IntPt *getGQHPts(int order)
{
if(order<2)return GQH[order];
if(order == 2)return GQH[3];
if(order == 3)return GQH[3];
int n = (order+3)/2;
int index = n-2 + 4;
if(!GQH[index])
{
double *pt,*wt;
// printf("o = %d n = %d i = %d\n",order,n*n*n,index);
gmshGaussLegendre1D(n,&pt,&wt);
GQH[index] = new IntPt[n*n*n];
int l = 0;
for(int i=0; i < n; i++) {
for(int j=0; j < n; j++) {
for(int k=0; k < n; k++) {
GQH[index][l].pt[0] = pt[i];
GQH[index][l].pt[1] = pt[j];
GQH[index][l].pt[2] = pt[k];
GQH[index][l++].weight = wt[i]*wt[j]*wt[k];
// printf ("%f %f %f %f\n",pt[i],pt[j],pt[k],wt[i]*wt[j]*wt[k]);
}
}
}
}
return GQH[index];
}
IntPt *getGQPriPts(int order)
{
int nLin = (order+3)/2;
int nTri = getNGQTPts(order);
int n = nLin*nTri;
int index = order;
if (order >= (int)(sizeof(GQP) / sizeof(IntPt*)))
Msg::Fatal("Increase size of GQP in gauss quadrature prism");
if(!GQP[index]){
double *linPt,*linWt;
IntPt *triPts = getGQTPts(order);
gmshGaussLegendre1D(nLin,&linPt,&linWt);
GQP[index] = new IntPt[n];
int l = 0;
for(int i=0; i < nTri; i++) {
for(int j=0; j < nLin; j++) {
GQP[index][l].pt[0] = triPts[i].pt[0];
GQP[index][l].pt[1] = triPts[i].pt[1];
GQP[index][l].pt[2] = linPt[j];
GQP[index][l++].weight = triPts[i].weight*linWt[j];
}
}
}
return GQP[index];
}
IntPt *getGQQPts(int order)
{
if(order<2)return GQQ[order];
if(order==2)return GQQ[3];
if(order==3)return GQQ[3];
int n = (order+3)/2;
int index = n-2 + 7;
if(!GQQ[index])
{
double *pt,*wt;
gmshGaussLegendre1D(n,&pt,&wt);
GQQ[index] = new IntPt[n*n];
int k = 0;
for(int i=0; i < n; i++) {
for(int j=0; j < n; j++) {
GQQ[index][k].pt[0] = pt[i];
GQQ[index][k].pt[1] = pt[j];
GQQ[index][k].pt[2] = 0.0;
GQQ[index][k++].weight = wt[i]*wt[j];
// printf ("%f %f %f\n",pt[i],pt[j],wt[i]*wt[j]);
}
}
}
return GQQ[index];
}
int GaussLegendreTri(int n1,int n2,IntPt *pts)
{
/* get degenerate n1Xn2 Gauss-Legendre scheme to integrate over a tri */
int i,j,index=0;
double *pt1,*pt2,*wt1,*wt2,dJ;
//const double two = 2.0000000000000000;
gmshGaussLegendre1D(n1,&pt1,&wt1);
gmshGaussLegendre1D(n2,&pt2,&wt2);
for(i=0; i < n1; i++) {
for(j=0; j < n2; j++) {
quadToTri(pt1[i],pt2[j],&(pts[index].pt[0]),&(pts[index].pt[1]),&dJ);
pts[index].pt[2] = 0;
pts[index++].weight = dJ*wt1[i]*wt2[j];
}
}
return index;
}
int GaussLegendreTet(int n1, int n2, int n3, IntPt *pts)
{
/* get degenerate n1Xn2Xn3 Gauss-Legendre scheme to integrate over a tet */
int i,j,k,index=0;
double *pt1,*pt2,*pt3,*wt1,*wt2,*wt3,dJ;
gmshGaussLegendre1D(n1,&pt1,&wt1);
gmshGaussLegendre1D(n2,&pt2,&wt2);
gmshGaussLegendre1D(n3,&pt3,&wt3);
for(i=0; i < n1; i++) {
for(j=0; j < n2; j++) {
for(k=0; k < n3; k++) {
brickToTet(pt1[i],pt2[j],pt3[k],&(pts[index].pt[0]),
&(pts[index].pt[1]),&(pts[index].pt[2]),&dJ);
pts[index++].weight = dJ*wt1[i]*wt2[j]*wt3[k];
}
}
}
return index;
}
IntPt *getGQPyrPts(int order)
{
int index = order;
if(index >= (int)(sizeof(GQPyr) / sizeof(IntPt*))){
Msg::Error("Increase size of GQPyr in gauss quadrature pyr");
index = 0;
}
if(!GQPyr[index]) {
int nbPtUV = order/2 + 1;
int nbPtW = order/2 + 1;
int nbPtUV2 = nbPtUV * nbPtUV;
double *linPt,*linWt;
gmshGaussLegendre1D(nbPtUV,&linPt,&linWt);
double *GJ20Pt, *GJ20Wt;
getGaussJacobiQuadrature(2, 0, nbPtW, &GJ20Pt, &GJ20Wt);
GQPyr[index] = new IntPt[getNGQPyrPts(order)];
int l = 0;
for (int i = 0; i < getNGQPyrPts(order); i++) {
// compose an integration rule for (1-w)^2 f(u,v,w) on the standard hexahedron
int iW = i / (nbPtUV2);
int iU = (i - iW*nbPtUV2)/nbPtUV;
int iV = (i - iW*nbPtUV2 - iU*nbPtUV);
// std::cout << "Points " << iU << " " << iV << " " << iW << std::endl;
int wt = linWt[iU]*linWt[iV]*GJ20Wt[iW];
double up = linPt[iU];
double vp = linPt[iV];
double wp = GJ20Pt[iW];
// now incorporate the Duffy transformation from pyramid to hexahedron
GQPyr[index][l].pt[0] = 0.5*(1-wp)*up;
GQPyr[index][l].pt[1] = 0.5*(1-wp)*vp;
GQPyr[index][l].pt[2] = 0.5*(1+wp);
wt *= 0.125;
GQPyr[index][l++].weight = wt;
}
}
return GQPyr[index];
}
double GEdge::length(const double &u0, const double &u1, const int nbQuadPoints)
{
double *t = 0, *w = 0;
gmshGaussLegendre1D(nbQuadPoints, &t, &w);
double L = 0.0;
const double rapJ = (u1 - u0) * .5;
for (int i = 0; i < nbQuadPoints; i++){
const double ui = u0 * 0.5 * (1. - t[i]) + u1 * 0.5 * (1. + t[i]);
SVector3 der = firstDer(ui);
const double d = norm(der);
L += d * w[i] * rapJ;
}
return L;
}
IntPt *getGQLPts(int order)
{
// Number of Gauss Point:
// (order + 1) / 2 *ROUNDED UP*
int n = (order + 1) / (double)2 + 0.5;
int index = n;
if(index >= (int)(sizeof(GQL) / sizeof(IntPt*))){
Msg::Error("Increase size of GQL in gauss quadrature line");
index = 0;
}
if(!GQL[index]) {
double *pt,*wt;
gmshGaussLegendre1D(n,&pt,&wt);
GQL[index] = new IntPt[n];
for(int i=0; i < n; i++) {
GQL[index][i].pt[0] = pt[i];
GQL[index][i].pt[1] = 0.0;
GQL[index][i].pt[2] = 0.0;
GQL[index][i].weight = wt[i];
}
}
return GQL[index];
}