Using computed facial feature points to position a product model relative to a model of a face is disclosed, comprising: obtaining a three-dimensional (3D) model of a user's face, wherein the 3D model of the user's face comprises a plurality of 3D points; determining a face normal that is normal to a plane that is determined based at least in part on a first subset of 3D points from the plurality of 3D points; determining a set of computed bridge points based at least in part on a second subset of 3D points from the plurality of 3D points and the face normal; and using the set of computed bridge points to determine an initial placement of a 3D model of a glasses frame relative to the 3D model of the user's face.