Research Topics in Focus

Free-form surfaces with irregular topology
- interpolating curve networks
- n-sided patches
- geometric continuity
- compatibility issues
Blending surfaces
- representing edge blends; avoiding self-intersections
- variable radius rolling ball blends
- vertex blending using setbacks
- topological issues in B-reps
- general blending paradigm
- blending and smoothing based on control polyhedra
Reverse Engineering I.: surface fitting over point clouds
1. Implicit surfaces
  - faithful geometric fitting for natural quadrics and tori
2. Parametric surfaces
  - initial parametrization, carrier surfaces
  - parameter correction, reparametrization
  - knot insertion strategies
  - hybrid smoothing functionals, automatic setting of weights
  - computational issues
3. Swept surfaces
  - recognizing translational and rotational symmetries
  - reconstructing free-form profiles and conventional (arc + straight) contours
4. Constrained fitting
  - surface approximation combined with interpolation
  - matching positional, cross-derivative and normal vector functions
  - simultaneous fitting of adjacent patchworks
  - fitting with constraints such as symmetry or fixed rotational axes etc.
5. Feature fitting
  - reconstructing free-form features such as
  - variable radius rolling ball blends, free-form steps, free-form pockets etc.
Reverse Engineering II.: from data acquisition to model building
1. Practical data acquisition problems
  - accuracy, occlusion, avoiding reflections, etc.
  - multiple views: three-ball techniques, using a rotary table
2. Triangulation and decimation
  - 3D triangulation (other than alpha-shapes)
  - decimation strategies - accuracy, preserving features
  - computational efficiency issues
3. Segmentation strategies
  - region growing for parametric patches
  - geometric region growing for regular and swept surfaces
  - region growing for blends and special feature elements
  - direct segmentation methods
  - segmentation methods based on evolute surfaces
4. Reconstructing free-form shapes
  - functional decomposition techniques
  - fitting with ignore areas
  - free-form feature reconstruction
  - reverse computer aided design
5. Reconstructing solid objects
  - direct segmentation
  - building consistent adjacency graphs
  - merging: a) point clouds b) partial B-rep models
  - building volumetric B-rep models
  - building stitched B-rep models
  - adding blending surfaces
  - beautifying reverse engineered models:
    1. topological consistency
    2. filling holes
    3. assuring symmetry, parallelism, orthogonality, concentricity etc.
Medial Axis Transform representations
- 2D Voronoi diagrams, offsetting, NC pocketing applications
- 3D MAT generation for polyhedral objects
Genetic algorithms
- genetic codes for geometric problems
- shape optimization with genetic algorithms
Other topics
1. representing and approximating curves on surfaces
2. photometric ray tracing
3. electronic books for teaching geometric modelling