void Eigenvalues(const Matrix2& A,Complex& lambda1,Complex& lambda2)
{
Real trace=A.trace();
Real det=A.determinant();
Complex temp2 = Sqr(trace) - 4.0*det;
Complex temp = Sqrt(temp2);
lambda1 = 0.5*(Complex(trace) + temp);
lambda2 = 0.5*(Complex(trace) - temp);
}
bool Eigenvalues(const Matrix2& A,Real& lambda1,Real& lambda2)
{
Real trace=A.trace();
Real det=A.determinant();
Real temp2 = Sqr(trace) - 4.0*det;
if(temp2 < 0) return false;
Real temp=Sqrt(temp2);
lambda1 = 0.5*(trace + temp);
lambda2 = 0.5*(trace - temp);
return true;
}
bool Segment2D::intersects(const Vector2& A,const Vector2& B,Vector2& p) const
{
//find (u,v) s.t. a+u(b-a) = A+v(B-A)
//=> (b-a | A-B)*(u,v)^T = (A-a)
Matrix2 M;
Vector2 res,uv;
M.setCol1(b-a);
M.setCol2(A-B);
res = A-a;
if(Math::FuzzyZero(M.determinant())) {
//they're parallel
Vector2 t = b-a;
Vector2 n; n.setPerpendicular(t);
Real D = dot(n,A);
Real d = dot(n,a);
if(Math::FuzzyEquals(d,D)) { //they overlap
ClosedInterval U,u;
u.a = 0;
u.b = t.normSquared();
U.a = dot(t,A-a);
U.b = dot(t,B-a);
if(U.intersects(u)) {
ClosedInterval i;
i.setIntersection(u,U);
Real param=0.5*(i.a+i.b);
p = a + t*(param/u.b);
return true;
}
}
return false;
}
M.inplaceInverse();
M.mul(res,uv);
if(uv.x>=Zero && uv.x<=One &&
uv.y>=Zero && uv.y<=One) {
interpolate(a,b,uv.x,p);
Vector2 temp;
interpolate(A,B,uv.y,temp);
if(temp.distance(p) > 1e-3) {
cout<<"Error: intersection points are too far away "<<endl;
cout<<A<<" -> "<<B<<endl;
cout<<a<<" -> "<<b<<endl;
cout<<"u,v "<<uv<<endl;
cout<<"inverse basis "<<endl<<M<<endl;
cout<<"p1,p2 "<<p<<", "<<temp<<endl;
abort();
}
return true;
}
/*
if(intersects(a,b)) {
if(Math::FuzzyZero(uv.x)) { p=a; return true; }
if(Math::FuzzyEquals(uv.x,One)) { p=b; return true; }
if(Math::FuzzyZero(uv.y)) { p=a; return true; }
if(Math::FuzzyEquals(uv.y,One)) { p=b; return true; }
cout<<"Error! segment is supposed to intersect, but we don't have that in the basis!"<<endl;
cout<<A<<" -> "<<B<<endl;
cout<<a<<" -> "<<b<<endl;
cout<<"u,v "<<uv<<endl;
cout<<"inverse basis "<<endl<<M<<endl;
abort();
}
*/
return false;
}
