In our 2D representation, an interval is a set of 3 points (corresponding to the
nominal point and two bounds). The spline interpolation is done (on 6
consecutive points) separately on each of the 3 corresponding curves (see
Figure 1). Note
that evaluation at any parameter yields 3 points on a line.
As indicated above, the determination of inclusion of one interval spline
within another is important. Figure 2 shows the case where
inclusion is true.
We have developed a technique to answer this question (see section 3.2.2). Moreover, if one interval contains another, then the 2-D difference of the two intervals is also possible to determine.