with(plots); -1 

`:=`(g, proc (r, theta) options 
operator, arrow; 0 end proc) 

proc (r, 
theta) options operator, arrow; 0 end proc (1)
 

`:=`(h, proc (r, theta) options 
operator, arrow; 4 end proc) 

proc (r, 
theta) options operator, arrow; 4 end proc (2)
 

`:=`(a, proc (theta) options 
operator, arrow; 1 end proc) 

proc 
(theta) options operator, arrow; 1 end proc (3)
 

`:=`(b, proc (theta) options 
operator, arrow; `+`(1, cos(theta)) end proc) 

proc 
(theta) options operator, arrow; `+`(1, cos(theta)) end proc (4)
 

`:=`(alpha, `+`(`-`(`*`(`/`(1, 
2), `*`(Pi))))) 

`+`(`-`(`*`(`/`(1, 2), `*`(Pi)))) (5)
 

`:=`(beta, `+`(`*`(`/`(1, 2), 
`*`(Pi)))) 

`+`(`*`(`/`(1, 2), `*`(Pi))) (6)
 

`:=`(`ς`, 6) 

6 (7)
 

`:=`(P1, plot3d([r, theta, 0], 
theta = alpha .. beta, r = a(theta) .. b(theta), coords = cylindrical, 
style = surface, color = blue)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (8)
 

`:=`(P2, plot3d([a(theta), 
theta, z], theta = alpha .. beta, z = 0 .. `ς`, coords = 
cylindrical, style = surface, color = grey)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (9)
 

`:=`(P3, plot3d([b(theta), 
theta, z], theta = alpha .. beta, z = 0 .. `ς`, coords = 
cylindrical, style = surface, color = grey)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431215e-14, (1, 1, 2) = -0.34914813388431215e-14, (1, 1, 
3) = -0.34914813388431215e-14, (1, 2, 1) = -.9999999999999966, (1, 2, 2)
 = -.9... (10)
 

`:=`(P4, plot3d([r, alpha, z], r
 = a(alpha) .. b(alpha), z = 0 .. `ς`, coords = 
cylindrical, style = surface, color = grey)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.2051033808e-9, (1, 1, 2) = -0.2051033808e-9, (1, 1, 3) = 
-0.2051033808e-9, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 2, 3) = -1.0, 
(1, 3, 1) = .0, (... (11)
 

`:=`(P5, plot3d([r, beta, z], r
 = a(beta) .. b(beta), z = 0 .. `ς`, coords = cylindrical, 
style = surface, color = grey)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.2051033808e-9, (1, 1, 2) = -0.2051033808e-9, (1, 1, 3) = 
-0.2051033808e-9, (1, 2, 1) = 1.0, (1, 2, 2) = 1.0, (1, 2, 3) = 1.0, (1,
 3, 1) = .0, (1, ... (12)
 

`:=`(P6, plot3d([r, theta, g(r,
 theta)], theta = alpha .. beta, r = a(theta) .. b(theta), coords = 
cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (13)
 

`:=`(P7, plot3d([r, theta, h(r,
 theta)], theta = alpha .. beta, r = a(theta) .. b(theta), coords = 
cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (14)
 

`:=`(P8, plot3d([a(theta), 
theta, z], theta = alpha .. beta, z = g(a(theta), theta) .. h(a(theta), 
theta), coords = cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (15)
 

`:=`(P9, plot3d([b(theta), 
theta, z], theta = alpha .. beta, z = g(b(theta), theta) .. h(b(theta), 
theta), coords = cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431215e-14, (1, 1, 2) = -0.34914813388431215e-14, (1, 1, 
3) = -0.34914813388431215e-14, (1, 2, 1) = -.9999999999999966, (1, 2, 2)
 = -.9... (16)
 

`:=`(P10, plot3d([r, alpha, z],
 r = a(alpha) .. b(alpha), z = g(r, alpha) .. h(r, alpha), coords = 
cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.2051033808e-9, (1, 1, 2) = -0.2051033808e-9, (1, 1, 3) = 
-0.2051033808e-9, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 2, 3) = -1.0, 
(1, 3, 1) = .0, (... (17)
 

