content_image/311989.jpg content_image/311990.jpg content_image/311991.jpg
<img src='content_image/311989.jpg'>

By taking λ ( s ) = − s, t$_{0}$ = 0 and the marching-scale functions as 

<img src='content_image/311990.jpg'>

we have the Eq. (4.12) is satisfied. So, we obtain the following surface as a member of the surface pencil with common line of curvature r ( s ) (Fig. 4.3) as 

<img src='content_image/311991.jpg'>

where 0 ≤ s ≤ 2 π, − 1 ≤ t ≤ 1 . 

Fig. 4.3. P$_{5}$ ( s, t ) as a member of the surface pencil and its line of curvature 

For the same curve let λ ( s ) = − sinh ( s ) , t$_{0}$ = 0 and the marching-scale functions 

u ( s, t ) = 4 ∑ k =1 sinh k ( t ) , v ( s, t ) ≡ 0 , w ( s, t ) = 4 ∑ k =1 sinh k ( s ) sinh k ( t ) . Now we have the Eq. (4.11) is satisfied. Thus, the surface 

