content_image/309227.jpg content_image/309226.jpg content_image/309222.jpg content_image/309223.jpg content_image/309224.jpg content_image/309225.jpg content_image/309221.jpg
a parameter t$_{0}$ ∈ [ T$_{1}$, T$_{2}$ ] such that P ( s, t$_{0}$ ) = r ( s ) L$_{1}$ ≤ s ≤ L$_{2}$, that is , 

<img src='content_image/309227.jpg'>

Fistly, we derive the condition for n$_{1}$ to be parallel to the normal vector n ( s, t ) of the surface P ( s, t ) : 

The normal vector can be expressed as 

<img src='content_image/309226.jpg'>

Thus, we get 

where 

<img src='content_image/309222.jpg'>

<img src='content_image/309223.jpg'>

<img src='content_image/309224.jpg'>

This follows that n$_{1}$ ( s ) //n ( s, t$_{0}$ ), L$_{1}$ ≤ s ≤ L$_{2}$ , if and only if there exits a function λ ( s ) ̸ = 0 such that 

<img src='content_image/309225.jpg'>

<img src='content_image/309221.jpg'>

