
Re: Cross Ratio of Four Concurrent Lines
Posted:
Jun 30, 2013 4:54 PM



> Cross Ratio can be defined in projective geometry > either for 4 collinear points or 4 concurrent lines. > > Point P connects 4 fixed points in xy plane. Find > locus of P so that cross ratio of the four ray pencil > is a positive constant. > > Regards > Narasimham
Hi Narasimham,
the problem is very interesting. I studied the special case A=[1 0], B=[0 1], C=[1 0], D=[0 1], where point P is element of the box [2 2]x[2 2], and tet=angle(APB), phi=angle(BPC), psi=angle(CPD). For the Cross Ratio we have
CR=sin(tet+phi)*sin(phi+psi)/(sin(tet+phi+psi)*sin(phi)).
The result is shown in the attachment.
Best regards, Avni

