Frégier’s Theorem in Three Dimensions

We present a three-dimensional analog of Frégier’s theorem. This yields Frégier quadrics associated with each quadric. The Frégier quadrics of regular quadrics can be obtained as so-called generalized offsets to quadrics with an offset function depending on the Gaussian curvature. Further, we shall discuss some of the common features and differences of the planar and spatial Frégier transform.