closure.clear();
closure.resize(2);
closure[0].push_back(0);
closure[1].push_back(order == 0 ? 0 : 1);
closure[0].type = MSH_PNT;
closure[1].type = MSH_PNT;
}
static void generate1dVertexClosureFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef, int order)
{
closure.clear();
closure.resize(2);
closure[0].push_back(0);
if (order != 0) {
closure[0].push_back(1);
closure[1].push_back(1);
}
closure[1].push_back(0);
for (int i = 0; i < order - 1; i++) {
closure[0].push_back(2 + i);
closure[1].push_back(2 + order - 2 - i);
}
closureRef.resize(2);
closureRef[0] = 0;
closureRef[1] = 0;
}
static void getFaceClosureTet(int iFace, int iSign, int iRotate,
nodalBasis::closure &closure, int order)
{
closure.clear();
closure.resize((order + 1) * (order + 2) / 2);
closure.type = nodalBasis::getTag(TYPE_TRI, order, false);
switch (order){
case 0:
closure[0] = 0;
break;
default:
int face[4][3] = {{-3, -2, -1}, {1, -6, 4}, {-4, 5, 3}, {6, 2, -5}};
int order1node[4][3] = {{0, 2, 1}, {0, 1, 3}, {0, 3, 2}, {3, 1, 2}};
for (int i = 0; i < 3; ++i){ int k = (3 + (iSign * i) + iRotate) % 3; //- iSign * iRotate
closure[i] = order1node[iFace][k];
}
for (int i = 0;i < 3; ++i){
int edgenumber = iSign *
face[iFace][(6 + i * iSign + (-1 + iSign) / 2 + iRotate) % 3]; //- iSign * iRotate
for (int k = 0; k < (order - 1); k++){
if (edgenumber > 0)
closure[3 + i * (order - 1) + k] =
4 + (edgenumber - 1) * (order - 1) + k;
else
closure[3 + i * (order - 1) + k] =
4 + (-edgenumber) * (order - 1) - 1 - k;
}
}
int fi = 3 + 3 * (order - 1);
int ti = 4 + 6 * (order - 1);
int ndofff = (order - 3 + 2) * (order - 3 + 1) / 2;
ti = ti + iFace * ndofff;
for (int k = 0; k < order / 3; k++){
int orderint = order - 3 - k * 3;
if (orderint > 0){
for (int ci = 0; ci < 3 ; ci++){
int shift = (3 + iSign * ci + iRotate) % 3; //- iSign * iRotate
closure[fi + ci] = ti + shift;
}
fi = fi + 3; ti = ti + 3;
for (int l = 0; l < orderint - 1; l++){
for (int ei = 0; ei < 3; ei++){
int edgenumber = (6 + ei * iSign + (-1 + iSign) / 2 + iRotate) % 3;
//- iSign * iRotate
if (iSign > 0)
closure[fi + ei * (orderint - 1) + l] =
ti + edgenumber * (orderint - 1) + l;
else
closure[fi + ei * (orderint - 1) + l] =
ti + (1 + edgenumber) * (orderint - 1) - 1 - l;
}
}
fi = fi + 3 * (orderint - 1); ti = ti + 3 * (orderint - 1);
}
else {
closure[fi] = ti;
ti++;
fi++;
}
}
break;
}
}
static void generate2dEdgeClosureFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef,
int order, int nNod, bool serendip)
{
closure.clear();
closure.resize(2*nNod);
closureRef.resize(2*nNod);
int shift = 0;
for (int corder = order; corder>=0; corder -= (nNod == 3 ? 3 : 2)) {
if (corder == 0) {
for (int r = 0; r < nNod ; r++){
closure[r].push_back(shift);
closure[r+nNod].push_back(shift);
}
break;
}
for (int r = 0; r < nNod ; r++){ for (int j = 0; j < nNod; j++) {
closure[r].push_back(shift + (r + j) % nNod);
closure[r + nNod].push_back(shift + (r - j + 1 + nNod) % nNod);
}
}
shift += nNod;
int n = nNod*(corder-1);
for (int r = 0; r < nNod ; r++){
for (int j = 0; j < n; j++){
closure[r].push_back(shift + (j + (corder - 1) * r) % n);
closure[r + nNod].push_back(shift + (n - j - 1 + (corder - 1) * (r + 1)) % n);
}
}
shift += n;
if (serendip) break;
}
for (int r = 0; r < nNod*2 ; r++) {
closure[r].type = nodalBasis::getTag(TYPE_LIN, order);
