void Foam::block::createPoints() const
{
// set local variables for mesh specification
const label ni = meshDensity().x();
const label nj = meshDensity().y();
const label nk = meshDensity().z();
const point& p000 = blockPoint(0);
const point& p100 = blockPoint(1);
const point& p110 = blockPoint(2);
const point& p010 = blockPoint(3);
const point& p001 = blockPoint(4);
const point& p101 = blockPoint(5);
const point& p111 = blockPoint(6);
const point& p011 = blockPoint(7);
// list of edge point and weighting factors
const List< List<point> >& p = blockEdgePoints();
const scalarListList& w = blockEdgeWeights();
//
// generate vertices
//
vertices_.clear();
vertices_.setSize(nPoints());
for (label k = 0; k <= nk; k++)
{
for (label j = 0; j <= nj; j++)
{
for (label i = 0; i <= ni; i++)
{
const label vertexNo = vtxLabel(i, j, k);
// points on edges
vector edgex1 = p000 + (p100 - p000)*w[0][i];
vector edgex2 = p010 + (p110 - p010)*w[1][i];
vector edgex3 = p011 + (p111 - p011)*w[2][i];
vector edgex4 = p001 + (p101 - p001)*w[3][i];
vector edgey1 = p000 + (p010 - p000)*w[4][j];
vector edgey2 = p100 + (p110 - p100)*w[5][j];
vector edgey3 = p101 + (p111 - p101)*w[6][j];
vector edgey4 = p001 + (p011 - p001)*w[7][j];
vector edgez1 = p000 + (p001 - p000)*w[8][k];
vector edgez2 = p100 + (p101 - p100)*w[9][k];
vector edgez3 = p110 + (p111 - p110)*w[10][k];
vector edgez4 = p010 + (p011 - p010)*w[11][k];
// calculate the importance factors for all edges
// x-direction
scalar impx1 =
(
(1.0 - w[0][i])*(1.0 - w[4][j])*(1.0 - w[8][k])
+ w[0][i]*(1.0 - w[5][j])*(1.0 - w[9][k])
);
scalar impx2 =
(
(1.0 - w[1][i])*w[4][j]*(1.0 - w[11][k])
+ w[1][i]*w[5][j]*(1.0 - w[10][k])
);
scalar impx3 =
(
(1.0 - w[2][i])*w[7][j]*w[11][k]
+ w[2][i]*w[6][j]*w[10][k]
);
scalar impx4 =
(
(1.0 - w[3][i])*(1.0 - w[7][j])*w[8][k]
+ w[3][i]*(1.0 - w[6][j])*w[9][k]
);
scalar magImpx = impx1 + impx2 + impx3 + impx4;
impx1 /= magImpx;
impx2 /= magImpx;
impx3 /= magImpx;
impx4 /= magImpx;
// y-direction
scalar impy1 =
(
(1.0 - w[4][j])*(1.0 - w[0][i])*(1.0 - w[8][k])
+ w[4][j]*(1.0 - w[1][i])*(1.0 - w[11][k])
);
scalar impy2 =
(
(1.0 - w[5][j])*w[0][i]*(1.0 - w[9][k])
+ w[5][j]*w[1][i]*(1.0 - w[10][k])
);
scalar impy3 =
(
(1.0 - w[6][j])*w[3][i]*w[9][k]
+ w[6][j]*w[2][i]*w[10][k]
);
scalar impy4 =
(
(1.0 - w[7][j])*(1.0 - w[3][i])*w[8][k]
+ w[7][j]*(1.0 - w[2][i])*w[11][k]
);
scalar magImpy = impy1 + impy2 + impy3 + impy4;
impy1 /= magImpy;
impy2 /= magImpy;
impy3 /= magImpy;
impy4 /= magImpy;
// z-direction
scalar impz1 =
(
(1.0 - w[8][k])*(1.0 - w[0][i])*(1.0 - w[4][j])
+ w[8][k]*(1.0 - w[3][i])*(1.0 - w[7][j])
