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Research Report FWF S9206 Helmut Pottmann Geometric Modeling & Industrial Geometry

Research Report FWF S9206 Helmut Pottmann Geometric Modeling & Industrial Geometry. Map labeling algorithm. Collision free initial position using digitized images Iterative improvement using force directed optimization. Surface fitting in feature sensitive metric. Integral invariants.

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Research Report FWF S9206 Helmut Pottmann Geometric Modeling & Industrial Geometry

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

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

  3. Surface fittingin feature sensitive metric

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

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

  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. 3D shape morphing based on geodesics in shape spaces

  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

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