void Mesh::samplePosition(const Point2f &sample, Point3f &p, Normal3f &n) const {
Point2f reusableSample = sample;
//get a random face
uint32_t faceIndex = m_dpdf->sampleReuse(reusableSample(0));
// sample the triangle of the face
Point2f uv = Warp::squareToTriangle(reusableSample);
//get the vertex index
uint32_t i0 = m_F(0, faceIndex), i1 = m_F(1, faceIndex), i2 = m_F(2, faceIndex);
//get the points
Point3f p0 = m_V.col(i0), p1 = m_V.col(i1), p2 = m_V.col(i2);
//compute the edge vectors
Vector3f edge1 = (p1 - p0);
Vector3f edge2 = (p2 - p0);
Vector3f e1 = uv(0) * edge1;
Vector3f e2 = uv(1) * edge2;
//compute the new point
p = p0 + e1 + e2;
//compute the normal base on baycentric coordinates
//get the vertex normals
if(m_N.cols() > 3) {
Normal3f n0 = m_N.col(i0), n1 = m_N.col(i1), n2 = m_N.col(i2);
Vector3f w0 = p0 - p;
Vector3f w1 = p1 - p;
Vector3f w2 = p2 - p;
float area = (edge1.cross(edge2)).norm();
if(area != 0.0f){
float u = (w0.cross(w1)).norm() / area;
float v = (w1.cross(w2)).norm() / area;
n = (1.0f - u - v) * n0 + v * n1 + u * n2;
n.normalized();
} else {
n = (e1.cross(e2)).normalized();
}
} else {
//no normals provided
n = (e1.cross(e2)).normalized();
if(isnan(n.sum())){
cout << "Normal is nan" << endl;
cout << "e1 " << e1 << endl;
cout << "e2 " << e2 << endl;
}
}
//n = uv(0) * n0 + uv(1) * n1 + (1.0f - uv(0) - uv(1)) * n2;
}
float Mesh::surfaceArea(uint32_t index) const {
uint32_t i0 = m_F(0, index), i1 = m_F(1, index), i2 = m_F(2, index);
const Point3f p0 = m_V.col(i0), p1 = m_V.col(i1), p2 = m_V.col(i2);
return 0.5f * Vector3f((p1 - p0).cross(p2 - p0)).norm();
}
void BoysFunction::setx(double x)
{
if (x <= 50){
m_F(m_nMax) = tabulated(m_nMax, x);
} else {
m_F(m_nMax) = asymptotic(m_nMax, x);
}
double ex = exp(-x);
for(int n = m_nMax; n > 0; n--){
m_F(n-1) = (2*x*m_F(n) + ex)/(2*n - 1);
}
}
bool Mesh::rayIntersect(uint32_t index, const Ray3f &ray, float &u, float &v, float &t) const {
uint32_t i0 = m_F(0, index), i1 = m_F(1, index), i2 = m_F(2, index);
const Point3f p0 = m_V.col(i0), p1 = m_V.col(i1), p2 = m_V.col(i2);
/* Find vectors for two edges sharing v[0] */
Vector3f edge1 = p1 - p0, edge2 = p2 - p0;
/* Begin calculating determinant - also used to calculate U parameter */
Vector3f pvec = ray.d.cross(edge2);
/* If determinant is near zero, ray lies in plane of triangle */
float det = edge1.dot(pvec);
if (det > -1e-8f && det < 1e-8f)
return false;
float inv_det = 1.0f / det;
/* Calculate distance from v[0] to ray origin */
Vector3f tvec = ray.o - p0;
/* Calculate U parameter and test bounds */
u = tvec.dot(pvec) * inv_det;
if (u < 0.0 || u > 1.0)
return false;
/* Prepare to test V parameter */
Vector3f qvec = tvec.cross(edge1);
/* Calculate V parameter and test bounds */
v = ray.d.dot(qvec) * inv_det;
if (v < 0.0 || u + v > 1.0)
return false;
/* Ray intersects triangle -> compute t */
t = edge2.dot(qvec) * inv_det;
return t >= ray.mint && t <= ray.maxt;
}
Point3f Mesh::getCentroid(uint32_t index) const {
return (1.0f / 3.0f) *
(m_V.col(m_F(0, index)) +
m_V.col(m_F(1, index)) +
m_V.col(m_F(2, index)));
}
BoundingBox3f Mesh::getBoundingBox(uint32_t index) const {
BoundingBox3f result(m_V.col(m_F(0, index)));
result.expandBy(m_V.col(m_F(1, index)));