closureRef[r] = 0;
}
}
static void addEdgeNodes(nodalBasis::clCont &closureFull, const int *edges, int order)
{
if (order < 2)
return;
int numNodes = 0;
for (int i = 0; edges[i] >= 0; ++i) {
numNodes = std::max(numNodes, edges[i] + 1);
}
std::vector<std::vector<int> > nodes2edges(numNodes, std::vector<int>(numNodes, -1));
for (int i = 0; edges[i] >= 0; i += 2) {
nodes2edges[edges[i]][edges[i + 1]] = i;
nodes2edges[edges[i + 1]][edges[i]] = i + 1;
}
for (unsigned int iClosure = 0; iClosure < closureFull.size(); iClosure++) {
std::vector<int> &cl = closureFull[iClosure];
for (int iEdge = 0; edges[iEdge] >= 0; iEdge += 2) {
if (cl.empty())
continue;
int n0 = cl[edges[iEdge]];
int n1 = cl[edges[iEdge + 1]];
int oEdge = nodes2edges[n0][n1];
if (oEdge == -1)
Msg::Error("invalid p1 closure or invalid edges list");
for (int i = 0 ; i < order - 1; i++)
cl.push_back(numNodes + oEdge/2 * (order - 1) + ((oEdge % 2) ? order - 2 - i : i));
}
}
}
static void generateFaceClosureTet(nodalBasis::clCont &closure, int order)
{
closure.clear();
for (int iRotate = 0; iRotate < 3; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 4; iFace++){
nodalBasis::closure closure_face;
getFaceClosureTet(iFace, iSign, iRotate, closure_face, order);
closure.push_back(closure_face);
}
}
}
}
static void generateFaceClosureTetFull(nodalBasis::clCont &closureFull,
std::vector<int> &closureRef,
int order, bool serendip)
{
closureFull.clear();
//input :
static const short int faces[4][3] = {{0,1,2}, {0,3,1}, {0,2,3}, {3,2,1}};
static const int edges[] = {0, 1, 1, 2, 2, 0, 3, 0, 3, 2, 3, 1, -1};
static const int faceOrientation[6] = {0,1,2,5,3,4};
closureFull.resize(24);
closureRef.resize(24);
for (int i = 0; i < 24; i ++)
closureRef[i] = 0;
if (order == 0) {
for (int i = 0; i < 24; i ++) {
closureFull[i].push_back(0);
}
return;
}
//Mapping for the p1 nodes
nodalBasis::clCont closure;
generateFaceClosureTet(closure, 1);
for (unsigned int i = 0; i < closureFull.size(); i++) {
std::vector<int> &clFull = closureFull[i];
std::vector<int> &cl = closure[i];
clFull.resize(4, -1);
closureRef[i] = 0;
for (unsigned int j = 0; j < cl.size(); j ++)
clFull[closure[0][j]] = cl[j];
for (int j = 0; j < 4; j ++)
if (clFull[j] == -1)
clFull[j] = (6 - clFull[(j + 1) % 4] - clFull[(j + 2) % 4] - clFull[(j + 3) % 4]);
}
int nodes2Faces[4][4][4];
for (int i = 0; i < 4; i++) {
for (int iRotate = 0; iRotate < 3; iRotate ++) {
short int n0 = faces[i][(3 - iRotate) % 3];
short int n1 = faces[i][(4 - iRotate) % 3];
short int n2 = faces[i][(5 - iRotate) % 3];
nodes2Faces[n0][n1][n2] = i * 6 + iRotate;
nodes2Faces[n0][n2][n1] = i * 6 + iRotate + 3;
}
}
nodalBasis::clCont closureTriangles;
std::vector<int> closureTrianglesRef;
if (order >= 3)
generate2dEdgeClosureFull(closureTriangles, closureTrianglesRef, order - 3, 3, false);
addEdgeNodes(closureFull, edges, order);
for (unsigned int iClosure = 0; iClosure < closureFull.size(); iClosure++) {
//faces
std::vector<int> &cl = closureFull[iClosure];
if (order >= 3) {
for (int iFace = 0; iFace < 4; iFace ++) {
int n0 = cl[faces[iFace][0]];
int n1 = cl[faces[iFace][1]];
int n2 = cl[faces[iFace][2]];
short int id = nodes2Faces[n0][n1][n2];
short int iTriClosure = faceOrientation [id % 6];
short int idFace = id/6;
int nOnFace = closureTriangles[iTriClosure].size();
