Convolution surfaces of quadratic triangular Bézier surfaces

Albrecht, 2002, The Veronese surface revisited, J. Geom., 73, 22, 10.1007/s00022-002-8583-7 Apery, 1987 Bloomenthal, 1991, Convolution surfaces, Computer Graphics, 25, 251, 10.1145/127719.122757 Coffmann, 1996, The algebra and geometry of Steiner and other quadratically parameterizable surfaces, Comp. Aided Geom. Design, 13, 257, 10.1016/0167-8396(95)00026-7 Degen, W.L.F., 1994. The types of triangular Bézier surfaces. In: IMA Conference on the Mathematics of Surfaces, pp. 153–170 Farin, 2002 Fladt, 1933, Die Umkehrungen der ebenen quadratischen Cremona Transformationen, J. Reine Angew. Math., 170, 64 Hoschek, 1993 Jüttler, B., 1998. Triangular Bézier surface patches with a linear normal vector field. In: The Mathematics of Surfaces VIII, Information Geometers pp. 431–446 Jüttler, 2000, Hermite interpolation by piecewise polynomial surfaces with rational offsets, Comp. Aided Geom. Design, 17, 361, 10.1016/S0167-8396(00)00002-9 Kummer, 1865, Über die Flächen vierten Grades, auf welchen Scharen von Kegelschnitten liegen, J. Reine Angew. Math., 64, 66, 10.1515/crll.1865.64.66 Lávička, M., Bastl, B., 2006. Rational parameterized curves and surfaces with rational convolutions. In: Algebraic Geometry and Geometric Modeling, Proc. of the Conf., Barcelona, 4–7 September 2006, pp. 74–79 Lee, 1998, Polynomial/rational approximation of Minkowski sum boundary curves, Graphical Models, 60, 136, 10.1006/gmip.1998.0464 Lee, I.K., Kim, M.S., Elber, G., 1998b. The Minkowski sum of 2D curved objects. In: Proceedings of Israel–Korea Bi-National Conference on New Themes in Computerized Geometrical Modeling, February 1998, Tel-Aviv University, pp. 155–164 Meyer, 1903-1915, Spezielle algebraische Flächen, vol. III C 10, 1483 Mühlthaler, 2003, Computing the Minkowski sum of ruled surfaces, Graphical Models, 65, 369, 10.1016/j.gmod.2003.07.003 Oeltze, 2005, Visualization of vasculature with convolution surfaces: Method, validation and evaluation, IEEE Transactions on Medical Imaging, 24, 540, 10.1109/TMI.2004.843196 Peternell, 2003, The convolution of a paraboloid and a parametrized surface, Journal for Geometry and Graphics, 7, 157 Peternell, 1998, A Laguerre geometric approach to rational offsets, Computer Aided Geometric Design, 15, 223, 10.1016/S0167-8396(97)00024-1 Pottmann, 1995, Rational curves and surfaces with rational offsets, Computer Aided Geometric Design, 12, 175, 10.1016/0167-8396(94)00008-G Pottmann, 1995, Studying NURBS curves and surfaces with classical geometry, 413 Peters, 1998, The 42 equivalence classes of quadratic surfaces in affine n-space, Comp. Aided Geom. Design, 15, 459, 10.1016/S0167-8396(97)00043-5 Sampoli, 2006, Exact parameterization of convolution surfaces and rational surfaces with linear normals, Computer Aided Geometric Design, 23, 179, 10.1016/j.cagd.2005.07.001 Schreier, 1961 Sederberg, 1985, Steiner surface patches, IEEE Comp. Graphics Applications, 5, 23, 10.1109/MCG.1985.276391 Sherstyuk, A., 1999. Convolution Surfaces in Computer Graphics. PhD thesis, Monash Univ., Australia Steiner, J., 1882. Gesammelte Werke II. Berlin, pp. 723–724, pp. 741–742 Wunderlich, 1962, Römerflächen mit ebenen Fallinien, Ann. Mat. Pura Appl., 57, 97, 10.1007/BF02417729 Wunderlich, 1968, Durch Schiebung erzeugbare Römerflächen, Sitzungsberichte der Österreischen Akademie der Wissenschaften, 176, 473 Wunderlich, 1969, Kinematisch erzeugbare Römerflächen, J. Reine Angew. Math., 236, 67, 10.1515/crll.1969.236.67