6.2.5 Ex. 6.1 Exercise Surface representations Develop surface representations for a quarter of a cone surface....

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6.2.5 Ex. 6.1 Exercise 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. x = cos(u) (1 cos(a)(1). - y = sin(u)(1 = v), z = 2v, u [0,1], v [0,1] (6.9) a. For the above conic surface representation, at parametric middle point ( compute surface point s(u, v), their partial derivatives. = 0.5,v = 0.5), as as Ju' Iv b. Approximate the conic surface with a Coons patch with the boundary curves coming from a S and the cylindrical surface. 0,2). Z ( 0, 2 ) 124 (0,1,0) y (1,0,0 x Figure 6.8: A cylindrical surface generated by sweeping a quarter circle. 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. 6.2.5 Ex. 6.1 Exercise 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. x = cos(u) (1 cos(a)(1). - y = sin(u)(1 = v), z = 2v, u [0,1], v [0,1] (6.9) a. For the above conic surface representation, at parametric middle point ( compute surface point s(u, v), their partial derivatives. = 0.5,v = 0.5), as as Ju' Iv b. Approximate the conic surface with a Coons patch with the boundary curves coming from a S and the cylindrical surface. 0,2). Z ( 0, 2 ) 124 (0,1,0) y (1,0,0 x Figure 6.8: A cylindrical surface generated by sweeping a quarter circle. 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.