Ray Tracing Box Intersection: (3,8) to (6,-1), (-2,3), and i-5j

[haddow64]

Ok, so this is probably a really basic question, and I've got a feeling that my brain is just too 'fuzzy' just now and that all my problem is is simple arithmetic, but here it goes...

1. Determine whether or not the box with vertices at (2,1), (5,1), (5,5), and (2,5) is intersected by the ray originating at (3,8) and:

(i) ends at (6,-1)
(ii) ends at (-2,3)
(iii) has direction i-5j



Box:
AB: (2+3u / 1) -(1)
CD: (5-3u / 5) -(2)
BC: (5 / 1+4u) -(3)
AD: (2 / 1+4u) -(4)

(i) Ray (3,8) to (6,-1)
(3+3t / 8-9t)

(1) & (i) -> (2+3u / 1) = (3+3t / 8-9t)


How do I get this down to give t and u to show that intersection occurs? I'm sorry that this is such a basic question, I've been working all day and don't seem to be able to think properly just now.

Thanks in advance for any help.

 

[Dick]

Take your ray for each of the problems and intersect with the lines that form the boundaries of the box, look at the intersection points and draw conclusions from there. Even a simple graphical sketch of the problem might tell you what which lines you have to consider and which you don't.