How to get equation (5)

[cx-tian]

My undestanding of the first condition is: the projection of o to x on the direction d should be between $t_0$ and $t_1$.

But I don't understand how to get the second condition. Can anyone help me?

[sergedesmedt]

I think they are calculating the cosine of the angle with respect to the centerlnie of the cone.

So basically, they are saying the cosine of the angle should be larger then the cosine of the angle made by a point on the surface of the cone. And as the cosine of a smaller angle is larger then of a large angle this means the angle must be smaller, hence the point must be inside the cone.

See also: angle between vectors