double Path::RaffineTk (Geom::Point pt, Geom::Point p0, Geom::Point p1, Geom::Point p2, Geom::Point p3, double it)
{
// Refinement of the tk values.
// Just one iteration of Newtow Raphson, given that we're approaching the curve anyway.
// [fr: vu que de toute facon la courbe est approchC)e]
double const Ax = pt[Geom::X] -
p0[Geom::X] * N03(it) -
p1[Geom::X] * N13(it) -
p2[Geom::X] * N23(it) -
p3[Geom::X] * N33(it);
double const Bx = (p1[Geom::X] - p0[Geom::X]) * N02(it) +
(p2[Geom::X] - p1[Geom::X]) * N12(it) +
(p3[Geom::X] - p2[Geom::X]) * N22(it);
double const Cx = (p0[Geom::X] - 2 * p1[Geom::X] + p2[Geom::X]) * N01(it) +
(p3[Geom::X] - 2 * p2[Geom::X] + p1[Geom::X]) * N11(it);
double const Ay = pt[Geom::Y] -
p0[Geom::Y] * N03(it) -
p1[Geom::Y] * N13(it) -
p2[Geom::Y] * N23(it) -
p3[Geom::Y] * N33(it);
double const By = (p1[Geom::Y] - p0[Geom::Y]) * N02(it) +
(p2[Geom::Y] - p1[Geom::Y]) * N12(it) +
(p3[Geom::Y] - p2[Geom::Y]) * N22(it);
double const Cy = (p0[Geom::Y] - 2 * p1[Geom::Y] + p2[Geom::Y]) * N01(it) +
(p3[Geom::Y] - 2 * p2[Geom::Y] + p1[Geom::Y]) * N11(it);
double const dF = -6 * (Ax * Bx + Ay * By);
double const ddF = 18 * (Bx * Bx + By * By) - 12 * (Ax * Cx + Ay * Cy);
if (fabs (ddF) > 0.0000001) {
return it - dF / ddF;
}
return it;
}
void dynamics_mul::compute_intensity_force(){
HMesh::HalfEdgeAttributeVector<int> touched(s_dsc->get_no_halfedges(), 0);
for (auto eit = s_dsc->halfedges_begin(); eit != s_dsc->halfedges_end(); eit++) {
if(s_dsc->is_interface(*eit) and !touched[*eit]){
auto hew = s_dsc->walker(*eit);
double c0 = mean_inten_[s_dsc->get_label(hew.face())];
double c1 = mean_inten_[s_dsc->get_label(hew.opp().face())];
// Loop on the edge
auto p0 = s_dsc->get_pos(hew.opp().vertex());
auto p1 = s_dsc->get_pos(hew.vertex());
Vec2 L01 = p1 - p0;
L01.normalize();
Vec2 N01(L01[1], -L01[0]); // Outward pointing normal
int length = (int)(p1 - p0).length();
double f0 = 0.0, f1 = 0.0;
Vec2 fg0(0.0), fg1(0.0);
for (int i = 0; i <= length; i++) {
auto p = p0 + (p1 - p0)*(double(i)/(double)length);
double I = s_img->get_intensity(p[0], p[1]);
// Normalize force
int normalizedF = 1;
double f ;
switch (normalizedF) {
case 1:
f = ( (c0-c1)*(2*I - c0 - c1)) / ((c0-c1)*(c0-c1));
break;
case 2:
f = ( (c0-c1)*(2*I - c0 - c1)) / std::abs((c0 - c1));
break;
case 3:
f = (c0-c1)*(2*I - c0 - c1);
break;
default:
f = 0.0;
break;
}
Vec2 fu = N01*(c0-c1)*(2*I - c0 - c1);
// Image gradient force
int lengthM = 10;
Vec2 gm(0.0); double max_grad = 0;
for (int l = 0; l < lengthM; l++) {
Vec2 curPt = p + fu*(l/(double)(lengthM));
Vec2 gg = s_img->grad((int)curPt[0], (int)curPt[1]);
if (max_grad < gg.length()) {
max_grad = gg.length();
gm = gg*(lengthM - l)/(double)lengthM;
}
}
Vec2 fg = gm*(2*I - c0 - c1);
Vec2 fv = (fu + fg)/((c0-c1)*(c0-c1));
fg0 += fv*(p-p1).length() / (double)length;
fg1 += fv*(p-p0).length() / (double)length;
// Barry Centric coordinate
f0 += f*(p-p1).length() / (double)length;
f1 += f*(p-p0).length() / (double)length;
// Image gradient force
// Vec2 fg = s_img->grad((int)p[0], (int)p[1]) * (2*I - c0 - c1) / ((c0-c1)*(c0-c1));
// fg0 += fg*(p-p1).length() / (double)length;
// fg1 += fg*(p-p0).length() / (double)length;
}
// Set force
Vec2 f_x0 = fg0; // N01*f0;
Vec2 f_x1 = fg1; // N01*f1;
s_dsc->add_node_external_force(hew.opp().vertex(), f_x0*g_param.beta);
s_dsc->add_node_external_force(hew.vertex(), f_x1*g_param.beta);
// Avoid retouch the edge
touched[*eit] = 1;
touched[hew.opp().halfedge()] = 1;
}
}
}
