If you started out with a circular hole on your target surface, it is actually possible though to extract the image of that curve in the UV space of the surface, that would then map back to a circle again if you reflowed it. But for a case like that you would have to start out with a projected cut on your surface to begin with, the usual method of doing flow is that you start with flat objects and then apply them to the object. It's not really possible to easily create the flat distorted version of the circle just by drawing it.

But to extract the UV space curves for a surface's trimming boundary this script will do that:

script: /* Create UV curves of selected faces */ var faces = moi.geometryDatabase.getSelectedObjects().getFaces(); for ( var iFace = 0; iFace < faces.length; ++iFace ) { var face = faces.item(iFace); var edges = face.getEdges(); for ( var iEdge = 0; iEdge < edges.length; ++iEdge ) { var edge = edges.item(iEdge); var uvcrvs = edge.getUVCurvesOfEdge(face); moi.geometryDatabase.addObjects( uvcrvs ); } }

- Michael