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Prof. Dr. sc. techn. Beat Brüderlin


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Interactive Freeform Shape Modeling

We developed an approach to editable free-form features. A piecewise polynomial (B-Spline) surface follows, for instance, the changes of a curve, maintaining a set of additional predefined constraints (e.g. incidence on one or several other curves, tangencies).


The main research issues have been:

  • Efficient set-up of the equations which express the constraint problem, using blossoming techniques, and a multi-index tree data structure.
  • Robust and efficient equation solving for under- and over-determined systems of linear equations, based on sparse singular value decomposition and regularization.
  • Expressing incidence, derivative, and integral constraints. Defining the so-called aliasing problem, and providing alternatives, such as local surface reparameterization, and smoothing.
  • Application for sketch-based surface sculpting, and editing of reverse-engineered models.


Paul Michalik, Beat Brüderlin, Dae-Hyun Kim:
Introducing Parametrization in Surface Models by Means of Geometric Constraints.
in: Proceedings of Numérisation 3D - Scanning 2001, Paris, France, 4-5 April 2001. UIC, Paris, France, April 2001.

Paul Michalik, Beat Brüderlin:
A Constraint-based Method for Sculpting Free-Form Surfaces.
in: Guido Brunnett, Hanspeter Bieri, Gerald Farin (Eds.): Geometric Modelling. Dagstuhl 1999. Computing Supplementa 14, Springer, Vienna, Austria, 2001, pp. 249-265.

Paul Michalik, Beat Brüderlin:
Computing Curve-Surface Incidence Constraints Efficiently.
in: Abdelkader Belhi, Pierre-Jean Erard, Abdelaziz Bouras (Eds.): Proceedings of Swiss Conference of CAD/CAM, Neuchâtel, Switzerland, 22-24 February 1999. Neuchâtel University, Neuchâtel, Switzerland, 1999, pp. 150-157.