for (int i = 0; i < nOnFace; i++) {
cl.push_back(4 + 6 * (order - 1) + idFace * nOnFace +
closureTriangles[iTriClosure][i]);
}
}
}
}
if (order >= 4 && !serendip) {
nodalBasis::clCont insideClosure; std::vector<int> fakeClosureRef;
generateFaceClosureTetFull(insideClosure, fakeClosureRef, order - 4, false);
for (unsigned int i = 0; i < closureFull.size(); i ++) {
unsigned int shift = closureFull[i].size();
for (unsigned int j = 0; j < insideClosure[i].size(); j++)
closureFull[i].push_back(insideClosure[i][j] + shift);
}
}
}
void rotateHex(int iFace, int iRot, int iSign, double uI, double vI,
double &uO, double &vO, double &wO)
{
if (iSign<0){
double tmp=uI;
uI=vI;
vI=tmp;
}
for (int i=0; i < iRot; i++){
double tmp=uI;
uI=-vI;
vI=tmp;
}
switch (iFace) {
case 0: uO = vI; vO = uI; wO=-1; break;
case 1: uO = uI; vO = -1; wO=vI; break;
case 2: uO =-1; vO = vI; wO=uI; break;
case 3: uO = 1; vO = uI; wO=vI; break;
case 4: uO =-uI; vO = 1; wO=vI; break;
case 5: uO =uI; vO = vI; wO=1; break;
}
}
void rotateHexFull(int iFace, int iRot, int iSign, double uI, double vI, double wI, double &uO, double &vO, double &wO)
{
switch (iFace) {
case 0: uO = uI; vO = vI; wO = wI; break;
case 1: uO = wI; vO = uI; wO = vI; break;
case 2: uO = vI; vO = wI; wO = uI; break;
case 3: uO = wI; vO = vI; wO =-uI; break;
case 4: uO = wI; vO =-uI; wO =-vI; break;
case 5: uO = vI; vO = uI; wO =-wI; break;
}
for (int i = 0; i < iRot; i++){
double tmp = uO;
uO = -vO;
vO = tmp;
}
if (iSign<0){
double tmp = uO;
uO = vO;
vO = tmp;
}
}
inline static double pow2(double x)
{
return x * x;
}
/*
static void checkClosure(int tag) {
printf("TYPE = %i\n", tag);
const nodalBasis &fs = *nodalBases::find(tag); for (int i = 0; i < fs.closures.size(); ++i) {
const std::vector<int> &clRef = fs.closures[fs.closureRef[i]];
const std::vector<int> &cl = fs.closures[i];
const std::vector<int> &clFull = fs.fullClosures[i];
printf("i = %i\n", i);
for (int j = 0; j < cl.size(); ++j) {
printf("%3i ", clFull[clRef[j]]);
}
printf("\n");
for (int j = 0; j < cl.size(); ++j) {
printf("%3i ", cl[j]);
}
printf("\n");
}
}
*/
static void generateFaceClosureHex(nodalBasis::clCont &closure, int order,
bool serendip, const fullMatrix<double> &points)
{
closure.clear();
const nodalBasis &fsFace = *BasisFactory::create(nodalBasis::getTag(TYPE_QUA, order, serendip));
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 6; iFace++) {
nodalBasis::closure cl;
cl.type = fsFace.type;
cl.resize(fsFace.points.size1());
for (unsigned int iNode = 0; iNode < cl.size(); ++iNode) {
double u,v,w;
rotateHex(iFace, iRotate, iSign, fsFace.points(iNode, 0),
fsFace.points(iNode, 1), u, v, w);
cl[iNode] = 0;
double D = std::numeric_limits<double>::max();
for (int jNode = 0; jNode < points.size1(); ++jNode) {
double d = pow2(points(jNode, 0) - u) + pow2(points(jNode, 1) - v) +
pow2(points(jNode, 2) - w);
if (d < D) {
cl[iNode] = jNode;
D = d;
}
}
}
closure.push_back(cl);
}
}
}
}
static void generateFaceClosureHexFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef,
int order, bool serendip,
const fullMatrix<double> &points)
{
closure.clear();
int clId = 0;
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 6; iFace++) {
nodalBasis::closure cl;
cl.resize(points.size1());
for (int iNode = 0; iNode < points.size1(); ++iNode) {
