I want to plot the following solid nicely.
$\{(\rho\cos\theta\sin\phi,\rho\sin\theta\sin\phi,\rho\cos\phi)\in\mathbb{R}^3\mid(\rho,\phi,\theta)\in[1,2]\times[0,\frac{\pi}{2}]\times[0,\frac{\pi}{2}]\}$.
The following code didn't work:
ParametricPlot3D[{r Cos[t] Sin[s], r Sin[t] Sin[s], r Cos[s]}, {r, 1, 2}, {s, 0, Pi/2}, {t, 0, Pi/2},ImageSize->Large, PlotStyle->Blue] Please tell me how to do.
ParametricPlot3D[ Table[{r Cos[t] Sin[s], r Sin[t] Sin[s], r Cos[s]}, {r, 1, 2, .02}] // Evaluate, {s, 0, Pi/2}, {t, 0, Pi/2}, ImageSize -> Large] Another Way
If we use the implicit expression of sphere, we can also construct the solids and it's complement by a relatively complex way.
SetOptions[ContourPlot3D, Boxed -> False, Axes -> False, Lighting -> Automatic, BoundaryStyle -> None, Mesh -> {{0}, {0}, {0}}]; f1 = x^2 + y^2 + z^2 - 1^2; f2 = x^2 + y^2 + z^2 - 2^2; f3 = x; f4 = y; f5 = z; pureFun[f_] := (Evaluate[ f /. {x -> Slot@1, y -> Slot@2, z -> Slot@3}]) &; s1 = ContourPlot3D[f1 == 0, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, MeshFunctions -> pureFun /@ {f3, f4, f5}, MeshShading -> {{{None, None}, {None, None}}, {{None, StippleShading[0.9]}, {None, None}}}, MeshStyle -> None]; s2 = ContourPlot3D[f2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f3, f4, f5}, MeshShading -> {{{None, None}, {None, None}}, {{None, HatchShading[]}, {None, None}}}, MeshStyle -> None]; s3 = ContourPlot3D[f3 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f4, f5}, MeshShading -> {{{{None, None}, {None, None}}, {{None, None}, {None, None}}}, {{{None, HalftoneShading[0.6, Orange]}, {None, None}}, {{None, None}, {None, None}}}}, MeshStyle -> None]; s4 = ContourPlot3D[f4 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f3, f5}, MeshShading -> {{{{None, None}, {None, None}}, {{None, None}, {None, None}}}, {{{None, None}, {None, None}}, {{None, HalftoneShading[0.6, Orange]}, {None, None}}}}, MeshStyle -> None]; s5 = ContourPlot3D[f5 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f3, f4}, MeshShading -> {{{{None, None}, {None, None}}, {{None, HalftoneShading[0.8, Orange]}, {None, None}}}, {{{None, None}, {None, None}}, {{None, None}, {None, None}}}}, MeshStyle -> None]; Show[s1, s2, s3, s4, s5, PlotRange -> All] 
The Complement
SetOptions[ContourPlot3D, Boxed -> False, Axes -> False, Lighting -> Automatic, BoundaryStyle -> None, Mesh -> {{0}, {0}, {0}}]; f1 = x^2 + y^2 + z^2 - 1^2; f2 = x^2 + y^2 + z^2 - 2^2; f3 = x; f4 = y; f5 = z; pureFun[f_] := (Evaluate[ f /. {x -> Slot@1, y -> Slot@2, z -> Slot@3}]) &; s1 = ContourPlot3D[f1 == 0, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, MeshFunctions -> pureFun /@ {f3, f4, f5}, MeshShading -> {{{None, None}, {None, None}}, {{None, StippleShading[0.9]}, {None, None}}}, MeshStyle -> None]; s2 = ContourPlot3D[f2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f3, f4, f5}, MeshShading -> {{{HatchShading[], HatchShading[]}, {HatchShading[], HatchShading[]}}, {{HatchShading[], None}, {HatchShading[], HatchShading[]}}}, MeshStyle -> None]; s3 = ContourPlot3D[f3 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f4, f5}, MeshShading -> {{{{None, None}, {None, None}}, {{None, None}, {None, None}}}, {{{None, HalftoneShading[0.6, Orange]}, {None, None}}, {{None, None}, {None, None}}}}, MeshStyle -> None]; s4 = ContourPlot3D[f4 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f3, f5}, MeshShading -> {{{{None, None}, {None, None}}, {{None, None}, {None, None}}}, {{{None, None}, {None, None}}, {{None, HalftoneShading[0.6, Orange]}, {None, None}}}}, MeshStyle -> None]; s5 = ContourPlot3D[f5 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, MeshFunctions -> pureFun /@ {f1, f2, f3, f4}, MeshShading -> {{{{None, None}, {None, None}}, {{None, HalftoneShading[0.8, Orange]}, {None, None}}}, {{{None, None}, {None, None}}, {{None, None}, {None, None}}}}, MeshStyle -> None]; Show[s1, s2, s3, s4, s5, PlotRange -> All] 
For the solid you can also use
pp1 = ParametricPlot3D[ Table[{r Cos[t] Sin[s], r Sin[t] Sin[s], r Cos[s]}, {r, {1, 2}}], {s, 0, Pi/2}, {t, 0, Pi/2}, ImageSize -> Large]; pp2 = ParametricPlot3D[ Table[{r Cos[t] Sin[s], r Sin[t] Sin[s], r Cos[s]}, {s, {0, Pi/2}}], {r, 1, 2}, {t, 0, Pi/2}, ImageSize -> Large]; pp3 = ParametricPlot3D[ Table[{r Cos[t] Sin[s], r Sin[t] Sin[s], r Cos[s]}, {t, {0, Pi/2}}], {r, 1, 2}, {s, 0, Pi/2}, ImageSize -> Large]; Show[pp1, pp2, pp3] 
From How to generate 3D spherical sector :
sphericalSegment[{r1_, r2_}, {θ1_, θ2_}, {ϕ1_, ϕ2_}] := Module[{plot, pts, surf, bdy}, plot = ParametricPlot3D[{Cos[θ] Sin[ϕ], Sin[θ] Sin[ϕ], Cos[ϕ]}, {θ, θ1, θ2}, {ϕ, ϕ1, ϕ2}, Mesh -> None, BoundaryStyle -> Black]; pts = First@Cases[plot, GraphicsComplex[p_, ___] :> p, Infinity]; surf = First@Cases[plot, Polygon[p_] :> p, Infinity]; bdy = First@Cases[plot, Line[p_] :> p, Infinity]; GraphicsComplex[ Join[r1*pts, r2*pts], {EdgeForm[], Polygon[surf], Polygon[Reverse /@ surf + Length@pts], Polygon[Join[#, Reverse@# + Length@pts], VertexNormals -> Cross[Subtract @@ pts[[#]], pts[[First@#]]]] & /@ Partition[bdy, 2, 1, 1]}, VertexNormals -> Join[-pts, pts]]] Graphics3D[sphericalSegment[{1, 2}, {0, Pi/2}, {0, Pi/2}]] 
You can use SphericalShell with RegionPlot3D:
RegionPlot3D[RegionIntersection[Cuboid[{0, 0, 0}, {2, 2, 2}], SphericalShell[{0, 0, 0}, {1, 2}]], Axes -> True, PlotPoints -> 50] 
RegionPlot3D[Region@SphericalShell[{0, 0, 0}, {1, 2}], PlotRange -> {{0, 2}, {0, 2}, {0, 2}}, Axes -> True, PlotPoints -> 50] same picture
Alternatively, you can use ImplicitRegion:
ir = ImplicitRegion[{1 <= x^2 + y^2 + z^2 <= 4, x >= 0, y >= 0, z >= 0}, {x, y, z}] RegionPlot3D[ir, PlotStyle -> Red, PlotPoints -> 80, Axes -> True] 
Graphics3D[sphericalSegment[{1, 2}, {0, Pi/2}, {0, Pi/2}]]) -- Related: mathematica.stackexchange.com/questions/17464/… $\endgroup$