Then you'll be happy to know I stumbled upon a solution early this morning.
Here is my solution it works just fine although it seems rather strange that this is how a fillets continuity has to be set:
private void CreateG2Fillet(PartDocument part_doc, TransientObjects trans_objects)
{
FilletFeatures fillets = device_part_doc.ComponentDefinition.Features.FilletFeatures; //Get the fillet features object
FilletDefinition = fillet_def = fillets.CreateFilletDefinition(); //Create a new fillet definition
EdgeCollection fillet_edges = trans_objects.CreateEdgeCollection();
fillet_edges = RetrieveEdges(); //Get the edges to fillet through whatever method you prefer / need
//Create a Constant radius edge set from the Fillet definition
FilletConstantRadiusEdgeSet fillet_edge_set = fillet_def.AddConstantRadiusEdgeSet(fillet_edges, fillet_radius);
//Set the continnuity type to curvature continuity using the Continuity Type enumerator.
fillet_edge_set.ContinuityType = ContinuityTypeEnum.kCurvatureContinuity;
fillets.Add(fillet_def); //Create a new fillet using the fillet definition we just created
//Update the part doc to process adding the fillet, this call could also be made from the block of code that calls
//this function.
part_doc.Update();
}
