Skisse av legeme 

Vi ser på et legeme gitt i kulekoordinater på formen 

 

 

 

La oss for eksempel ta 

 

`:=`(a, 0) 

0 (2.1)
 

`:=`(b, `+`(`*`(`/`(1, 3), `*`(Pi)))) 

`+`(`*`(`/`(1, 3), `*`(Pi))) (2.2)
 

`:=`(c, `+`(`*`(`/`(1, 4), `*`(Pi)))) 

`+`(`*`(`/`(1, 4), `*`(Pi))) (2.3)
 

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

`+`(`*`(`/`(1, 2), `*`(Pi))) (2.4)
 

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

proc (theta, `ϕ`) options operator, arrow; 1 end proc (2.5)
 

`:=`(g, proc (theta, `ϕ`) options operator, arrow; `+`(2, cos(`ϕ`)) end proc) 

proc (theta, `ϕ`) options operator, arrow; `+`(2, cos(`ϕ`)) end proc (2.6)
 

 

Vi bruker Maple til å tegne de seks flatene som avgrenser legemet, 

 

`:=`(P1, plot3d([f(theta, `ϕ`), theta, `ϕ`], theta = a .. b, `ϕ` = c .. d, coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = .7071067811865472, (1, 1, 2) = .7071067811865472, (1, 1, 3) = .7071067811865472, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 2, 3) = .0, (1, 3, 1) = .7071067... (2.7)
 

`:=`(P2, plot3d([rho, a, `ϕ`], `ϕ` = c .. d, rho = f(a, `ϕ`) .. g(a, `ϕ`), coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = .7071067811865472, (1, 1, 2) = .7071067811865472, (1, 1, 3) = .7071067811865472, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 2, 3) = .0, (1, 3, 1) = .7071067... (2.8)
 

`:=`(P3, plot3d([rho, b, `ϕ`], `ϕ` = c .. d, rho = f(b, `ϕ`) .. g(b, `ϕ`), coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = .353553390734695, (1, 1, 2) = .353553390734695, (1, 1, 3) = .353553390734695, (1, 2, 1) = .6123724356360871, (1, 2, 2) = .6123724356360871, (1, 2, 3)... (2.9)
 

`:=`(P4, plot3d([rho, theta, c], theta = a .. b, rho = f(theta, c) .. g(theta, c), coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = .7071067813, (1, 1, 2) = .7071067813, (1, 1, 3) = .7071067813, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 2, 3) = .0, (1, 3, 1) = .7071067811, (1, 3, 2) = .... (2.10)
 

`:=`(P5, plot3d([rho, theta, d], theta = a .. b, rho = f(theta, d) .. g(theta, d), coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 1.0, (1, 1, 2) = 1.0, (1, 1, 3) = 1.0, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 2, 3) = .0, (1, 3, 1) = -0.2051033808e-9, (1, 3, 2) = -0.2051033808e-9, (1... (2.11)
 

`:=`(P6, plot3d([g(theta, `ϕ`), theta, `ϕ`], theta = a .. b, `ϕ` = c .. d, coords = spherical, style = surface)) 

PLOT3D(MESH(Array(1..25, 1..25, 1..3, {(1, 1, 1) = 1.9142135623730945, (1, 1, 2) = 1.9142135623730945, (1, 1, 3) = 1.9142135623730945, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 2, 3) = .0, (1, 3, 1) = 1.914... (2.12)
 

 

og viser dem i samme bilde: 

 

display(P1, P2, P3, P4, P5, P6, lightmodel = light4, scaling = constrained, projection = .95) 

Plot
 

 

Merk: Du kan også ta vekk "style=surface" fra kommandoene over; det gir "gitter" på overflaten. 

 

Til slutt en animasjon som tydeliggjør hvordan legemet avgrenses av de enkelte flatene, som kommer inn en etter en. Klikk på figuren for å aktivere animasjonskontrollene i toolbar, og bruk disse til å klikke deg gjennom bildene i animasjonen. 

 

display(P1, display(P1, P2), display(P1, P2, P3), display(P1, P2, P3, P4), display(P1, P2, P3, P4, P5), display(P1, P2, P3, P4, P5, P6), insequence = true, lightmodel = light4, scaling = constrained, ...
display(P1, display(P1, P2), display(P1, P2, P3), display(P1, P2, P3, P4), display(P1, P2, P3, P4, P5), display(P1, P2, P3, P4, P5, P6), insequence = true, lightmodel = light4, scaling = constrained, ...
display(P1, display(P1, P2), display(P1, P2, P3), display(P1, P2, P3, P4), display(P1, P2, P3, P4, P5), display(P1, P2, P3, P4, P5, P6), insequence = true, lightmodel = light4, scaling = constrained, ... 

Plot