(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), 321.
[Zbl], [MR].

J.H. Yoon, H. Pottmann, and Y.S. Lee.
Locally optimal cutting positions for fiveaxis sculptured surface machining.
ComputerAided Design 35 (2003), 6981.

J.H. Yoon.
Tool tip gouging avoidance and optimal tool positioning for 5axis sculptured
surface machining.
Intl. J. Production Research 41 (2003), 21252142.

T. Smith, R. T. Farouki, M. al Kandari, and H. Pottmann.
Optimal slicing of
freeform surfaces.
Comput. Aided Geom. Design 19 (2002), 4364.

J. Wallner, T. Sakkalis, T. Maekawa, H. Pottmann, and G. Yu.
Selfintersections
of offset curves and surfaces.
Int. J. Shape Modeling 7 (2001), 121.

J. Wallner.
Selfintersections and smoothness of general offset surfaces.
J. Geom. 70 (2001), 176190.
[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 417432. Vanderbilt University
Press, Nashville, 2000, ISBN 0826513565.

G. Glaeser, J. Wallner, and H. Pottmann.
Collisionfree
3axis milling and selection of cutting tools.
ComputerAided Design 31 (1999), 225232.
[Zbl].

J. Wallner, G. Glaeser, and H. Pottmann.
Geometric
contributions to 3axis milling of sculptured surfaces.
In G. J. Olling, B. K. Choi, and R. B. Jerard, editors, Machining
Impossible Shapes, pages 3341. Kluwer Academic Publ., Boston, 1999.

H. Pottmann.
General offset surfaces.
Neural, Parallel & Scient. Comput. 5 (1997), 5580.

H. Pottmann, J. Wallner, G. Glaeser, and B. Ravani.
Geometric
criteria for gougefree threeaxis milling of sculptured surfaces.
ASME J. Mech. Design 121 (1999), 241248.

J. Wallner, H.Y. Chen, and H. Pottmann.
Galilei
Laguerre geometry and rational circular offsets.
Beitr. Algebra Geom. 39 (1998), 291305.
[Zbl], [MR].

H. Pottmann and B. Ravani.
Singularities of motions constrained by contacting surfaces.
Mech. Mach. Theory 35 (2000), 963984.

J. Wallner.
Configuration
space of surfacesurface contact.
Geom. Dedicata 80 (2000), 173185.
[Zbl], [MR], [doi].