double u,v,w;
rotateHexFull(iFace, iRotate, iSign, points(iNode, 0), points(iNode, 1),
points(iNode, 2), u, v, w);
int J = 0; double D = std::numeric_limits<double>::max();
for (int jNode = 0; jNode < points.size1(); ++jNode) {
double d = pow2(points(jNode, 0) - u) + pow2(points(jNode, 1) - v) +
pow2(points(jNode, 2) - w);
if (d < D) {
J = jNode;
D = d;
}
}
cl[J] = iNode;
}
closure.push_back(cl);
closureRef.push_back(0);
clId ++;
}
}
}
}
static void getFaceClosurePrism(int iFace, int iSign, int iRotate,
nodalBasis::closure &closure, int order)
{
if (order > 2)
Msg::Error("FaceClosure not implemented for prisms of order %d",order);
bool isTriangle = iFace<2;
int nNodes = isTriangle ? (order+1)*(order+2)/2 : (order+1)*(order+1);
closure.clear();
if (isTriangle && iRotate > 2) return;
closure.resize(nNodes);
if (order==0) {
closure[0] = 0;
return;
}
int order1node[5][4] = {{0, 2, 1, -1}, {3, 4, 5, -1}, {0, 1, 4, 3}, {0, 3, 5, 2},
{1, 2, 5, 4}};
int order2node[5][5] = {{7, 9, 6, -1, -1}, {12, 14, 13, -1, -1}, {6, 10, 12, 8, 15},
{8, 13, 11, 7, 16}, {9, 11, 14, 10, 17}};
// int order2node[5][4] = {{7, 9, 6, -1}, {12, 14, 13, -1}, {6, 10, 12, 8},
// {8, 13, 11, 7}, {9, 11, 14, 10}};
int nVertex = isTriangle ? 3 : 4;
closure.type = nodalBasis::getTag(isTriangle ? TYPE_TRI : TYPE_QUA, order);
for (int i = 0; i < nVertex; ++i){
int k = (nVertex + (iSign * i) + iRotate) % nVertex; //- iSign * iRotate
closure[i] = order1node[iFace][k];
}
if (order==2) {
for (int i = 0; i < nVertex; ++i){
int k = (nVertex + (iSign==-1?-1:0) + (iSign * i) + iRotate) % nVertex;
//- iSign * iRotate
closure[nVertex+i] = order2node[iFace][k];
}
if (!isTriangle)
closure[nNodes-1] = order2node[iFace][4]; // center
}
}
static void generateFaceClosurePrism(nodalBasis::clCont &closure, int order)
{
closure.clear();
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 5; iFace++){
nodalBasis::closure closure_face;
getFaceClosurePrism(iFace, iSign, iRotate, closure_face, order);
closure.push_back(closure_face);
} }
}
}
static void generateFaceClosurePrismFull(nodalBasis::clCont &closureFull,
std::vector<int> &closureRef, int order)
{
nodalBasis::clCont closure;
closureFull.clear();
closureFull.resize(40);
closureRef.resize(40);
generateFaceClosurePrism(closure, 1);
int ref3 = -1, ref4a = -1, ref4b = -1;
for (unsigned int i = 0; i < closure.size(); i++) {
std::vector<int> &clFull = closureFull[i];
std::vector<int> &cl = closure[i];
if (cl.size() == 0)
continue;
clFull.resize(6, -1);
int &ref = cl.size() == 3 ? ref3 : (cl[0] / 3 + cl[1] / 3) % 2 ? ref4b : ref4a;
if (ref == -1)
ref = i;
closureRef[i] = ref;
for (unsigned int j = 0; j < cl.size(); j ++)
clFull[closure[ref][j]] = cl[j];
for (int j = 0; j < 6; j ++) {
if (clFull[j] == -1) {
int k = ((j / 3) + 1) % 2 * 3;
int sum = (clFull[k + (j + 1) % 3] + clFull[k + (j + 2) % 3]);
clFull[j] = ((sum / 6 + 1) % 2) * 3 + (12 - sum) % 3;
}
}
}
static const int edges[] = {0, 1, 0, 2, 0, 3, 1, 2, 1, 4, 2, 5,
3, 4, 3, 5, 4, 5, -1};
addEdgeNodes(closureFull, edges, order);
if ( order < 2 )
return;
// face center nodes for p2 prism
static const int faces[5][4] = {{0, 2, 1, -1}, {3, 4, 5, -1}, {0, 1, 4, 3},
{0, 3, 5, 2}, {1, 2, 5, 4}};
if ( order == 2 ) {
int nextFaceNode = 15;
int numFaces = 5;
int numFaceNodes = 4;
std::map<int,int> nodeSum2Face;
for (int iFace = 0; iFace < numFaces ; iFace ++) {
int nodeSum = 0;
for (int iNode = 0; iNode < numFaceNodes; iNode++ ) {
nodeSum += faces[iFace][iNode];
}
nodeSum2Face[nodeSum] = iFace;
}
for (unsigned int i = 0; i < closureFull.size(); i++ ) {
if (closureFull[i].empty())
continue;
for (int iFace = 0; iFace < numFaces; iFace++ ) {
int nodeSum = 0;
for (int iNode = 0; iNode < numFaceNodes; iNode++)
nodeSum += faces[iFace][iNode] < 0 ? faces[iFace][iNode] :
closureFull[i][ faces[iFace][iNode] ];
std::map<int,int>::iterator it = nodeSum2Face.find(nodeSum);
if (it == nodeSum2Face.end() )
Msg::Error("Prism face not found");
int mappedFaceId = it->second;
if ( mappedFaceId > 1) {
closureFull[i].push_back(nextFaceNode + mappedFaceId - 2); }
}
}
} else {
Msg::Error("FaceClosureFull not implemented for prisms of order %d",order);
}
}
static void generate2dEdgeClosure(nodalBasis::clCont &closure, int order, int nNod = 3)
{
closure.clear();
closure.resize(2*nNod);
for (int j = 0; j < nNod ; j++){
closure[j].push_back(j);
closure[j].push_back((j+1)%nNod);
closure[nNod+j].push_back((j+1)%nNod);
closure[nNod+j].push_back(j);
for (int i=0; i < order-1; i++){
closure[j].push_back( nNod + (order-1)*j + i );
closure[nNod+j].push_back(nNod + (order-1)*(j+1) -i -1);
}
closure[j].type = closure[nNod+j].type = nodalBasis::getTag(TYPE_LIN, order);
}
}
static void generateClosureOrder0(nodalBasis::clCont &closure, int nb)
{
closure.clear();
closure.resize(nb);
for (int i=0; i < nb; i++) {
closure[i].push_back(0);
closure[i].type = MSH_PNT;
}
}
nodalBasis::nodalBasis(int tag)
{
type = tag;
switch (tag) {
case MSH_PNT : parentType = TYPE_PNT; order = 0; serendip = false; break;
case MSH_LIN_1 : parentType = TYPE_LIN; order = 0; serendip = false; break;
case MSH_LIN_2 : parentType = TYPE_LIN; order = 1; serendip = false; break;
case MSH_LIN_3 : parentType = TYPE_LIN; order = 2; serendip = false; break;
case MSH_LIN_4 : parentType = TYPE_LIN; order = 3; serendip = false; break;
case MSH_LIN_5 : parentType = TYPE_LIN; order = 4; serendip = false; break;
case MSH_LIN_6 : parentType = TYPE_LIN; order = 5; serendip = false; break;
case MSH_LIN_7 : parentType = TYPE_LIN; order = 6; serendip = false; break;
case MSH_LIN_8 : parentType = TYPE_LIN; order = 7; serendip = false; break;
case MSH_LIN_9 : parentType = TYPE_LIN; order = 8; serendip = false; break;
case MSH_LIN_10 : parentType = TYPE_LIN; order = 9; serendip = false; break;
case MSH_LIN_11 : parentType = TYPE_LIN; order = 10;serendip = false; break;
case MSH_TRI_1 : parentType = TYPE_TRI; order = 0; serendip = false; break;
case MSH_TRI_3 : parentType = TYPE_TRI; order = 1; serendip = false; break;
case MSH_TRI_6 : parentType = TYPE_TRI; order = 2; serendip = false; break;
case MSH_TRI_10 : parentType = TYPE_TRI; order = 3; serendip = false; break;
case MSH_TRI_15 : parentType = TYPE_TRI; order = 4; serendip = false; break;
case MSH_TRI_21 : parentType = TYPE_TRI; order = 5; serendip = false; break;
case MSH_TRI_28 : parentType = TYPE_TRI; order = 6; serendip = false; break;
case MSH_TRI_36 : parentType = TYPE_TRI; order = 7; serendip = false; break;
case MSH_TRI_45 : parentType = TYPE_TRI; order = 8; serendip = false; break;
case MSH_TRI_55 : parentType = TYPE_TRI; order = 9; serendip = false; break; case MSH_TRI_66 : parentType = TYPE_TRI; order = 10;serendip = false; break;
case MSH_TRI_9 : parentType = TYPE_TRI; order = 3; serendip = true; break;
case MSH_TRI_12 : parentType = TYPE_TRI; order = 4; serendip = true; break;
case MSH_TRI_15I : parentType = TYPE_TRI; order = 5; serendip = true; break;
case MSH_TRI_18 : parentType = TYPE_TRI; order = 6; serendip = true; break;
case MSH_TRI_21I : parentType = TYPE_TRI; order = 7; serendip = true; break;
case MSH_TRI_24 : parentType = TYPE_TRI; order = 8; serendip = true; break;
case MSH_TRI_27 : parentType = TYPE_TRI; order = 9; serendip = true; break;
case MSH_TRI_30 : parentType = TYPE_TRI; order = 10;serendip = true; break;
case MSH_TET_1 : parentType = TYPE_TET; order = 0; serendip = false; break;
case MSH_TET_4 : parentType = TYPE_TET; order = 1; serendip = false; break;
case MSH_TET_10 : parentType = TYPE_TET; order = 2; serendip = false; break;
case MSH_TET_20 : parentType = TYPE_TET; order = 3; serendip = false; break;
case MSH_TET_35 : parentType = TYPE_TET; order = 4; serendip = false; break;
case MSH_TET_56 : parentType = TYPE_TET; order = 5; serendip = false; break;
case MSH_TET_84 : parentType = TYPE_TET; order = 6; serendip = false; break;
case MSH_TET_120 : parentType = TYPE_TET; order = 7; serendip = false; break;
case MSH_TET_165 : parentType = TYPE_TET; order = 8; serendip = false; break;
case MSH_TET_220 : parentType = TYPE_TET; order = 9; serendip = false; break;
case MSH_TET_286 : parentType = TYPE_TET; order = 10;serendip = false; break;
case MSH_TET_34 : parentType = TYPE_TET; order = 4; serendip = true; break;
case MSH_TET_52 : parentType = TYPE_TET; order = 5; serendip = true; break;
case MSH_TET_74 : parentType = TYPE_TET; order = 6; serendip = true; break;
case MSH_TET_100 : parentType = TYPE_TET; order = 7; serendip = true; break;
case MSH_TET_130 : parentType = TYPE_TET; order = 8; serendip = true; break;
case MSH_TET_164 : parentType = TYPE_TET; order = 9; serendip = true; break;
case MSH_TET_202 : parentType = TYPE_TET; order = 10;serendip = true; break;
case MSH_QUA_1 : parentType = TYPE_QUA; order = 0; serendip = false; break;
case MSH_QUA_4 : parentType = TYPE_QUA; order = 1; serendip = false; break;
case MSH_QUA_9 : parentType = TYPE_QUA; order = 2; serendip = false; break;
case MSH_QUA_16 : parentType = TYPE_QUA; order = 3; serendip = false; break;
case MSH_QUA_25 : parentType = TYPE_QUA; order = 4; serendip = false; break;
case MSH_QUA_36 : parentType = TYPE_QUA; order = 5; serendip = false; break;
case MSH_QUA_49 : parentType = TYPE_QUA; order = 6; serendip = false; break;
case MSH_QUA_64 : parentType = TYPE_QUA; order = 7; serendip = false; break;
case MSH_QUA_81 : parentType = TYPE_QUA; order = 8; serendip = false; break;
case MSH_QUA_100 : parentType = TYPE_QUA; order = 9; serendip = false; break;
case MSH_QUA_121 : parentType = TYPE_QUA; order = 10;serendip = false; break;
case MSH_QUA_8 : parentType = TYPE_QUA; order = 2; serendip = true; break;
case MSH_QUA_12 : parentType = TYPE_QUA; order = 3; serendip = true; break;
case MSH_QUA_16I : parentType = TYPE_QUA; order = 4; serendip = true; break;
case MSH_QUA_20 : parentType = TYPE_QUA; order = 5; serendip = true; break;
case MSH_QUA_24 : parentType = TYPE_QUA; order = 6; serendip = true; break;
