public override Vector3 intersect(Vector3Pair ray)
{
double ax = ray.origin().x();
double ay = ray.origin().y();
double az = ray.origin().z();
double bx = ray.direction().x();
double by = ray.direction().y();
double bz = ray.direction().z();
/*
* find intersection point between conical section and ray,
* telescope optics, page 266
*/
double a = (_sh * MathUtils.square(bz) + MathUtils.square(by) + MathUtils.square(bx));
double b = ((_sh * bz * az + by * ay + bx * ax) / _roc - bz) * 2.0;
double c = (_sh * MathUtils.square(az) + MathUtils.square(ay) + MathUtils.square(ax))
/ _roc
- 2.0 * az;
double t;
if (a == 0)
{
t = -c / b;
}
else
{
double d = MathUtils.square(b) - 4.0 * a * c / _roc;
if (d < 0)
{
return(null); // no intersection
}
double s = Math.Sqrt(d);
if (a * bz < 0)
{
s = -s;
}
if (_sh < 0)
{
s = -s;
}
t = (2.0 * c) / (s - b);
}
if (t <= 0) // ignore intersection if before ray origin
{
return(null);
}
return(ray.origin().plus(ray.direction().times(t)));
}
protected Vector3 base_intersect(Vector3Pair ray)
{
Vector3 origin;
// initial intersection with z=0 plane
{
double s = ray.direction().z();
if (s == 0)
{
return(null);
}
double a = -ray.origin().z() / s;
if (a < 0)
{
return(null);
}
origin = ray.origin().plus(ray.direction().times(a));
}
int n = 32; // avoid infinite loop
while (n-- > 0)
{
double new_sag = sagitta(origin.project_xy());
double old_sag = origin.z();
// project previous intersection point on curve
origin = new Vector3(origin.x(), origin.y(), new_sag);
// stop if close enough
if (Math.Abs(old_sag - new_sag) < 1e-10)
{
break;
}
// get curve tangeante plane at intersection point
Vector3 norm = normal(origin);
// intersect again with new tangeante plane
Vector3Pair p = new Vector3Pair(origin, norm);
double a = p.pl_ln_intersect_scale(ray);
if (a < 0)
{
return(null);
}
// See https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection
origin = ray.origin().plus(ray.direction().times(a));
}
return(origin);
}
/*
*
* ligne AB A + t * B
* sphere passant par C(Cx, 0, 0), rayon R
*
* d = Ax - R - Cx
* (Bz*t+Az)^2+(By*t+Ay)^2+(Bx*t+d)^2=R^2
*
* t=-(sqrt((Bz^2+By^2+Bx^2)*R^2+(-Bz^2-By^2)*d^2+(2*Az*Bx*Bz+2*Ay*Bx*By)
* d-Ay^2*Bz^2+2*Ay*Az*By*Bz-Az^2*By^2+(-Az^2-Ay^2)*Bx^2)+Bx*d+Az*Bz+Ay*By)/(Bz^2+By^2+Bx^2),
*
* t= (sqrt((Bz^2+By^2+Bx^2)*R^2+(-Bz^2-By^2)*d^2+(2*Az*Bx*Bz+2*Ay*Bx*By)
* d-Ay^2*Bz^2+2*Ay*Az*By*Bz-Az^2*By^2+(-Az^2-Ay^2)*Bx^2)-Bx*d-Az*Bz-Ay*By)/(Bz^2+By^2+Bx^2)
*
*/
override public Vector3 intersect(Vector3Pair ray)
{
double ax = (ray.origin().x());
double ay = (ray.origin().y());
double az = (ray.origin().z());
double bx = (ray.direction().x());
double by = (ray.direction().y());
double bz = (ray.direction().z());
// double bz2_by2_bx2 = math::square(bx) + math::square(by) +
// math::square(bx);
// == 1.0
double d = az - _roc;
double ay_by = ay * by;
double ax_bx = ax * bx;
double s = +MathUtils.square(_roc) // * bz2_by2_bx2
+ 2.0 * (ax_bx + ay_by) * bz * d + 2.0 * ax_bx * ay_by
- MathUtils.square(ay * bx) - MathUtils.square(ax * by)
- (MathUtils.square(bx) + MathUtils.square(by)) * MathUtils.square(d)
- (MathUtils.square(ax) + MathUtils.square(ay)) * MathUtils.square(bz);
// no sphere/ray colision
if (s < 0)
{
return(null);
}
s = Math.Sqrt(s);
// there are 2 possible sphere/line collision point, keep the right
// one depending on ray direction
if (_roc * bz > 0)
{
s = -s;
}
double t = (s - (bz * d + ax_bx + ay_by)); // / bz2_by2_bx2;
// do not collide if line intersection is before ray start position
if (t <= 0)
{
return(null);
}
// intersection point
return(ray.origin().plus(ray.direction().times(t)));
}
override public Vector3 intersect(Vector3Pair ray)
{
//static int count = 0;
//count++;
if (_feder_algo)
{
Vector3Pair v3p = compute_intersection(ray.origin(), ray.direction(), this);
if (v3p == null)
{
return(null);
}
return(v3p.point());
// normal.normalize();
// if (ok && count % 25 == 0)
// {
// printf ("{ %.16f, %.16f", this->_r, this->_k);
