Can you give some tests? The stars coordinates aren't natural numbers?

Why precision of 10^-5 is needed? Should the algorithm ignore cases when scalar product of normal vector of the plane and "star"-vector is negative (the angle between vectors will be 90<x<270 so star's rays won't reach solar battery of esp. this plane)?

Integer output also works, but you need int64_t.

Note that it is not enough for normal/star angle to be less than pi/2, you also need to have correct normal -- the one that is opposite to the fourth vertex.