ClearAll[orbit];
orbit // Options = {ColorFunction -> None};
orbit[OptionsPattern[]] :=
With[{cf = OptionValue[ColorFunction],
rot = ( {
{1, 0, 1/10},
{0, 1, 1/10}
} )},
Polygon[CirclePoints[1., 120].DiagonalMatrix[{0.3, 1.}].rot ->
CirclePoints[{-0.07, 0.}, 0.82,
120].DiagonalMatrix[{0.3, 1.1}].rot,
VertexColors -> (cf /. {None | Automatic -> Automatic,
f_ :> f /@ (Range[120]/120.)})]
];
paths = With[{sph = 0.85 {Cos[-0.85] + 0.05, Sin[-0.85]} {0.3, 1.1}},
Graphics3D[{
EdgeForm[{Thickness@Medium, White}]
, {orbit[ColorFunction ->
(Blend[{Hue[0.05, 1, 0.8], Darker[Yellow, 0.1]},
Cos[Pi # + Pi/4]^2] &)]}
, GeometricTransformation[
{orbit[ColorFunction ->
(Blend[{Hue[0.55, 0.9, 0.7], Darker[Cyan, 0.1]},
Cos[Pi # + Pi/4]^2] &)]},
RotationTransform[-2 Pi/3, {0, 0, 1}]
]
, GeometricTransformation[
{orbit[ColorFunction ->
(Blend[{Darker[Green, 0.4], Darker[Yellow, 0.2]},
Cos[Pi # + Pi/4]^2] &)]},
RotationTransform[2 Pi/3, {0, 0, 1}]
]
}, PlotRange -> 1, PlotRangePadding -> Scaled[.05],
ViewPoint -> Top, Boxed -> False, Lighting -> "Neutral"]
]];
spheres = With[{sph = 0.85 {Cos[-0.85] + 0.05, Sin[-0.85]} {0.3, 1.1}},
Graphics[{
Inset[
Graphics3D[{Specularity[White, 5], Black, Sphere[]},
Boxed -> False, Lighting -> {{"Point", White, {0, 0, 3}}}],
Center, Center, Scaled[0.25]],
, {
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[Graphics3D[{Specularity[White, 5], Hue[0.05, 1, 0.8],
Sphere[]}, Boxed -> False,
Lighting -> {{"Point", Hue[0.1, 1, 1], {0, 0, 3}}, {"Ambient",
GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]}
, GeometricTransformation[
{
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[
Graphics3D[{Specularity[White, 5], Hue[0.55, 0.9, 0.75],
Sphere[]}, Boxed -> False,
Lighting -> {{"Point", Darker[Cyan, 0.2],
RotationTransform[2 Pi/3, {1.3, -2.4, 2}]@{0, 0,
3}}, {"Ambient", GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]},
RotationTransform[-2 Pi/3]
]
, GeometricTransformation[
{
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[
Graphics3D[{Specularity[White, 5], Darker[Green, 0.3],
Sphere[]},
Boxed -> False,
Lighting -> {{"Point", Darker[Yellow, 0.3],
RotationTransform[-2 Pi/3, {1.3, -2.4, 2}]@{0, 0,
3}}, {"Ambient", GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]},
RotationTransform[2 Pi/3]
]
}, PlotRange -> 1, PlotRangePadding -> Scaled[.05]]
];
Show[
Graphics[Inset[paths, Center, Center, Scaled[1.8]],
PlotRange -> 1, PlotRangePadding -> Scaled[.05]],
spheres]
Bells and whistles. Doesn't replicate the crossings of the orbits in the artwork, but it's more consistent. Colors and lighting are a bit hard to get right.
ClearAll[orbit];
orbit // Options = {ColorFunction -> None};
orbit[OptionsPattern[]] :=
With[{cf = OptionValue[ColorFunction],
rot = ( {
{1, 0, 1/10},
{0, 1, 1/10}
} )},
Polygon[CirclePoints[1., 120].DiagonalMatrix[{0.3, 1.}].rot ->
CirclePoints[{-0.07, 0.}, 0.82,
120].DiagonalMatrix[{0.3, 1.1}].rot,
VertexColors -> (cf /. {None | Automatic -> Automatic,
f_ :> f /@ (Range[120]/120.)})]
];
paths = With[{sph = 0.85 {Cos[-0.85] + 0.05, Sin[-0.85]} {0.3, 1.1}},
Graphics3D[{
EdgeForm[{Thickness@Medium, White}]
, {orbit[ColorFunction ->
(Blend[{Hue[0.05, 1, 0.8], Darker[Yellow, 0.1]},
Cos[Pi # + Pi/4]^2] &)]}
, GeometricTransformation[
{orbit[ColorFunction ->
(Blend[{Hue[0.55, 0.9, 0.7], Darker[Cyan, 0.1]},
Cos[Pi # + Pi/4]^2] &)]},
RotationTransform[-2 Pi/3, {0, 0, 1}]
]
, GeometricTransformation[
{orbit[ColorFunction ->
(Blend[{Darker[Green, 0.4], Darker[Yellow, 0.2]},
Cos[Pi # + Pi/4]^2] &)]},
RotationTransform[2 Pi/3, {0, 0, 1}]
]
}, PlotRange -> 1, PlotRangePadding -> Scaled[.05],
ViewPoint -> Top, Boxed -> False, Lighting -> "Neutral"]
]
spheres = With[{sph = 0.85 {Cos[-0.85] + 0.05, Sin[-0.85]} {0.3, 1.1}},
Graphics[{
Inset[
Graphics3D[{Specularity[White, 5], Black, Sphere[]},
Boxed -> False, Lighting -> {{"Point", White, {0, 0, 3}}}],
Center, Center, Scaled[0.25]],
, {
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[Graphics3D[{Specularity[White, 5], Hue[0.05, 1, 0.8],
Sphere[]}, Boxed -> False,
Lighting -> {{"Point", Hue[0.1, 1, 1], {0, 0, 3}}, {"Ambient",
GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]}
, GeometricTransformation[
{
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[
Graphics3D[{Specularity[White, 5], Hue[0.55, 0.9, 0.75],
Sphere[]}, Boxed -> False,
Lighting -> {{"Point", Darker[Cyan, 0.2],
RotationTransform[2 Pi/3, {1.3, -2.4, 2}]@{0, 0,
3}}, {"Ambient", GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]},
RotationTransform[-2 Pi/3]
]
, GeometricTransformation[
{
{EdgeForm[White], White, Disk[sph, 0.08]},
Inset[
Graphics3D[{Specularity[White, 5], Darker[Green, 0.3],
Sphere[]},
Boxed -> False,
Lighting -> {{"Point", Darker[Yellow, 0.3],
RotationTransform[-2 Pi/3, {1.3, -2.4, 2}]@{0, 0,
3}}, {"Ambient", GrayLevel[0.6]}}],
sph, Center, Scaled[0.12]]},
RotationTransform[2 Pi/3]
]
}, PlotRange -> 1, PlotRangePadding -> Scaled[.05]]
];
Show[
Graphics[Inset[paths, Center, Center, Scaled[1.8]],
PlotRange -> 1, PlotRangePadding -> Scaled[.05]],
spheres]
