void CRocheLobe_FF::ComputeRadii(const double pot_surface, const double separation, const double q, const double P)
{
// Compute the radii for the pixels and corners:
for(unsigned int i = 0; i < pixel_radii.size(); i++)
pixel_radii[i] = ComputeRadius(pot_surface, separation, q, P, pixel_theta[i], pixel_phi[i]);
for(unsigned int i = 0; i < corner_radii.size(); i++)
corner_radii[i] = ComputeRadius(pot_surface, separation, q, P, corner_theta[i], corner_phi[i]);
}
void CRocheLobe_FF::preRender(double & max_flux)
{
if (!mModelReady)
Init();
// See if the user change the tesselation
const unsigned int n_sides = pow(2, mParams["n_side_power"].getValue());
if(mParams["n_side_power"].isDirty())
{
Init();
}
const double T_eff_pole = mParams["T_eff_pole"].getValue();
const double von_zeipel_beta = mParams["von_zeipel_beta"].getValue();
const double separation = mParams["separation"].getValue();
const double q = mParams["q"].getValue();
const double P = mParams["P"].getValue();
const double F = mParams["F"].getValue();
//printf("%lf %lf %lf %lf", q, P, F, separation);
// First find the position of L1 point on the axis
double r_L1 = separation * ComputeRL1(q, P);
// Potential at L1 point
double pot_L1, dpot_L1;
ComputePotential(pot_L1, dpot_L1, r_L1, PI/2., 0.0, separation, q, P);
// Potential at F surface
double pot_surface = (pot_L1 + 0.5*q*q/(1.+q))/F - 0.5*q*q/(1.+q);
// Compute r_pole
double r_pole = ComputeRadius(pot_surface, separation, q, P, 0.0, 0.0);
// Compute gravity at pole
double g_pole, tempx, tempy, tempz;
ComputeGravity(separation, q, P, r_pole, 0.0, 0.0, tempx, tempy, tempz, g_pole);
// Compute Radii for all Healpix pixels
ComputeRadii(pot_surface, separation, q, P);
// Compute Gravity for all Healpix pixels
ComputeGravity(separation, q, P);
bool feature_dirty = false;
for(auto feature: mFeatures)
feature_dirty |= feature->isDirty();
if(feature_dirty || mParams["T_eff_pole"].isDirty() || mParams["von_zeipel_beta"].isDirty())
VonZeipelTemperatures(T_eff_pole, g_pole, von_zeipel_beta);
for(auto feature: mFeatures)
feature->apply(this);
TemperatureToFlux(mPixelTemperatures, mFluxTexture, mWavelength, max_flux);
GenerateVBO(n_pixels, n_sides, mVBOData);
}
/// Computes the geometry of the spherical Healpix surface
void CRocheLobe_FF::GenerateModel(vector<vec3> & vbo_data,
vector<unsigned int> & elements)
{
const double T_eff_pole = mParams["T_eff_pole"].getValue();
const double von_zeipel_beta = mParams["von_zeipel_beta"].getValue();
const unsigned int n_sides = pow(2, mParams["n_side_power"].getValue());
const double separation = mParams["separation"].getValue();
const double q = mParams["q"].getValue();
const double P = mParams["P"].getValue();
const double F = mParams["F"].getValue();
// Generate a unit Healpix sphere
GenerateHealpixSphere(n_pixels, n_sides);
// recomputing the sphereoid is very expensive. Make use of the dirty flags
// to only compute that which is absolutely necessary.
double r_L1 = separation * ComputeRL1(q, P);
// Potential at L1 point
double pot_L1, dpot_L1;
ComputePotential(pot_L1, dpot_L1, r_L1, PI/2., 0.0, separation, q, P);
// Potential at F surface
double pot_surface = (pot_L1 + 0.5*q*q/(1.+q))/F - 0.5*q*q/(1.+q);
// Compute r_pole
double r_pole = ComputeRadius(pot_surface, separation, q, P, 0.0, 0.0);
// Compute gravity at pole
double g_pole, tempx, tempy, tempz;
ComputeGravity(separation, q, P, r_pole, 0.0, 0.0, tempx, tempy, tempz, g_pole);
// Compute Radii for all Healpix pixels
ComputeRadii(pot_surface, separation, q, P);
// Compute Gravity for all Healpix pixels
ComputeGravity(separation, q, P);
// Compute Temperatures for all Healpix pixels
VonZeipelTemperatures(T_eff_pole, g_pole, von_zeipel_beta);
for(auto feature: mFeatures)
feature->apply(this);
// Find the maximum temperature
double max_temperature = 0;
for(unsigned int i = 0; i < mPixelTemperatures.size(); i++)
{
if(mPixelTemperatures[i] > max_temperature)
max_temperature = mPixelTemperatures[i];
}
// Convert temperatures to fluxes.
