B ( s ) = (0 , − 1 , 0) , τ = 0 . u ( s, t ) = sinh ( t ) , v ( s, t ) = 0 , w ( s, t ) = cosh ( st ) P$_{5}$ ( s, t ) = (cosh ( s ) + sinh ( t ) sinh ( s ) , − cosh ( s ∗ t ) , sinh ( s ) + cosh ( s ) sinh ( t )) , 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 21 Fig. 4.3. P$_{5}$ ( s, t ) as a member of the surface pencil and its line of curvature 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 where 0 ≤ s ≤ 2 π, − 1 ≤ t ≤ 1 . By taking λ ( s ) = − s, t$_{0}$ = 0 and the marching-scale functions as