Sphere::Sphere(double x, double y, double z, material_t material, double radius)
{
init(vector3_t({x, y, z}), material, radius);
}
complex_t FormFactorTriangle(real_t qx, real_t qy, complex_t qz,
RotMatrix_t & rot, triangle_t & tri) {
complex_t ff = CMPLX_ZERO_;
complex_t unitc = CMPLX_ONE_;
complex_t n_unitc = CMPLX_MINUS_ONE_;
// do the rotation
std::vector<complex_t> mq = rot.rotate (qx, qy, qz);
// calculate q^2
real_t q_sqr = 0.;
for(int i=0; i<3; i++) q_sqr += std::norm(mq[i]);
// form vertices
std::vector<vector3_t> vertex;
vertex.resize(3);
vertex[0] = vector3_t(tri.v1[0], tri.v1[1], tri.v1[2]);
vertex[1] = vector3_t(tri.v2[0], tri.v2[1], tri.v2[2]);
vertex[2] = vector3_t(tri.v3[0], tri.v3[1], tri.v3[2]);
// form edges
std::vector<vector3_t> edge;
edge.resize(3);
edge[0] = vertex[1] - vertex[0];
edge[1] = vertex[2] - vertex[1];
edge[2] = vertex[0] - vertex[2];
// calculate projection of n_t on q
vector3_t n_t = cross(edge[0], edge[1]);
real_t t_area = 0.5 * n_t.abs();
n_t = n_t / n_t.abs();
// dot(q, n_t)
complex_t q_dot_nt = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_nt += mq[i] * n_t[i];
// proj_tq
real_t proj_tq = q_sqr - std::norm(q_dot_nt);
// CASE 1
if (std::abs(proj_tq) < TINY_){
complex_t q_dot_v = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_v += mq[i] * tri.v1[i];
// calculate form-factor (Case 1)
ff = unitc * q_dot_nt * t_area / q_sqr * std::exp(n_unitc * q_dot_v);
} else {
// iterate of each edge to compute form-factor
for (int e = 0; e < 3; e++) {
// edge-normal
vector3_t n_e = cross(edge[e], n_t);
n_e = n_e / n_e.abs();
// dot (q, n_e)
complex_t q_dot_ne = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_ne += mq[i] * n_e[i];
// proj_eq
real_t proj_eq = proj_tq - std::norm(q_dot_ne);
// CASE 2
if (std::abs(proj_eq) < TINY_){
// q_dot_v
complex_t q_dot_v = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_v += mq[i] * vertex[e][i];
real_t f0 = edge[e].abs() / (q_sqr * proj_tq);
complex_t c0 = - q_dot_nt * q_dot_ne;
complex_t c1 = std::exp(n_unitc * q_dot_v);
ff += f0 * c0 * c1;
} else {
// CASE 3 (General case)
// denominator
real_t f0 = q_sqr * proj_tq * proj_eq;
// dot(q, v_a) vertex a
complex_t q_dot_v = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_v += mq[i] * vertex[e][i];
// vertrex-normal a
vector3_t n_v = edge[e] / edge[e].abs();
// dot(q, n_v)
complex_t q_dot_nv = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_nv += mq[i] * n_v[i];
// calculate contribution of vertex a
complex_t c0 = n_unitc * q_dot_nt * q_dot_ne * q_dot_nv;
complex_t c1 = std::exp(n_unitc * q_dot_v);
ff += c0 * c1 / f0;
// dot(q, v) the other vertex in the edge
q_dot_v = CMPLX_ZERO_;
int ep = (e+1)%3;
for (int i=0; i<3; i++) q_dot_v += mq[i] * vertex[ep][i];
// dot (q, n_v)
q_dot_nv = CMPLX_ZERO_;
for (int i=0; i<3; i++) q_dot_nv -= mq[i] * n_v[i];
// calculate contribution of the other vertex
c0 = n_unitc * q_dot_nt * q_dot_ne * q_dot_nv;
c1 = std::exp(n_unitc * q_dot_v);
ff += c0 * c1 / f0;
}
}
}
return ff;
}
vector3_t min <vector3_t> (vector3_t a, vector3_t b) {
return vector3_t((a[0] < b[0] ? a[0] : b[0]), (a[1] < b[1] ? a[1] : b[1]),
(a[2] < b[2] ? a[2] : b[2]));
} // min <vector3_t>
vector3_t max <vector3_t> (vector3_t a, vector3_t b) {
return vector3_t((a[0] > b[0] ? a[0] : b[0]), (a[1] > b[1] ? a[1] : b[1]),
(a[2] > b[2] ? a[2] : b[2]));
} // max <vector3_t>
/**
* specialized floor function
*/
vector3_t floor(vector3_t a) {
return vector3_t(std::floor(a[0]), std::floor(a[1]), std::floor(a[2]));
} // floor()