case MSH_QUA_28 : parentType = TYPE_QUA; order = 7; serendip = true; break;
case MSH_QUA_32 : parentType = TYPE_QUA; order = 8; serendip = true; break;
case MSH_QUA_36I : parentType = TYPE_QUA; order = 9; serendip = true; break;
case MSH_QUA_40 : parentType = TYPE_QUA; order = 10;serendip = true; break;
case MSH_PRI_1 : parentType = TYPE_PRI; order = 0; serendip = false; break;
case MSH_PRI_6 : parentType = TYPE_PRI; order = 1; serendip = false; break;
case MSH_PRI_18 : parentType = TYPE_PRI; order = 2; serendip = false; break;
case MSH_PRI_40 : parentType = TYPE_PRI; order = 3; serendip = false; break;
case MSH_PRI_75 : parentType = TYPE_PRI; order = 4; serendip = false; break;
case MSH_PRI_126 : parentType = TYPE_PRI; order = 5; serendip = false; break;
case MSH_PRI_196 : parentType = TYPE_PRI; order = 6; serendip = false; break;
case MSH_PRI_288 : parentType = TYPE_PRI; order = 7; serendip = false; break;
case MSH_PRI_405 : parentType = TYPE_PRI; order = 8; serendip = false; break;
case MSH_PRI_550 : parentType = TYPE_PRI; order = 9; serendip = false; break;
case MSH_PRI_15 : parentType = TYPE_PRI; order = 2; serendip = true; break;
case MSH_PRI_38 : parentType = TYPE_PRI; order = 3; serendip = true; break;
case MSH_PRI_66 : parentType = TYPE_PRI; order = 4; serendip = true; break;
case MSH_PRI_102 : parentType = TYPE_PRI; order = 5; serendip = true; break;
case MSH_PRI_146 : parentType = TYPE_PRI; order = 6; serendip = true; break;
case MSH_PRI_198 : parentType = TYPE_PRI; order = 7; serendip = true; break;
case MSH_PRI_258 : parentType = TYPE_PRI; order = 8; serendip = true; break;
case MSH_PRI_326 : parentType = TYPE_PRI; order = 9; serendip = true; break;
case MSH_HEX_1 : parentType = TYPE_HEX; order = 0; serendip = false; break;
case MSH_HEX_8 : parentType = TYPE_HEX; order = 1; serendip = false; break;
case MSH_HEX_27 : parentType = TYPE_HEX; order = 2; serendip = false; break;
case MSH_HEX_64 : parentType = TYPE_HEX; order = 3; serendip = false; break;
case MSH_HEX_125 : parentType = TYPE_HEX; order = 4; serendip = false; break; case MSH_HEX_216 : parentType = TYPE_HEX; order = 5; serendip = false; break;
case MSH_HEX_343 : parentType = TYPE_HEX; order = 6; serendip = false; break;
case MSH_HEX_512 : parentType = TYPE_HEX; order = 7; serendip = false; break;
case MSH_HEX_729 : parentType = TYPE_HEX; order = 8; serendip = false; break;
case MSH_HEX_1000: parentType = TYPE_HEX; order = 9; serendip = false; break;
case MSH_HEX_20 : parentType = TYPE_HEX; order = 2; serendip = false; break;
case MSH_HEX_56 : parentType = TYPE_HEX; order = 3; serendip = true; break;
case MSH_HEX_98 : parentType = TYPE_HEX; order = 4; serendip = true; break;
case MSH_HEX_152 : parentType = TYPE_HEX; order = 5; serendip = true; break;
case MSH_HEX_218 : parentType = TYPE_HEX; order = 6; serendip = true; break;
case MSH_HEX_296 : parentType = TYPE_HEX; order = 7; serendip = true; break;
case MSH_HEX_386 : parentType = TYPE_HEX; order = 8; serendip = true; break;
case MSH_HEX_488 : parentType = TYPE_HEX; order = 9; serendip = true; break;
case MSH_PYR_5 : parentType = TYPE_PYR; order = 1; serendip = false; break;
case MSH_PYR_14 : parentType = TYPE_PYR; order = 2; serendip = false; break;
