(this research was performed at TU Wien, with H. Pottmann as principal investigator) We study geometrical problems concerning milling of sculptured surfaces. These include simulation of the manufacturing process, optimal choice of the cutting tool, cutter paths, data reduction, local and global collisions avoidance, and general offset surfaces. Among other things, we studied the configuration manifolds of tool positions relative to a workpiece: Objects of investigation are the degree of freedom of the motion of the tool, the correspondence between the contact point and the tool position, and the presence and absence of unwanted collisions between tool and workpiece.

• J. Wallner. Gliding spline motions and applications. Comput. Aided Geom. Design 21 (2004), 3-21. [Zbl], [MR].
• J.-H. Yoon, H. Pottmann, and Y.-S. Lee. Locally optimal cutting positions for five-axis sculptured surface machining. Computer-Aided Design 35 (2003), 69-81.
• J.-H. Yoon. Tool tip gouging avoidance and optimal tool positioning for 5-axis sculptured surface machining. Intl. J. Production Research 41 (2003), 2125-2142.
• T. Smith, R. T. Farouki, M. al Kandari, and H. Pottmann. Optimal slicing of free-form surfaces. Comput. Aided Geom. Design 19 (2002), 43-64.
• J. Wallner, T. Sakkalis, T. Maekawa, H. Pottmann, and G. Yu. Self-intersections of offset curves and surfaces. Int. J. Shape Modeling 7 (2001), 1-21.
• J. Wallner. Self-intersections and smoothness of general offset surfaces. J. Geom. 70 (2001), 176-190. [Zbl], [MR].
• J. Wallner and H. Pottmann. On the geometry of sculptured surface machining. In P.-J. Laurent, P. Sablonnière, and L. L. Schumaker, editors, Curve and Surface Design: Saint Malo 1999, pages 417-432. Vanderbilt University Press, Nashville, 2000, ISBN 0-8265-1356-5.
• G. Glaeser, J. Wallner, and H. Pottmann. Collision-free 3-axis milling and selection of cutting tools. Computer-Aided Design 31 (1999), 225-232. [Zbl].
• J. Wallner, G. Glaeser, and H. Pottmann. Geometric contributions to 3-axis milling of sculptured surfaces. In G. J. Olling, B. K. Choi, and R. B. Jerard, editors, Machining Impossible Shapes, pages 33-41. Kluwer Academic Publ., Boston, 1999.
• H. Pottmann. General offset surfaces. Neural, Parallel & Scient. Comput. 5 (1997), 55-80.
• H. Pottmann, J. Wallner, G. Glaeser, and B. Ravani. Geometric criteria for gouge-free three-axis milling of sculptured surfaces. ASME J. Mech. Design 121 (1999), 241-248.
• J. Wallner, H.-Y. Chen, and H. Pottmann. Galilei Laguerre geometry and rational circular offsets. Beitr. Algebra Geom. 39 (1998), 291-305. [Zbl], [MR].
• H. Pottmann and B. Ravani. Singularities of motions constrained by contacting surfaces. Mech. Mach. Theory 35 (2000), 963-984.
• J. Wallner. Configuration space of surface-surface contact. Geom. Dedicata 80 (2000), 173-185. [Zbl], [MR], [doi].