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I am trying to build a face from the attached wire but BRepBuilderAPI_MakeFace seems to be stuck in an infinite loop. What can be the problem?.
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The problem may be that your wire is not plane (I think this is mandatory for using BRepBuilderAPI_MakeFace).
Check out this https://www.opencascade.com/content/create-face-non-planar-wire-using-oc... or if your wire is supposed to be plane try using this constructor
BRepBuilderAPI_MakeFace::BRepBuilderAPI_MakeFace(const gp_Pln &P, const TopoDS_Wire &W, const Standard_Boolean Inside = Standard_True) that takes a plane as an argument. This should be the plane your wire should lie in.
I don't think BRepBuilderAPI_MakeFace is only for planar faces, from documentation .
Find a surface from the wire and make a face. if <OnlyPlane> is true, the computed surface will be a plane. If it is not possible to find a plane, the flag NotDone will be set.
And attached you can see a face I got from using the class.