case MSH_PYR_30 : parentType = TYPE_PYR; order = 3; serendip = false; break;
case MSH_PYR_55 : parentType = TYPE_PYR; order = 4; serendip = false; break;
case MSH_PYR_91 : parentType = TYPE_PYR; order = 5; serendip = false; break;
case MSH_PYR_140 : parentType = TYPE_PYR; order = 6; serendip = false; break;
case MSH_PYR_204 : parentType = TYPE_PYR; order = 7; serendip = false; break;
case MSH_PYR_285 : parentType = TYPE_PYR; order = 8; serendip = false; break;
case MSH_PYR_385 : parentType = TYPE_PYR; order = 9; serendip = false; break;
case MSH_PYR_13 : parentType = TYPE_PYR; order = 2; serendip = false; break;
case MSH_PYR_29 : parentType = TYPE_PYR; order = 3; serendip = true; break;
case MSH_PYR_50 : parentType = TYPE_PYR; order = 4; serendip = true; break;
case MSH_PYR_77 : parentType = TYPE_PYR; order = 5; serendip = true; break;
case MSH_PYR_110 : parentType = TYPE_PYR; order = 6; serendip = true; break;
case MSH_PYR_149 : parentType = TYPE_PYR; order = 7; serendip = true; break;
case MSH_PYR_194 : parentType = TYPE_PYR; order = 8; serendip = true; break;
case MSH_PYR_245 : parentType = TYPE_PYR; order = 9; serendip = true; break;
default :
Msg::Error("Unknown function space %d: reverting to TET_4", tag);
parentType = TYPE_TET; order = 1; serendip = false; break;
}
switch (parentType) {
case TYPE_PNT :
numFaces = 1;
dimension = 0;
points = generate1DPoints(0);
break;
case TYPE_LIN :
numFaces = 2;
dimension = 1;
points = generate1DPoints(order);
generate1dVertexClosure(closures, order);
generate1dVertexClosureFull(fullClosures, closureRef, order);
break;
case TYPE_TRI :
numFaces = 3;
dimension = 2;
points = gmshGeneratePointsTriangle(order, serendip);
if (order == 0) {
generateClosureOrder0(closures, 6);
generateClosureOrder0(fullClosures, 6);
closureRef.resize(6, 0);
}
else {
generate2dEdgeClosure(closures, order);
generate2dEdgeClosureFull(fullClosures, closureRef, order, 3, serendip);
}
break;
case TYPE_QUA :
numFaces = 4;
dimension = 2;
points = gmshGeneratePointsQuad(order, serendip);
if (order == 0) {
generateClosureOrder0(closures, 8);
generateClosureOrder0(fullClosures, 8); closureRef.resize(8, 0);
}
else {
generate2dEdgeClosure(closures, order, 4);
generate2dEdgeClosureFull(fullClosures, closureRef, order, 4, serendip);
}
break;
case TYPE_TET :
numFaces = 4;
dimension = 3;
points = gmshGeneratePointsTetrahedron(order, serendip);
if (order == 0) {
generateClosureOrder0(closures,24);
generateClosureOrder0(fullClosures, 24);
closureRef.resize(24, 0);
}
else {
generateFaceClosureTet(closures, order);
generateFaceClosureTetFull(fullClosures, closureRef, order, serendip);
}
break;
case TYPE_PRI :
numFaces = 5;
dimension = 3;
points = gmshGeneratePointsPrism(order, serendip);
if (order == 0) {
generateClosureOrder0(closures,48);
generateClosureOrder0(fullClosures,48);
closureRef.resize(48, 0);
}
else {
generateFaceClosurePrism(closures, order);
generateFaceClosurePrismFull(fullClosures, closureRef, order);
}
break;
case TYPE_HEX :
numFaces = 6;
dimension = 3;
points = gmshGeneratePointsHex(order, serendip);
generateFaceClosureHex(closures, order, serendip, points);
generateFaceClosureHexFull(fullClosures, closureRef, order, serendip, points);
break;
case TYPE_PYR :
numFaces = 5;
dimension = 3;
points = gmshGeneratePointsPyramid(order, serendip);
break;
}
}