Geometry Nodes: Vertex Positions for each face

Hi fellow geometry noders!
I have a triangulated mesh (Each face has only three vertices that define it)
I am attempting to draw the Steiner Ellipse of each face using a mesh circle
To do this, at the very least, I need to be able to reference the positions of the three vertices that make up each face.
I’ve struggled with this for quite a while, attempting edge splitting, mesh islands and attribute transfers, to no avail. I am starting to doubt whether Geometry nodes currently even has the capability to do this…

Anyone got an amazing and insightful solution?
Thanks :smile:

This may get you closer, I can’t yet get the correlaton between scale and face area though.

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There is a lot of valuable information buried in this old megathread.

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The position at face corners was the solution! Thank you!

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For anyone who comes looking, here’s my final solution to Steiner Inellipses. You can do Steiner Circumellipses too with some simple scaling. Works on any triangulated mesh.
Steiner Ellipse Testing.blend (1.5 MB)

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