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6.4 Intersection curve at tangential intersection points

Now, let us assume that the two surfaces $ A$ and $ B$ intersect tangentially at a point $ P$ on the intersection curve $ {\bf c}(s)$ , i.e. $ {\bf N}^A$ $ \parallel$ $ {\bf N}^B$ at $ P$ . By orienting the surfaces appropriately we can assume that $ {\bf N}^A = {\bf N}^B \equiv {\bf N}$ (see Fig. 6.2). In this case, (6.23) is invalid. Therefore, we have to find new methods to compute the differential geometry properties of $ {\bf c}(s)$ . In the following Sect. 6.4.1 we also classify these tangential contact points $ P$ in several categories.

Figure 6.2: Tangential intersection of two surfaces (adapted from [458])
\begin{figure}\centerline{ \psfig{file=fig/tang_int1.eps,height=4in} }\end{figure}


Subsections
December 2009