// printf (", %.16f, %.16f, %.16f, %.16f, %.16f, %.16f",
//this->_A4, this->_A6, this->_A8, this->_A10, this->_A12, this->_A14);
// printf (", %.16f, %.16f, %.16f", ray.origin ().x (),
// ray.origin ().y (), ray.origin ().z ());
// printf (", %.16f, %.16f, %.16f", ray.direction ().x (),
// ray.direction ().y (), ray.direction ().z ());
// printf (", %.16f, %.16f, %.16f },\n", point.x (), point.y
//(), point.z ());
// }
}
else
{
return(base_intersect(ray));
}
}
TracedRay trace_ray(Surface surface, TraceIntensityMode m,
RayTraceResults result, TracedRay incident,
Vector3Pair local,
Vector3Pair pt)
{
incident.set_len((pt.origin().minus(local.origin())).len());
incident.set_intercept(surface, pt.origin());
if (m == TraceIntensityMode.Simpletrace)
{
incident.set_intercept_intensity(1.0);
return(trace_ray_simple(surface, result, incident, local, pt));
}
else
{
// apply absorbtion from current material
double i_intensity
= incident.get_intensity()
* incident.get_material().get_internal_transmittance(
incident.get_wavelen(), incident.get_len());
incident.set_intercept_intensity(i_intensity);
// FIXME
// if (i_intensity < _discard_intensity)
// return;
if (m == TraceIntensityMode.Intensitytrace)
{
return(trace_ray_intensity(surface, result, incident, local, pt));
}
else if (m == TraceIntensityMode.Polarizedtrace)
{
return(trace_ray_polarized(surface, result, incident, local, pt));
}
else
{
throw new InvalidOperationException();
}
}
}
TracedRay trace_ray_simple(Stop surface, RayTraceResults result, TracedRay incident, Vector3Pair local,
Vector3Pair intersect)
{
Vector2 v = intersect.origin().project_xy();
bool ir = true; // FIXME _intercept_reemit || result.get_params ().is_sequential ();
if (ir && surface.get_shape().inside(v))
{
// re-emit incident ray
TracedRay r = result.newRay(intersect.origin(), incident.get_ray().direction());
r.set_wavelen(incident.get_wavelen());
r.set_intensity(incident.get_intensity());
r.set_material(incident.get_material());
r.set_creator(surface);
incident.add_generated(r);
return(r);
}
return(null);
}
public Vector3Pair transform_line(Vector3Pair v)
{
return(new Vector3Pair(transform(v.origin()), apply_rotation(v.direction())));
}
private TracedRay trace_ray_simple(OpticalSurface surface, RayTraceResults result, TracedRay incident,
Vector3Pair local, Vector3Pair intersect)
{
bool right_to_left = intersect.normal().z() > 0;
Medium prev_mat = surface.get_material(right_to_left ? 1 : 0);
Medium next_mat = surface.get_material(!right_to_left ? 1 : 0);
// check ray didn't "escaped" from its material
// std::cout << prev_mat->name << " " << next_mat->name <<
// " " << incident.get_material()->name << std::endl;
if (prev_mat != incident.get_material())
{
return(null);
}
double wl = incident.get_wavelen();
double index = prev_mat.get_refractive_index(wl)
/ next_mat.get_refractive_index(wl);
// refracted ray direction
Vector3 direction = refract(surface, local, intersect.normal(), index);
if (direction == null)
{
// total internal reflection
Vector3 o = intersect.origin();
Vector3 dir = reflect(surface, local, intersect.normal());
TracedRay r = result.newRay(o, dir);
r.set_wavelen(wl);
r.set_intensity(incident.get_intensity());
r.set_material(prev_mat);
r.set_creator(surface);
incident.add_generated(r);
return(r);
}
// transmit
if (!next_mat.is_opaque())
{
Vector3 o = intersect.origin();
TracedRay r = result.newRay(o, direction);
r.set_wavelen(wl);
r.set_intensity(incident.get_intensity());
r.set_material(next_mat);
r.set_creator(surface);
incident.add_generated(r);
return(r);
}
// reflect
if (next_mat.is_reflecting())
{
Vector3 o = intersect.origin();
Vector3 dir = reflect(surface, local, intersect.normal());
TracedRay r = result.newRay(o, dir);
r.set_wavelen(wl);
r.set_intensity(incident.get_intensity());
r.set_material(prev_mat);
r.set_creator(surface);
incident.add_generated(r);
return(r);
}
return(null);
}