);
scalar impz2 =
(
(1.0 - w[9][k])*w[0][i]*(1.0 - w[5][j])
+ w[9][k]*w[3][i]*(1.0 - w[6][j])
);
scalar impz3 =
(
(1.0 - w[10][k])*w[1][i]*w[5][j]
+ w[10][k]*w[2][i]*w[6][j]
);
scalar impz4 =
(
(1.0 - w[11][k])*(1.0 - w[1][i])*w[4][j]
+ w[11][k]*(1.0 - w[2][i])*w[7][j]
);
scalar magImpz = impz1 + impz2 + impz3 + impz4;
impz1 /= magImpz;
impz2 /= magImpz;
impz3 /= magImpz;
impz4 /= magImpz;
// calculate the correction vectors
vector corx1 = impx1*(p[0][i] - edgex1);
vector corx2 = impx2*(p[1][i] - edgex2);
vector corx3 = impx3*(p[2][i] - edgex3);
vector corx4 = impx4*(p[3][i] - edgex4);
vector cory1 = impy1*(p[4][j] - edgey1);
vector cory2 = impy2*(p[5][j] - edgey2);
vector cory3 = impy3*(p[6][j] - edgey3);
vector cory4 = impy4*(p[7][j] - edgey4);
vector corz1 = impz1*(p[8][k] - edgez1);
vector corz2 = impz2*(p[9][k] - edgez2);
vector corz3 = impz3*(p[10][k] - edgez3);
vector corz4 = impz4*(p[11][k] - edgez4);
// multiply by the importance factor
// x-direction
edgex1 *= impx1;
edgex2 *= impx2;
edgex3 *= impx3;
edgex4 *= impx4;
// y-direction
edgey1 *= impy1;
edgey2 *= impy2;
edgey3 *= impy3;
edgey4 *= impy4;
// z-direction
edgez1 *= impz1;
edgez2 *= impz2;
edgez3 *= impz3;
edgez4 *= impz4;
// add the contributions
vertices_[vertexNo] =
(
edgex1 + edgex2 + edgex3 + edgex4
+ edgey1 + edgey2 + edgey3 + edgey4
+ edgez1 + edgez2 + edgez3 + edgez4
) / 3.0;
vertices_[vertexNo] +=
(
corx1 + corx2 + corx3 + corx4
+ cory1 + cory2 + cory3 + cory4
+ corz1 + corz2 + corz3 + corz4
);
}
}
}
}
void Foam::block::createPoints()
{
// Set local variables for mesh specification
const label ni = density().x();
const label nj = density().y();
const label nk = density().z();
const point& p000 = blockPoint(0);
const point& p100 = blockPoint(1);
const point& p110 = blockPoint(2);
const point& p010 = blockPoint(3);
const point& p001 = blockPoint(4);
const point& p101 = blockPoint(5);
const point& p111 = blockPoint(6);
const point& p011 = blockPoint(7);
// List of edge point and weighting factors
pointField p[12];
scalarList w[12];
label nCurvedEdges = edgesPointsWeights(p, w);
points_.setSize(nPoints());
points_[pointLabel(0, 0, 0)] = p000;
points_[pointLabel(ni, 0, 0)] = p100;
points_[pointLabel(ni, nj, 0)] = p110;
points_[pointLabel(0, nj, 0)] = p010;
points_[pointLabel(0, 0, nk)] = p001;
points_[pointLabel(ni, 0, nk)] = p101;
points_[pointLabel(ni, nj, nk)] = p111;
points_[pointLabel(0, nj, nk)] = p011;
for (label k=0; k<=nk; k++)
{
for (label j=0; j<=nj; j++)
{
for (label i=0; i<=ni; i++)
{
// Skip block vertices
if (vertex(i, j, k)) continue;
