Prof. Dr. Ulrich Reif

Geometrie und Approximation

Aufgabenbereich

Geometrie und Approximation

Kontakt

work +49 6151 16-22491

Work S2|15 306
Schlossgartenstraße 7
64289 Darmstadt

on appointment

Thesis and monographs:

• U. Reif and J. Peters, Subdivision Surfaces, Series Geometry and Computing, Vol. 3, Springer (2008)

• U. Reif, Analyse und Konstruktion von Subdivisionsalgorithmen für Freiformflächen beliebiger Topologie, Habilitationsschrift, Shaker Verlag (1999)

• U. Reif, Neue Aspekte in der Theorie der Freiformflächen beliebiger Topologie, Doktorarbeit, Universität Stuttgart (1993)

Journal papers:

• N. Lehmann, LB. Maier, S. Odathuparambil, and U. Reif, Ambient Approximation on Hypersurfaces, Constr Approx (2018). doi.org/10.1007/s00365-018-9419-5

• C. Apprich, K. Höllig, J. Hörner and U. Reif, Collocation with WEB-Splines, Advances in Computational Mathematics, Volume 42, Number 4 (2016), 823-842

• J. Hakenberg and U. Reif, On the volume of sets bounded by refinable functions [pdf], Applied Mathematics and Computation 272 (2016), 2-19

• T. Ewald, U. Reif, and M. Sabin, Hölder Regularity of Geometric Subdivision Schemes [pdf], Constructive Approximation, Volume 42, Issue 3 (2015), 425-458

• C. Möller and U. Reif, A Tree-Based Approach to Joint Spectral Radius Determination [pdf], Linear Algebra and its Applications 463 (2014), 154–170

• U. Reif and N. Sissouno, Approximation with Diversified B-Splines [pdf],CAGD 31 (2014), 510-520

• O. Davydov, J. Prasiswa, and U. Reif, Two-stage approximation methods with extended B-splines [pdf], Mathematics of Computation 83 (2014), 809-833

• T. Cashman, K. Hormann, and U. Reif, Generalized Lane-Riesenfeld algorithms [pdf], CAGD 30 (2013), 298-409

• U. Reif, Polynomial approximation on domains bounded by diffeomorphic images of graphs, Journal of Approximation Theory 164 (2012), 954--970

• N. Lehmann and U. Reif, Notes on the curvature tensor, Graphical Models 74 (2012), 321-325

• A. App and U. Reif, Piecewise linear orthogonal approximation, SIAM Journal on Numerical Analysis, Volume 48, Issue 3 (2010), 840-856

• B. Mößner and U. Reif, Error bounds for polynomial tensor product interpolation, Computing, Vol. 86, Issue 2 (2009), 185-197

• J. Hechler, B. Mößner, and U. Reif, C1-continuity of the generalized four-point scheme, Linear Algebra and its Applications, Volume 430, Issues 11-12 (2009), 3019-3029

• B. Mößner and U. Reif, Stability of tensor product B-splines on domains, Journal of Approximation Theory, Volume 154, Issue 1 (2008), 1-19

• B. Dietz, B. Mößner, T. Papenbrock, U. Reif, and A. Richter, Bouncing ball orbits and symmetry breaking effects in three-dimensional chaotic billiard, Physical Review E, vol. 77, Issue 4 (2008), id. 046221

• M. Floater, A.F. Rasmussen, and U. Reif, ExtrNumerical Algorithms Volume 44, Number 3 (2007), 235-248, apolation methods for approximating arc length and surface area,

• K. Karciauskas, J. Peters, and U. Reif, Shape characterization of subdivision surfaces – case studies, CAGD, 21 (2004), 601-614

• J. Peters and U. Reif, Shape characterization of subdivision surfaces – basic principles, CAGD, 21 (2004), 585-599

