How do we differentiate the cases where the ray runs parallel to the plane and that which ray is on the plane? That seems like an important distinction to make in application.
enzyme
@brandino If the ray is on the plane, that means it's origin point must be on the plane, which we can check easily.
bcagan
I was going to ask about the case when the ray is on the plane but it seems people have already gotten to that!
Osoii
If the ray is on the plane, then the direction d must on the plane, and the origin point o also lies on the plane, so NTd = 0, NTo = c, which makes the equation NT(o+td)=c an identical equation (which means there are infinite solutions)
emmurphy
How about the ray runs parallel to the plane but not on the plane? 0 solution?
keenan
@emmurphy Great question. What does $t$ equal in this case?
How do we differentiate the cases where the ray runs parallel to the plane and that which ray is on the plane? That seems like an important distinction to make in application.
@brandino If the ray is on the plane, that means it's origin point must be on the plane, which we can check easily.
I was going to ask about the case when the ray is on the plane but it seems people have already gotten to that!
If the ray is on the plane, then the direction d must on the plane, and the origin point o also lies on the plane, so NTd = 0, NTo = c, which makes the equation NT(o+td)=c an identical equation (which means there are infinite solutions)
How about the ray runs parallel to the plane but not on the plane? 0 solution?
@emmurphy Great question. What does $t$ equal in this case?