result.expandBy(m_V.col(m_F(2, index)));
return result;
}
double BoysFunction::returnValue(int n)
{
return m_F(n);
}
//------------------------------------------------------------------------------
void PD_OSP::calculateForces(const std::pair<int, int> &idCol)
{
const int pId = idCol.first;
const int col_i = idCol.second;
const double a_i = m_data(col_i, m_indexA);
const double b_i = m_data(col_i, m_indexB);
const double d_i = m_data(col_i, m_indexD);
const double theta_i = m_data(col_i, m_indexTheta);
vector<pair<int, vector<double>>> & PDconnections = m_particles.pdConnections(pId);
double r_i[3];
double r0_i[3];
double f_i[3];
for(int d=0; d<m_dim; d++)
{
f_i[d] = 0;
r_i[d] = m_r(d, col_i);
r0_i[d] = m_r0(d, col_i);
}
const int nConnections = PDconnections.size();
double dr_ij[3];
double thetaNew = 0;
for(int l_j=0; l_j<nConnections; l_j++)
{
auto &con = PDconnections[l_j];
if(con.second[m_indexConnected] <= 0.5)
continue;
const int id_j = con.first;
const int j = m_pIds[id_j];
const double a_j = m_data(j, m_indexA);
const double b_j = m_data(j, m_indexB);
const double d_j = m_data(j, m_indexD);
const double theta_j = m_data(j, m_indexTheta);
const double vol_j = m_data(j, m_indexVolume);
const double dr0 = con.second[m_indexDr0];
const double volumeScaling = con.second[m_indexVolumeScaling];
const double a_ij = 0.5*(a_i + a_j);
const double b_ij = 0.5*(b_i + b_j);
const double d_ij = 0.5*(d_i + d_j);
const double Gd_ij = con.second[m_indexForceScalingDilation];
const double Gb_ij = con.second[m_indexForceScalingBond];
double dr2 = 0;
double A_ij = 0; // The lambda-factor
for(int d=0; d<m_dim; d++)
{
dr_ij[d] = m_r(d, j) - r_i[d];
dr2 += dr_ij[d]*dr_ij[d];
A_ij += dr_ij[d]*(m_r0(d, j) - r0_i[d]);
}
const double dr = sqrt(dr2);
A_ij /= (dr0*dr);
double ds = dr - dr0;
// To avoid roundoff errors
if (fabs(ds) < THRESHOLD)
ds = 0.0;
const double s = ds/dr0;
const double fbond = (a_ij*d_ij*Gd_ij*A_ij/dr0*(theta_i + theta_j) + b_ij*Gb_ij*s)
*vol_j*volumeScaling/dr;
for(int d=0; d<m_dim; d++)
{
f_i[d] += dr_ij[d]*fbond;
}
thetaNew += d_ij*s*A_ij*vol_j*volumeScaling;
con.second[m_indexStretch] = s;
}
for(int d=0; d<m_dim; d++)
{
m_F(d, col_i) += m_delta*f_i[d];
}
m_data(col_i, m_indexThetaNew) = m_delta*thetaNew;
}
//------------------------------------------------------------------------------
void PD_LPS_porosity_adrmc::calculateForces(const int id, const int i) {
const double theta_i = m_data(i, m_iTheta);
const double m_i = m_data(i, m_iMass);
const double a_i = m_data(i, m_iA);
const double b_i = m_data(i, m_iA);
vector<pair<int, vector<double>>> &PDconnections =
m_particles.pdConnections(id);
const int nConnections = PDconnections.size();
double dr0_ij[m_dim];
double dr_ij[m_dim];
_F.zeros();
double thetaNew = 0;
int nConnected = 0;
//----------------------------------
// TMP - standard stress calc from
// m_data(i, m_indexStress[0]) = 0;
// m_data(i, m_indexStress[1]) = 0;
// m_data(i, m_indexStress[2]) = 0;
//----------------------------------
for (int l_j = 0; l_j < nConnections; l_j++) {
auto &con = PDconnections[l_j];
if (con.second[m_iConnected] <= 0.5)
continue;
const int id_j = con.first;
const int j = m_idToCol_v[id_j];
const double m_j = m_data(j, m_iMass);
