Line<T, Dim>::Line(const Hyperplane<T, 2>& plane) {
static_assert(Dim == 2, "Line dimension must be two, since it a plane in 2 dimensional space.");
// Intersect plane's line with line through origo perpendicular to plane to find suitable base
T a = plane.Normal()(0);
T b = plane.Normal()(1);
T d = plane.Scalar();
T div = (a*a + b*b);
base = { a*d / div, b*d / div };
direction = { b, -a };
}
Vector3d getPlaneIntersection( const Hyperplane<double,3> &plane1, const Hyperplane<double,3> &plane2, double lambda)
{
double dot = plane1.normal().dot(plane2.normal());
Vector3d cross = plane1.normal().cross(plane2.normal());
double c1 = (plane1.offset() - plane2.offset()*dot )/(1.0-dot*dot);
double c2 = (plane2.offset() - plane1.offset()*dot )/(1.0-dot*dot);
Vector3d r = (c1*plane1.normal() + c2*plane2.normal() ) + lambda*(cross);
return r;
}
bool OjaData::derivative(const Point& x,const Point& direction,double& Dpos
,double& Dneg) const
{
Point d=direction;
d.normalize();
Index I(dim(),size());
Hyperplane H;
double D; // Apumuuttuja yhden termi laskemiseen
double sum=0.0; // Summa positiiviseen suuntaan
double sum_=0.0; // Summa negatiiviseen suuntaan
double k=1.0 / double(fact(dim()));
double sgn;
for(int i=0; i<hyperplanes(); i++)
{
if(planes)
H=hyperplane(i);
else
{
H.get(*this,I);
I++;
}
H.normalize();
D = k * (H|d);
sgn = H.side(x);
if(sgn > 0) // Piste ei ole hypertasolla
sum += D, sum_ -= D;
else if (sgn < 0)
sum -= D, sum_ += D;
else // Piste on hypertasolla
sum += fabs(D), sum_ += fabs(D);
}
Dpos = sum;
Dneg = sum_;
return Dpos >= 0.0 && Dneg >= 0.0;
}
Vector3d getReflected(const Vector3d &p, const Hyperplane<double,3> &plane)
{ Vector3d r = p- 2*plane.signedDistance(p)*plane.normal();
return r;
}