Mathematica Asked on March 31, 2021
How can we replace the vertices in a 3-dim graph with individual Graphics3D
objects?
In my concrete case I want to visualize a chemical network and replace vertices with their respective MoleculePlot3D
representations. As a teaser, that is the current 3D Graph I am working with. You can probably imagine the final application 🙂
I used the ideas from this post to set up the coordinates.
The red Spheres should be replaced with 3-dim molecule plots.
Consider this minimal example:
Graph3D[{"CO" [DirectedEdge] "C", "CO" [DirectedEdge] "O"}]
Setting up the corresponding MoleculePlot3D
instances:
vert = AssociationThread[
{"CO", "C", "O"} -> {
MoleculePlot3D[Molecule[{Atom["[C]"], Atom["[O]"]}, {Bond[{1, 2}, "Double"]}]],
MoleculePlot3D[Molecule[{Atom["[C]"]}]],
MoleculePlot3D[Molecule[{Atom["[O]"]}]]}]
However, I have difficulties to replace the vertices in the Graph3D
programatically. I managed to modify the 2D Graph:
Graph[{
Annotation["CO", VertexShapeFunction -> (Inset[vert["CO"], #1, Center, 2*#3] &), VertexSize -> 0.2],
Annotation["C", VertexShapeFunction -> (Inset[vert["C"], #1, Center, 2*#3] &), VertexSize -> 0.2],
Annotation["O", VertexShapeFunction -> (Inset[vert["O"], #1, Center, 2*#3] &), VertexSize -> 0.2]},
{"CO" [DirectedEdge] "C", "CO" [DirectedEdge] "O"}]
How can I do this in Graph3D? In the full case I will be working with the following molecules:
{"C", "C+", "CH", "CH+", "CN", "CO", "CS", "CS+", "H", "H2", "HCO+",
"HCS+", "He", "N", "O", "OH", "S", "SO", "CH2+", "CO+", "O+", "OCS+",
"S+", "SO+", "CH2", "CN+", "H2O", "HCN", "HS", "H3O+", "HS+", "CH3+",
"HNC", "H3CO+", "CH4", "N+", "N2", "H+", "OH+", "OCS", "H2O+", "H2+",
"H2S+", "H3+", "He+", "O2", "SO2"}
So relatively small molecules without the need to do extreme scaling in the MoleculePlots.
This answer avoids Inset
altogether and grabs the graphics primitives from inside the expression from a system MoleculePlot3D
, and is therefore a bit fragile because it could break in a future version that restructures the output from MoleculePlot3D
.
Inspection shows that the Graphics3D returned by MoleculePlot3D always contains a GraphicsComplex
with all the atoms and bonds. So we can use that GraphicsComplex
and wrap it in GeometricTransformation
to make the vertex shape function
molVertex[mol_][coords_, vertex_, scale_] := Module[
{graphic = MoleculePlot3D @ mol, gc},
gc = Cases[graphic, _GraphicsComplex, Infinity];
GeometricTransformation[
gc,
TranslationTransform[coords] @* ScalingTransform[scale]
]
]
Here is an example,
SeedRandom @ 42;
g = RandomGraph @ {5, 8};
mols = Map[
Molecule,
{"CCCC(C)(C)OCC", "SC1CCCC1", "O=P(O)(O)CCO", "CCCC", "F[Ti](Cl)(Cl)Cl"}
];
Graph3D[
Annotation[#,
VertexShapeFunction -> molVertex[mols[[#]]],
VertexSize -> 0.2
]& /@ VertexList[g],
EdgeList @ g
]
Correct answer by Jason B. on March 31, 2021
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