• U. Reif, In memoriam Josef Hoschek, CAGD, 20 (2003), 493-499

• K. Höllig and U. Reif, Nonuniform web-splines, CAGD, 20 (2003), 277-294

• K. Höllig, U. Reif, and J. Wipper, Multigrid methods with web-splines,Numerische Mathematik 91, No 2, (2002), 237-256

• K. Höllig, U. Reif, and J. Wipper, Weighted extended B-spline approximation of Dirichlet problems, SIAM Journal on Numerical Analysis 39, No 2, (2001), 442-462

• U. Reif and P. Schröder, Curvature Smoothness of Subdivision Surfaces, Advances in Computational Mathematics 14, No 2, (2001), 157-174

• J. Peters and U. Reif, Least squares approximation of Bezier coefficients provides best degree reduction in the L2-norm, Journal of Approximation Theory, Vol. 104, No. 1, (2000), 90-97

• U. Reif, Best bounds on the approximation of polynomials and splines by their control structure, CAGD 17 (2000), 579-589

• D. Lutterkort, J. Peters, and U. Reif, Polynomial degree reduction in the L2-norm equals best Euclidean, approximation of Bezier coefficients, CAGD 16 (1999), 607-612

• A. Kipp and U. Reif, On the existence of solutions to non-parametric fairing problems, CAGD (1999), 217-221

• H. Prautzsch and U. Reif, Degree estimates for C^k-piecewise polynomial subdivision surfaces, Advances in Computational Mathematics 10 (1999), 209-217

• U. Reif, On the local existence of the quadratic geometric Hermite interpolant, CAGD 16, Issue 3, (1999), 217-221

• J. Peters and U. Reif, The 42 equivalence classes of quadratic surfaces in affine n-space, CAGD 15 (1998), 459-473

• J. Peters and U. Reif, Analysis of algorithm, SIAM J. on Numer. Anal. Vol 35, No 2, (1998), 728-748s generalizing B-spline subdivision,

• J. Peters and U. Reif, The simplest subdivision scheme for smoothing polyhedra, ACM TOG 16 (1997), 420-431

• U. Reif, Uniform B-spline approximation in Sobolev spaces, Numerical Algorithms 15 (1997), 1-14

• H. Bohl and U. Reif, Degenerate Bezier patches with continuous curvature, CAGD 14 (1997), 749-761

• U. Reif, TURBS – topologically unrestricted rational B-splines, Constr. Approx. 14 (1998), 47-77

• U. Reif, Orthogonality of cardinal B-Splines in weighted Sobolev spaces, SIAM J. Math. Anal., Vol. 28, No. 5, (1997), 1258-1263

• U. Reif, On constructing topologically unrestricted B-splines, ZAMM 76 (1996), Suppl. 1, 73-74

• U. Reif, A refinable space of smooth spline surfaces of arbitrary topological genus, Journal of Approximation Theory, Vol 90, No 2 (1997), 174-199

• U. Reif, A degree estimate for subdivision surfaces of higher regularity,Proc. of the AMS, Vol. 124, Nr. 7, (1996), 2167-2174

• U. Reif, A unified approach to subdivision algorithms near extraordinary vertices, CAGD 12 (1995), 153-174

• U. Reif, Biquadratic G-spline surfaces, CAGD 12 (1995), 193-205

• U. Reif, A note on degenerate triangular Bezier patches, CAGD 12 (1995), 547-550

• G. Aumann, U. Reif, and K. Spitzmüller, A counterexample to a corollary of Kim et al., CAGD 12 (1995), 853-855

Other refereed papers:

• U. Reif and J. Peters, Structural Analysis of Subdivision Surfaces – A Summary, in Topics in Multivariate Approximation and interpolation, K. Jetter et al. (eds.), Elsevier, (2006), 149-190

• K. Höllig, U. Reif, and J. Wipper, Error estimates for the web-method, in Mathematical Methods for Curves and Surfaces: Oslo 2000, T. Lyche und L.L. Schumaker (eds.), Vanderbilt University Press, Nashville, TN, (2001), 195-209

