I'm not a mathematician, just an amateur. I'm looking at interval arithmetic at the moment and have a stumbling block which derives from trying to do some geometry with interval arithmetic...

The problem involves using interval arithmetic and vectors....

I have a vector q which is defined as three intervals ( xi, yi, zi ) where
xi is the closed interval [x0, x1]
yi is the closed interval [y0, y1]
zi is the closed interval [z0, z1]

I also have two equations:

u = a - dot( q, b )
v = c - dot( q, d )

where the vectors b, d are constant, and the scalars a,c are constant.
Therefore u and v are also vectors whose components are intervals.

I also know that both intervals u,v have negative low and positive high values. I need a way of determining whether or not there exists a value of q ( ie. specific values of its scalar components ) which will give me a positive 'u' and a positive 'v'. I do not need to know the value, only to determine if a valid solution exists within the intervals of vector q.

I hope this is clear... cheers.