const label vijk = pointLabel(i, j, k);
// Calculate the weighting factors for all edges
// x-direction
scalar wx1 = (1 - w0)*(1 - w4)*(1 - w8) + w0*(1 - w5)*(1 - w9);
scalar wx2 = (1 - w1)*w4*(1 - w11) + w1*w5*(1 - w10);
scalar wx3 = (1 - w2)*w7*w11 + w2*w6*w10;
scalar wx4 = (1 - w3)*(1 - w7)*w8 + w3*(1 - w6)*w9;
const scalar sumWx = wx1 + wx2 + wx3 + wx4;
wx1 /= sumWx;
wx2 /= sumWx;
wx3 /= sumWx;
wx4 /= sumWx;
// y-direction
scalar wy1 = (1 - w4)*(1 - w0)*(1 - w8) + w4*(1 - w1)*(1 - w11);
scalar wy2 = (1 - w5)*w0*(1 - w9) + w5*w1*(1 - w10);
scalar wy3 = (1 - w6)*w3*w9 + w6*w2*w10;
scalar wy4 = (1 - w7)*(1 - w3)*w8 + w7*(1 - w2)*w11;
const scalar sumWy = wy1 + wy2 + wy3 + wy4;
wy1 /= sumWy;
wy2 /= sumWy;
wy3 /= sumWy;
wy4 /= sumWy;
// z-direction
scalar wz1 = (1 - w8)*(1 - w0)*(1 - w4) + w8*(1 - w3)*(1 - w7);
scalar wz2 = (1 - w9)*w0*(1 - w5) + w9*w3*(1 - w6);
scalar wz3 = (1 - w10)*w1*w5 + w10*w2*w6;
scalar wz4 = (1 - w11)*(1 - w1)*w4 + w11*(1 - w2)*w7;
const scalar sumWz = wz1 + wz2 + wz3 + wz4;
wz1 /= sumWz;
wz2 /= sumWz;
wz3 /= sumWz;
wz4 /= sumWz;
// Points on straight edges
const vector edgex1 = p000 + (p100 - p000)*w0;
const vector edgex2 = p010 + (p110 - p010)*w1;
const vector edgex3 = p011 + (p111 - p011)*w2;
const vector edgex4 = p001 + (p101 - p001)*w3;
const vector edgey1 = p000 + (p010 - p000)*w4;
const vector edgey2 = p100 + (p110 - p100)*w5;
const vector edgey3 = p101 + (p111 - p101)*w6;
const vector edgey4 = p001 + (p011 - p001)*w7;
const vector edgez1 = p000 + (p001 - p000)*w8;
const vector edgez2 = p100 + (p101 - p100)*w9;
const vector edgez3 = p110 + (p111 - p110)*w10;
const vector edgez4 = p010 + (p011 - p010)*w11;
// Add the contributions
points_[vijk] =
(
wx1*edgex1 + wx2*edgex2 + wx3*edgex3 + wx4*edgex4
+ wy1*edgey1 + wy2*edgey2 + wy3*edgey3 + wy4*edgey4
+ wz1*edgez1 + wz2*edgez2 + wz3*edgez3 + wz4*edgez4
)/3;
// Apply curved-edge correction if block has curved edges
if (nCurvedEdges)
{
// Calculate the correction vectors
const vector corx1 = wx1*(p[0][i] - edgex1);
const vector corx2 = wx2*(p[1][i] - edgex2);
const vector corx3 = wx3*(p[2][i] - edgex3);
const vector corx4 = wx4*(p[3][i] - edgex4);
const vector cory1 = wy1*(p[4][j] - edgey1);
const vector cory2 = wy2*(p[5][j] - edgey2);
const vector cory3 = wy3*(p[6][j] - edgey3);
const vector cory4 = wy4*(p[7][j] - edgey4);
const vector corz1 = wz1*(p[8][k] - edgez1);
const vector corz2 = wz2*(p[9][k] - edgez2);
const vector corz3 = wz3*(p[10][k] - edgez3);
const vector corz4 = wz4*(p[11][k] - edgez4);
points_[vijk] +=
(
corx1 + corx2 + corx3 + corx4
+ cory1 + cory2 + cory3 + cory4