TemperatureToFlux(mPixelTemperatures, mFluxTexture, mWavelength, max_temperature);
GenerateVBO(n_pixels, n_sides, vbo_data);
// Create the lookup indicies.
GenerateHealpixVBOIndicies(n_pixels, elements);
}
ConformalMap<Real>::ConformalMap (int numPoints,
const Vector3<Real>* points, int numTriangles, const int* indices,
int punctureTriangle)
{
// Construct a vertex-triangle-edge representation of mesh.
BasicMesh mesh(numPoints, points, numTriangles, indices);
int numEdges = mesh.GetNumEdges();
const BasicMesh::Edge* edges = mesh.GetEdges();
const BasicMesh::Triangle* triangles = mesh.GetTriangles();
mPlanes = new1<Vector2<Real> >(numPoints);
mSpheres = new1<Vector3<Real> >(numPoints);
// Construct sparse matrix A nondiagonal entries.
typename LinearSystem<Real>::SparseMatrix AMat;
int i, e, t, v0, v1, v2;
Real value = (Real)0;
for (e = 0; e < numEdges; ++e)
{
const BasicMesh::Edge& edge = edges[e];
v0 = edge.V[0];
v1 = edge.V[1];
Vector3<Real> E0, E1;
const BasicMesh::Triangle& T0 = triangles[edge.T[0]];
for (i = 0; i < 3; ++i)
{
v2 = T0.V[i];
if (v2 != v0 && v2 != v1)
{
E0 = points[v0] - points[v2];
E1 = points[v1] - points[v2];
value = E0.Dot(E1)/E0.Cross(E1).Length();
}
}
const BasicMesh::Triangle& T1 = triangles[edge.T[1]];
for (i = 0; i < 3; ++i)
{
v2 = T1.V[i];
if (v2 != v0 && v2 != v1)
{
E0 = points[v0] - points[v2];
E1 = points[v1] - points[v2];
value += E0.Dot(E1)/E0.Cross(E1).Length();
}
}
value *= -(Real)0.5;
AMat[std::make_pair(v0, v1)] = value;
}
// Aonstruct sparse matrix A diagonal entries.
Real* tmp = new1<Real>(numPoints);
memset(tmp, 0, numPoints*sizeof(Real));
typename LinearSystem<Real>::SparseMatrix::iterator iter = AMat.begin();
typename LinearSystem<Real>::SparseMatrix::iterator end = AMat.end();
for (/**/; iter != end; ++iter)
{
v0 = iter->first.first;
v1 = iter->first.second;
value = iter->second;
assertion(v0 != v1, "Unexpected condition\n");
tmp[v0] -= value;
tmp[v1] -= value;
}
for (int v = 0; v < numPoints; ++v)
{
AMat[std::make_pair(v, v)] = tmp[v];
}
assertion(numPoints + numEdges == (int)AMat.size(),
"Mismatch in sizes\n");
// Construct column vector B (happens to be sparse).
const BasicMesh::Triangle& tri = triangles[punctureTriangle];
v0 = tri.V[0];
v1 = tri.V[1];
v2 = tri.V[2];
Vector3<Real> V0 = points[v0];
Vector3<Real> V1 = points[v1];
Vector3<Real> V2 = points[v2];
Vector3<Real> E10 = V1 - V0;
Vector3<Real> E20 = V2 - V0;
Vector3<Real> E12 = V1 - V2;
Vector3<Real> cross = E20.Cross(E10);
Real len10 = E10.Length();
Real invLen10 = ((Real)1)/len10;
Real twoArea = cross.Length();
Real invLenCross = ((Real)1)/twoArea;
Real invProd = invLen10*invLenCross;
Real re0 = -invLen10;
Real im0 = invProd*E12.Dot(E10);
Real re1 = invLen10;
Real im1 = invProd*E20.Dot(E10);
Real re2 = (Real)0;
Real im2 = -len10*invLenCross;
// Solve sparse system for real parts.
