B ( s ) = (0 , 0 , 1) , τ = 0 . If we let θ (0) = 0$_{,}$then we have θ ( s ) = 0 . By taking λ ( s ) = s, t$_{0}$ = 0 and the marching-scale functions as then the Eq. (4.6) is satisfied. So, we have the following surface as a member of the surface pencil with common line of curvature r ( s ) (Fig. 4.1) as where 0 < s ≤ 2 π, − 1 ≤ t ≤ 1 . Fig. 4.1. P$_{3}$ ( s, t ) as a member of the surface pencil and its line of curvature For the same curve if we choose t$_{0}$ = 0 , λ ( s ) = − cosh ( s ) and the marching- scale functions as we have the Eqn. (4.5) is satisfied. Thus, the surface is a member of the surface pencil with common line of curvature r ( s ), where − 1 . 1 ≤ s ≤ 1 . 1 , − 0 . 7 ≤ t ≤ 0 . 2 (Fig.4 2). 16 P$_{4}$ ( s, t ) = (cos ( s ) − sin ( s ) 4 ∑ k =1 sin $^{k}$( s ) sin $^{k}$( t ) , sin ( s )+cos ( s ) 4 ∑ k =1 sin k ( s ) sin k ( t ) , 4 ∑ k =1 cosh k ( s ) sinh k ( t )) u ( s, t ) = 4 ∑ k =1 sin k ( s ) sin k ( t ) , v ( s, t ) = 0 , w ( s, t ) = 4 ∑ k =1 cosh k ( s ) sinh $^{k}$( t ) P$_{3}$ ( s, t ) = (cos ( s ) − sin ( t ) sin ( s ) , sin ( s ) + cos ( s ) sin ( t ) , sinh ( ts )) , u ( s, t ) = sin t, v ( s, t ) = 0 , w ( s, t ) = − sinh ( ts )