+ corz1 + corz2 + corz3 + corz4
);
}
}
}
}
if (!nCurvedFaces()) return;
// Apply curvature correction to face points
FixedList<pointField, 6> facePoints(this->facePoints(points_));
correctFacePoints(facePoints);
// Loop over points and apply the correction from the from the i-faces
for (label ii=0; ii<=ni; ii++)
{
// Process the points on the curved faces last
label i = (ii + 1)%(ni + 1);
for (label j=0; j<=nj; j++)
{
for (label k=0; k<=nk; k++)
{
// Skip non-curved faces and edges
if (flatFaceOrEdge(i, j, k)) continue;
const label vijk = pointLabel(i, j, k);
scalar wf0 =
(
(1 - w0)*(1 - w4)*(1 - w8)
+ (1 - w1)*w4*(1 - w11)
+ (1 - w2)*w7*w11
+ (1 - w3)*(1 - w7)*w8
);
scalar wf1 =
(
w0*(1 - w5)*(1 - w9)
+ w1*w5*(1 - w10)
+ w2*w5*w10
+ w3*(1 - w6)*w9
);
const scalar sumWf = wf0 + wf1;
wf0 /= sumWf;
wf1 /= sumWf;
points_[vijk] +=
(
wf0
*(
facePoints[0][facePointLabel(0, j, k)]
- points_[pointLabel(0, j, k)]
)
+ wf1
*(
facePoints[1][facePointLabel(1, j, k)]
- points_[pointLabel(ni, j, k)]
)
);
}
}
}
// Loop over points and apply the correction from the from the j-faces
for (label jj=0; jj<=nj; jj++)
{
// Process the points on the curved faces last
label j = (jj + 1)%(nj + 1);
for (label i=0; i<=ni; i++)
{
for (label k=0; k<=nk; k++)
{
// Skip flat faces and edges
if (flatFaceOrEdge(i, j, k)) continue;
const label vijk = pointLabel(i, j, k);
scalar wf2 =
(
(1 - w4)*(1 - w1)*(1 - w8)
+ (1 - w5)*w0*(1 - w9)
+ (1 - w6)*w3*w9
+ (1 - w7)*(1 - w3)*w8
);
scalar wf3 =
(
w4*(1 - w1)*(1 - w11)
+ w5*w1*(1 - w10)
+ w6*w2*w10
+ w7*(1 - w2)*w11
);
const scalar sumWf = wf2 + wf3;
wf2 /= sumWf;
wf3 /= sumWf;
points_[vijk] +=
(
wf2
*(
facePoints[2][facePointLabel(2, i, k)]
- points_[pointLabel(i, 0, k)]
)
+ wf3
*(
facePoints[3][facePointLabel(3, i, k)]
- points_[pointLabel(i, nj, k)]
)
);
}
}
}
// Loop over points and apply the correction from the from the k-faces
for (label kk=0; kk<=nk; kk++)
{
// Process the points on the curved faces last
label k = (kk + 1)%(nk + 1);
for (label i=0; i<=ni; i++)
{
for (label j=0; j<=nj; j++)
{
// Skip flat faces and edges
if (flatFaceOrEdge(i, j, k)) continue;
const label vijk = pointLabel(i, j, k);
scalar wf4 =
(
(1 - w8)*(1 - w0)*(1 - w4)
+ (1 - w9)*w0*(1 - w5)
+ (1 - w10)*w1*w5
+ (1 - w11)*(1 - w1)*w4
);
scalar wf5 =
(
w8*(1 - w3)*(1 - w7)
+ w9*w3*(1 - w6)
+ w10*w2*w6
+ w11*(1 - w2)*w7
);
const scalar sumWf = wf4 + wf5;
wf4 /= sumWf;
wf5 /= sumWf;
points_[vijk] +=
(
wf4
*(
facePoints[4][facePointLabel(4, i, j)]
- points_[pointLabel(i, j, 0)]
)
+ wf5
*(
facePoints[5][facePointLabel(5, i, j)]
- points_[pointLabel(i, j, nk)]
)
);
}
}
}
}