`:=`(P11, plot3d([r, beta, z], r
 = a(beta) .. b(beta), z = g(r, beta) .. h(r, beta), coords = 
cylindrical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.2051033808e-9, (1, 1, 2) = -0.2051033808e-9, (1, 1, 3) = 
-0.2051033808e-9, (1, 2, 1) = 1.0, (1, 2, 2) = 1.0, (1, 2, 3) = 1.0, (1,
 3, 1) = .0, (1, ... (18)
 

 

 

 

display(P1, display(P1, P2, P3,
 P4, P5), display(P1, P2, P3, P4, P5, transparency = .3), display(P2, 
P3, P4, P5, P6, P7, transparency = .3), display(P6, P7, P8, P9, P10, 
P11), insequence = true, light...
display(P1, display(P1, P2, P3, P4, P5), display(P1, P2, P3, P4, 
P5, transparency = .3), display(P2, P3, P4, P5, P6, P7, transparency = 
.3), display(P6, P7, P8, P9, P10, P11), insequence = true, light...
 

Plot
 

display(P6, P7, P8, P9, P10, 
P11, lightmodel = light4) 

Plot
 

`:=`(M, int(int(int(r, z = g(r,
 theta) .. h(r, theta)), r = a(theta) .. b(theta)), theta = alpha .. 
beta)) 

`+`(8, 
Pi) (19)
 

`:=`(Myz, 
int(int(int(`*`(`*`(r, `*`(cos(theta))), r), z = g(r, theta) .. h(r, 
theta)), r = a(theta) .. b(theta)), theta = alpha .. beta)) 

`+`(`*`(`/`(5, 2), `*`(Pi)), `/`(16, 3)) (20)
 

`:=`(Mxz, 
int(int(int(`*`(`*`(r, `*`(sin(theta))), r), z = g(r, theta) .. h(r, 
theta)), r = a(theta) .. b(theta)), theta = alpha .. beta)) 

0 (21)
 

`:=`(Mxy, int(int(int(`*`(z, 
`*`(r)), z = g(r, theta) .. h(r, theta)), r = a(theta) .. b(theta)), 
theta = alpha .. beta)) 

`+`(16, 
`*`(2, `*`(Pi))) (22)
 

`:=`(xx, `/`(`*`(Myz), 
`*`(M))) 

`/`(`*`(`+`(`*`(`/`(5, 2), `*`(Pi)), `/`(16, 3))), `*`(`+`(8, 
Pi))) (23)
 

 

1.1835 (24)
 

`:=`(yy, `/`(`*`(Mxz), 
`*`(M))) 

0 (25)
 

 

0. (26)
 

`:=`(zz, `/`(`*`(Mxy), 
`*`(M))) 

`/`(`*`(`+`(16, `*`(2, `*`(Pi)))), `*`(`+`(8, Pi))) (27)
 

 

1.9999 (28)
 

`:=`(c, .2) 

.2 (29)
 

`:=`(P12, 
implicitplot3d(`+`(`*`(`^`(`+`(x, `-`(xx)), 2)), `*`(`^`(`+`(y, 
`-`(yy)), 2)), `*`(`^`(`+`(z, `-`(zz)), 2))) = `*`(`^`(c, 2)), x = 
`+`(xx, `-`(c)) .. `+`(xx, c), y = `+`(yy, `-`(c)) .. `+`(y...
`:=`(P12, 
implicitplot3d(`+`(`*`(`^`(`+`(x, `-`(xx)), 2)), `*`(`^`(`+`(y, 
`-`(yy)), 2)), `*`(`^`(`+`(z, `-`(zz)), 2))) = `*`(`^`(c, 2)), x = 
`+`(xx, `-`(c)) .. `+`(xx, c), y = `+`(yy, `-`(c)) .. `+`(y...
 

PLOT3D(ISOSURFACE(Array(1..10, 1..10, 1..10, 1..4, {(1, 1, 1, 1) = 
.98361130022635, (1, 1, 1, 2) = .98361130022635, (1, 1, 1, 3) = 
.98361130022635, (1, 1, 1, 4) = .98361130022635, (1, 1, 2, 1) = 
.9836... (30)
 

`:=`(P13, display(P6, P7, P8, 
P9, P10, P11, transparency = .5, lightmodel = light4)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 
-0.34914813388431334e-14, (1, 1, 2) = -0.34914813388431334e-14, (1, 1, 
3) = -0.34914813388431334e-14, (1, 2, 1) = -1.0, (1, 2, 2) = -1.0, (1, 
2, 3) =... (31)
 

display(P12, P13) 

Plot