How to rotate elements of a mesh (a.k.a Mesh Islands) individually in Blender 3.3 Geometry Nodes

Question

TLDR: I need to randomly rotate meshes within an object individually (based on their individual origins), using Geo nodes.

We now have a "Scale Elements" Node in Geometry Nodes that will take separate parts of a mesh and scale each according to a value that you choose. What I am trying to do is very similar to this node but instead of scaling I want to individually rotate the different parts of a mesh that are separate from one another. The separate meshes of the same object might be described as "Mesh Islands". The Mesh Island node seems confirm this as it indexes each of my rock meshes as a separate 'island'.

The ability to rotate mesh islands individually would be very useful in my project where I want to make a procedural "tilled earth" generator, where clods/chunks of earth will naturally be found at different angles but also be somewhat flat looking on one side most of the time (think like a clay-rich soil broken up roughly).

The tutorial I'm working from to achieve the foundation of my node system is this one on Youtube by Default Cube:
Turning ANYTHING into Rocks - Blender Geometry Nodes

What I have so far:

My Node Tree (similar to one seen in video- not exact):

End of Node Tree

I have a feeling I'm overlooking something very basic here. Seems like a foundational technique that should be simple to achieve? After all it's just rotation individual parts of an object, easy to do outside of geometry nodes.

Answer 1

I didn't look at your file, since I wrote the answer before you published it, but a solution might look something like this:

The trick here is to find the center of rotation of a mesh island.

There are probably other ways, but this solution still works quite well.

Here I first accumulate the positions of the points that are connected with faces (the mesh islands).

Then I scale the accumulated vector with the value $1/numberOfPointsPerMeshIsland$, and get a mean value, which serves me as center for Vector Rotate.

_{(Blender 3.2+)}

Answer 2

Quellenform's answer is better, more fool-proof, but if like me you're no good at math, here's a more brute-force method. We need the individual 'origin's of the mesh islands, so first I collapse them into their centers, using a Merge by Distance. If we use the default All mode, they'll all collapse into one single point for the whole mesh, so we use the Connected mode instead:

Then, using a Sample Index node (before 3.4, Transfer Attribute) we capture the positions of these points by their Island Index to feed the Center socket of a Vector Rotate node: