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.

Publications

	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.