• U. Reif, Orthogonality Relations for Cardinal B-Splines over Bounded Intervals, in Geometric Modeling: Theory and Practice, W. Strasser, R. Klein, and R. Rau (eds.), Springer, (1998)

• K. Höllig, J. Hahn, and U. Reif, Glattes Füllen n-seitiger Lücken, in Mathematik – Schlüsseltechnologie für die Zukunft, K.-H. Hoffmann et al (eds.), Springer, 347-367, (1997)

• U. Reif, Some new results on subdivision algorithms for meshes of arbitrary topology, In Wavelets and Multilevel Approximation, Charles K. Chui and Larry L. Schumaker (eds.), (1995), 367-374

Current PhD students and postdocs:

• Tobias Ewald

• Lars-Benjamin Maier

• Ba Duong Chu

Former PhD students:

• Sonja Odathuparambil, Ambient Spline Approximation on Manifolds, TU Darmstadt 2016

• Claudia Möller, A New Strategy for Exact Determination of the Joint Spectral Radius, TU Darmstadt, 2015

• Nicole Lehmann, Modeling with Ambient B-Splines, TU Darmstadt, 2013

• Nada Sissouno, Multivariate Splineapproximation auf Gebieten, TU Darmstadt, 2011

• Rene Hartmann, Subdivision Surfaces: C2-schemes and generalized control nets, TU Darmstadt, 2011

• Jennifer Prasiswa, Lokale und globale Algorithmen zur Approximation mit erweiterten B-Splines, TU Darmstadt, 2009

• Jochen Hechler, Optimierung von Freiformflächen mittels Raumdeformation, TU Darmstadt, 2007

• Bernhard Mößner, B-Splines als Finite Elemente, TU Darmstadt, 2005

• Andreas App, Optimierung von Reflektoren in Straßenleuchten mittels Bezier-Raum-Deformation, Universität Stuttgart, 2005

• Joachim Gaukel, Effiziente Lösung polynomialer und nichtpolynomialer Gleichungssysteme mit Hilfe von Subdivisionsalgorithmen, TU Darmstadt, 2003

I (co)-organized the following conferences and workshops:

  • Mathematische Methoden der Geometrischen Datenverarbeitung, Oberwolfach Workshop 2002
  • Geometric Modeling and Differential Geometry, Erbach 2003
  • Analytical and Numerical Methods in Image and Surface Processing, Oberwolfach Workshop 2005
  • Industry Challenges in Geometric Modeling, CAD and Simulation, Darmstadt 2001-2013 (annually)
  • New Trends in Applied Geometry I, Bad Herrenalb 2010
  • New Trends in Applied Geometry IV, Bad Herrenalb 2013
  • Geometry & Computation for Interactive Simulation, Banff Workshop 2017
  • Symposium on Approximation of Curves and Surfaces, Session of ICNAAM 2018
  • Interactive Design and Simulation, Dagstuhl Workshop 2019

I am associate editor of the following journals:

I have guest-edited the following volumes:

  • Geometric Modelling and Differential Geometry, Special Issue of CAGD, Vol. 22, Issue 7 (2005)
  • Subdivision
  • Algorithms, Special Issue of CAGD, Vol. 18, Issue 5 (2001)

Short CV of Ulrich Reif

  • Qualification
    • 1990: Diplom (eq. Master) in mathematics, University of Stuttgart
    • 1993: Promotion, University of Stuttgart
    • 1998: Habilitation, University of Stuttgart
  • Appointments
    • 1990-1999: Scientific employee, University of Stuttgart
    • 1999 : Deputy chair for Approximation, University of Dortmund
    • 2000-today: Full professor for Geometry and Approximation, TU Darmstadt
  • Scientific Interests
    • Subdivision algorithms
    • Spline approximation
    • Discrete differential geometry
  • Honors
    • John Gregory Memorial Award, 2014
    • Athene-Preis für gute Lehre, TU Darmstadt, 2015

Work:

Hobby: