Geometric methods for 3D shape understanding and reconstruction

                      Helmut Pottmann

              Vienna University of Technology

Geometry provides a rich source of knowledge and methods for
understanding and reconstructing 3D shapes from measurement data. We
will illustrate this at hand of line geometry and Laguerre
geometry. Line geometric methods are applied to the system of
estimated surface normals at data points, whereas the Laguerre
geometric approach addresses estimated tangent planes at data
points. The combination of classical geometric results with tools from
scientific computing yields algorithms for the detection and
reconstruction of special surfaces such as rotational and helical
surfaces, ruled surfaces, developable surfaces (including general
cylinders and cones) and canal surfaces. We address various industrial
applications and outline directions for future research.