The following parametric curves have been used to define the shape of a turbine blade for a new jet engine. The two curves represent the bottom and top edges of the blade.

P1 (u) = (3u, u2 + 1, 1-u)

P3 (u) = (4-u2, 2u, 5)

where u varies between 0 and 1.

(i) Create a linear loft in the w direction between the two curves, and show the equation describing the lofted surface.

(ii) Calculate the points on the surface corresponding to the following pairs of u and w: (1,0), 0.5,0.5)

(iii)The fluid mechanics department sends two more “edge” curves to represent the blade:

P2 (w) = (4w2, 1-w, 1+4w2) P4 (w) = (3, 2, 5w2)

Use bi-directional lofting (linear Coons Surface) to represent the new surface.

(iv) Plot using any software and calculate the points on the new surface corresponding to the following pairs of u and w: (1,0), (0.5,0.5)