memset(tmp, 0, numPoints*sizeof(Real));
tmp[v0] = re0;
tmp[v1] = re1;
tmp[v2] = re2;
Real* result = new1<Real>(numPoints);
bool solved = LinearSystem<Real>().SolveSymmetricCG(numPoints, AMat, tmp,
result);
assertion(solved, "Failed to solve linear system\n");
WM5_UNUSED(solved);
for (i = 0; i < numPoints; ++i)
{
mPlanes[i].X() = result[i];
}
// Solve sparse system for imaginary parts.
memset(tmp, 0, numPoints*sizeof(Real));
tmp[v0] = -im0;
tmp[v1] = -im1;
tmp[v2] = -im2;
solved = LinearSystem<Real>().SolveSymmetricCG(numPoints, AMat, tmp,
result);
assertion(solved, "Failed to solve linear system\n");
for (i = 0; i < numPoints; ++i)
{
mPlanes[i].Y() = result[i];
}
delete1(tmp);
delete1(result);
// Scale to [-1,1]^2 for numerical conditioning in later steps.
Real fmin = mPlanes[0].X(), fmax = fmin;
for (i = 0; i < numPoints; i++)
{
if (mPlanes[i].X() < fmin)
{
fmin = mPlanes[i].X();
}
else if (mPlanes[i].X() > fmax)
{
fmax = mPlanes[i].X();
}
if (mPlanes[i].Y() < fmin)
{
fmin = mPlanes[i].Y();
}
else if (mPlanes[i].Y() > fmax)
{
fmax = mPlanes[i].Y();
}
}
Real halfRange = ((Real)0.5)*(fmax - fmin);
Real invHalfRange = ((Real)1)/halfRange;
for (i = 0; i < numPoints; ++i)
{
mPlanes[i].X() = -(Real)1 + invHalfRange*(mPlanes[i].X() - fmin);
mPlanes[i].Y() = -(Real)1 + invHalfRange*(mPlanes[i].Y() - fmin);
}
// Map plane points to sphere using inverse stereographic projection.
// The main issue is selecting a translation in (x,y) and a radius of
// the projection sphere. Both factors strongly influence the final
// result.
// Use the average as the south pole. The points tend to be clustered
// approximately in the middle of the conformally mapped punctured
// triangle, so the average is a good choice to place the pole.
Vector2<Real> origin((Real)0 ,(Real)0 );
for (i = 0; i < numPoints; ++i)
{
origin += mPlanes[i];
}
origin /= (Real)numPoints;
for (i = 0; i < numPoints; ++i)
{
mPlanes[i] -= origin;
}
mPlaneMin = mPlanes[0];
mPlaneMax = mPlanes[0];
for (i = 1; i < numPoints; ++i)
{
if (mPlanes[i].X() < mPlaneMin.X())
{
mPlaneMin.X() = mPlanes[i].X();
}
else if (mPlanes[i].X() > mPlaneMax.X())
{
mPlaneMax.X() = mPlanes[i].X();
}
if (mPlanes[i].Y() < mPlaneMin.Y())
{
mPlaneMin.Y() = mPlanes[i].Y();
}
else if (mPlanes[i].Y() > mPlaneMax.Y())
{
mPlaneMax.Y() = mPlanes[i].Y();
}
}
// Select the radius of the sphere so that the projected punctured
// triangle has an area whose fraction of total spherical area is the
// same fraction as the area of the punctured triangle to the total area
// of the original triangle mesh.
Real twoTotalArea = (Real)0;
for (t = 0; t < numTriangles; ++t)
{
const BasicMesh::Triangle& T0 = triangles[t];
const Vector3<Real>& V0 = points[T0.V[0]];
const Vector3<Real>& V1 = points[T0.V[1]];
const Vector3<Real>& V2 = points[T0.V[2]];
Vector3<Real> E0 = V1 - V0, E1 = V2 - V0;
twoTotalArea += E0.Cross(E1).Length();
}
mRadius = ComputeRadius(mPlanes[v0], mPlanes[v1], mPlanes[v2],
twoArea/twoTotalArea);
Real radiusSqr = mRadius*mRadius;
// Inverse stereographic projection to obtain sphere coordinates. The
// sphere is centered at the origin and has radius 1.
for (i = 0; i < numPoints; i++)
{
Real rSqr = mPlanes[i].SquaredLength();
Real mult = ((Real)1)/(rSqr + radiusSqr);
Real x = ((Real)2)*mult*radiusSqr*mPlanes[i].X();
Real y = ((Real)2)*mult*radiusSqr*mPlanes[i].Y();
Real z = mult*mRadius*(rSqr - radiusSqr);
mSpheres[i] = Vector3<Real>(x,y,z)/mRadius;
}
}
