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 vectorqwhich is defined as three intervals (xi, yi, zi )where

xiis the closed interval[x0, x1]

yiis the closed interval[y0, y1]

ziis the closed interval[z0, z1]

I also have two equations:

u=a- dot(q,b)

v=c- dot(q,d)

where the vectorsb, dare constant, and the scalarsa,care constant.

Therefore u and v are also vectors whose components are intervals.

I also know that both intervalsu,vhave negative low and positive high values. I need a way of determining whether or not there exists a value ofq( 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 vectorq.

I hope this is clear... cheers.