Ex. 6.1 Surface representations Develop surface representations for a quarter of a cone surface. The cone surface is shown in figure (Fig. 6.8). The bottom quarter circle has a unit radius and is centered at (0, 0, 0). The top quarter circle has a radius of and z = 2. The surface can be represented as follows. = 1 sin(u)(1 --v) z = 2v, u = [0, 1], v = [0, 1] 9 x = cos(-u)(1 /12v), y = a. For the above conic surface representation, at parametric middle point (u 0 s compute surface point s(, ), their partial derivatives s s du' dv and udv b. Approximate the conic surface with a Coons patch with the boundary curves coming from the cylindrical surface. = 0.5, v = (6.9) 0.5), (2=0,), 1 Z 211,0,07 (0,22.) (0,1,0) y Figure 6.8: A cylindrical surface generated by sweeping a quarter circle. 124 c. Approximate the conic surface with a bicubic patch with geometric coefficients derived from (6.9). d. Approximate the conic surface with a Ferguson's patch. e. Compare the surfaces in (b)-(d) with the exact surface in (6.9) at the parametric midpoint.