1. Research Report FWF S9206 Helmut Pottmann Geometric Modeling & Industrial Geometry

2. 2 Map labeling algorithm Collision free initial position using digitized images Iterative improvement using force directed optimization

3. 3 Surface fitting in feature sensitive metric

4. 4 Integral invariants Integration over local neighborhoods „Curvature“ on various scales

5. 5 Minkowski sum boundary surfaces of 3D objects Minkowski sum A+B of objects A and B is the outer envelope of B with respect to all translations determined by points a  A.

6. 6 Parametrization of rational and convolution surfaces The convolution surface A*B is the generalized offset of A w.r.t. B. Thm.: The convolution of any rational surface and a polynomial surface with a linear normal vector field is always rational.

7. 7 Line element geometry Line element = line + point on it Surface recognition, reconstruction; segmentation

8. 8 Geometric automatic extraction of sulcal fundi Fundi = deepest regions of cortex; use a geodesic depth measure w.r.t. to hull surface computed with level set method

9. 9 3D shape morphing based on geodesics in shape spaces

10. 10 Scientific talks H. Pottmann: Univ. Innsbruck, Tsinghua Univ., Seoul Nat. Univ.: Integral invariants M. Peternell, SIAM’05: Envelopes of moving solids M. Peternell, SIAM’05: Constrained Surface Approximation from a Geometric Optimization Perspective M. Hofer, SIAM’05: 3D Shape Recognition and Reconstruction Based on Line Element Geometry