const double theta_j = m_data(j, m_iTheta);
const double vol_j = m_data(j, m_iVolume);
const double dr0 = con.second[m_iDr0];
const double volumeScaling = con.second[m_iVolumeScaling];
const double vol = vol_j * volumeScaling;
const double w = weightFunction(dr0);
const double a_j = m_data(j, m_iA);
const double b_j = m_data(j, m_iB);
double dr2 = 0;
for (int d = 0; d < m_dim; d++) {
dr0_ij[d] = m_r0(j, d) - m_r0(i, d);
dr_ij[d] = m_r(j, d) - m_r(i, d);
dr2 += dr_ij[d] * dr_ij[d];
}
const double dr = sqrt(dr2);
const double ds = dr - dr0;
double bond = (b_i * theta_i / m_i + b_j * theta_j / m_j) * dr0;
bond += (a_i / m_i + a_j / m_j) * ds;
bond *= w * vol / dr;
thetaNew += w * dr0 * ds * vol;
for (int d = 0; d < m_dim; d++) {
m_F(i, d) += dr_ij[d] * bond;
for (int d2 = 0; d2 < m_dim; d2++) {
_F(d, d2) += w * dr_ij[d] * dr0_ij[d2] * vol;
}
}
con.second[m_iStretch] = ds / dr0;
//----------------------------------
// TMP - standard stres calc from
// m_data(i, m_indexStress[0]) += 0.5*dr_ij[0]*dr_ij[0]*bond;
// m_data(i, m_indexStress[1]) += 0.5*dr_ij[1]*dr_ij[1]*bond;
// m_data(i, m_indexStress[2]) += 0.5*dr_ij[0]*dr_ij[1]*bond;
//----------------------------------
nConnected++;
}
if (nConnections <= 3) {
m_data(i, m_iThetaNew) = 0;
} else {
m_data(i, m_iThetaNew) = m_dim / m_i * thetaNew;
}
//----------------------------------
// TMP - standard stres calc from
//----------------------------------
// if(nConnected > 5) {
// computeStress(id, i, nConnected);
// }
computeStress(id, i, nConnected);
//--------------------
m_continueState = false;
}
//------------------------------------------------------------------------------
void PD_LPS::calculateForces(const std::pair<int, int> &idCol)
{
const int pId = idCol.first;
const int i = idCol.second;
const double theta_i = m_data(i, m_iTheta);
const double m_i = m_data(i, m_iMass);
double alpha;
if(m_dim == 3)
alpha = 15*m_mu;
else
alpha = 8*m_mu;
const double c = (3*m_k - 5*m_mu);
vector<pair<int, vector<double>>> & PDconnections = m_particles.pdConnections(pId);
double r_i[m_dim];
double r0_i[m_dim];
double f_i[m_dim];
for(int d=0; d<m_dim; d++)
{
f_i[d] = 0;
r_i[d] = m_r(d, i);
r0_i[d] = m_r0(d, i);
}
const int nConnections = PDconnections.size();
double dr_ij[m_dim];
double thetaNew = 0;
for(int l_j=0; l_j<nConnections; l_j++)
{
auto &con = PDconnections[l_j];
if(con.second[m_iConnected] <= 0.5)
continue;
const int id_j = con.first;
const int j = m_pIds[id_j];
const double m_j = m_data(j, m_iMass);
const double theta_j = m_data(j, m_iTheta);
const double vol_j = m_data(j, m_iVolume);
const double dr0 = con.second[m_iDr0];
const double volumeScaling = con.second[m_iVolumeScaling];
const double gb_ij = con.second[m_iForceScalingBond];
const double gd_ij = con.second[m_iForceScalingDilation];
double dr2 = 0;
for(int d=0; d<m_dim; d++)
{
dr_ij[d] = m_r(d, j) - r_i[d];
dr2 += dr_ij[d]*dr_ij[d];
}
const double dr = sqrt(dr2);
const double ds = dr - dr0;
double bond = gd_ij*c*(theta_i/m_i + theta_j/m_j)*dr0;
bond += gb_ij*alpha*(1./m_i + 1./m_j)*ds;
bond *= vol_j*volumeScaling/dr;
thetaNew += dr0*ds*vol_j*volumeScaling;
for(int d=0; d<m_dim; d++)
{
m_F(d, i) += dr_ij[d]*bond;
}
con.second[m_iStretch] = ds/dr0;
}
m_data(i, m_iThetaNew) = m_dim/m_i*thetaNew;
}
