1. MINGLE Mid-Term Meeting (June 26, 2002)1 DISI - University of Genova Leila De Floriani MINGLE Mid-Term Meeting St. Malo, June 26, 2002

2. MINGLE Mid-Term Meeting (June 26, 2002)2 Outline Research activityDISI team Research activity within MINGLE of the DISI team Research activitytask #8 multiresolution geometric modeling Research activity within task #8: data structures for multiresolution geometric modeling Connections with other MINGLE tasks Connections with other MINGLE tasks

3. MINGLE Mid-Term Meeting (June 26, 2002)3 DISI: Geometric Modeling and Computer Graphics Group DISI staff: DISI staff: –Leila De Floriani (scientist-in-charge) –Paola Magillo –Enrico Puppo –PhD students –PhD students (five) Young researchers in MINGLE: Young researchers in MINGLE: –Carlos Andujar (postdoc, Spain) –Debora Gil (predoc, Spain) –Mostefa Mesmoudi (postdoc, France) –Raquel Viania Fernandez (predoc, Spain)

4. MINGLE Mid-Term Meeting (June 26, 2002)4 Research activity in MINGLE Data structures for multiresolution geometric modeling () Data structures for multiresolution geometric modeling (Task #8) –data structures and algorithms multiresolution meshes –data structures and algorithms for representing and manipulating multiresolution meshes –applications: terrain modeling volume data modeling modeling non-manifold objects modeling geographic maps

5. MINGLE Mid-Term Meeting (June 26, 2002)5 Research activity in MINGLE Subtask 8.1: Subtask 8.1: Compact data structures for multiresolution (manifold) simplicial meshes (C.Andujar, D.Gil) Subtask 8.2: Subtask 8.2: Multiresolution representations for non- manifold meshes (M.Mesmoudi) Subtask 8.3: Subtask 8.3: Analysis of field topology for multiresolution modeling (M.Mesmoudi) Subtask 8.4: Subtask 8.4: Multiresolution representations for maps based on cell complexes (R.Viania Fernandez)

6. MINGLE Mid-Term Meeting (June 26, 2002)6 Subtask 8.1: Compact data structures for multiresolution simplicial meshes irregular triangle meshes vertex insertion/removal Multiresolution irregular triangle meshes built through vertex insertion/removal (Andujar and De Floriani, 2001; Danovaro et al., 2001; Gil and Magillo, 2001, De Floriani and Magillo, 2002) MINGLE tasks Connections with other MINGLE tasks: –Task #4: –Task #4: Coding of triangle meshes –Task #6: –Task #6: Hierarchical meshes

7. MINGLE Mid-Term Meeting (June 26, 2002)7 Subtask 8.1: Compact data structures for multiresolution simplicial meshes tetrahedral meshes: Multiresolution tetrahedral meshes: –irregular meshesedge collapsevertex insertion –irregular meshes built through edge collapse and vertex insertion (Cignoni et al., 2002: Danovaro et al., 2001; Danovaro et al. 2002) –regular nested meshes tetrahedron bisection –regular nested meshes generated through tetrahedron bisection (Lee et al., 2001; De Floriani and Lee, 2002) MINGLE tasks Connections with MINGLE tasks: –Task #2: –Task #2: Subdivision surfaces

8. MINGLE Mid-Term Meeting (June 26, 2002)8 A multiresolution model for triangulated surfaces Multiresolution data structure

9. MINGLE Mid-Term Meeting (June 26, 2002)9 A multiresolution model for 3D scalar fields Multiresolution data structure

10. MINGLE Mid-Term Meeting (June 26, 2002)10 Subtask 8.2: Multiresolution representations for non-manifold meshes Our aim: d- dimensional simplicial complexes Our aim: develop multiresolution data structures for d- dimensional simplicial complexes representing non- manifold, non-regular objects Our work: Our work: –A mathematical framework for describing d-dimensional simplicial complexes as assembly of simpler components, that we call quasi-manifolds (Mesmoudi et al., 2002) multiresolution model 2D simplicial complexes –A multiresolution model for non-manifold objects described by 2D simplicial complexes (De Floriani et al., 2002) MINGLE tasks Connection with other MINGLE tasks: –Task #4: –Task #4: Coding of triangle meshes

11. MINGLE Mid-Term Meeting (June 26, 2002)11 Non-Manifold Multi-Triangulation

12. MINGLE Mid-Term Meeting (June 26, 2002)12 Subtask 8.3: Analysis of field topology for multiresolution modeling Our aim: multiresolution models d-dimensional scalar fields topological structure Our aim: develop multiresolution models based on irregular meshes for d-dimensional scalar fields which take into account the topological structure of the field. Our work: Our work: –Discrete decompositiond-dimensional scalar field –Discrete decomposition of the domain of a d-dimensional scalar field extending Morse-Smale theory for differentiable functions ( De Floriani, Mesmoudi and Danovaro, ICPR 2002 ) critical pointscritical nets2D case –Extraction of critical points and critical nets in the 2D case (De Floriani, Mesmoudi and Danovaro, Eurographics 2002) subtask 8.1 Support to subtask 8.1

13. MINGLE Mid-Term Meeting (June 26, 2002)13 Discrete decomposition for a terrain

14. MINGLE Mid-Term Meeting (June 26, 2002)14 Subtask 8.4: Multiresolution representations for maps based on cell complexes Our aim: multiresolution models geographicmaps Our aim: develop multiresolution models based on cell complexes for geographic maps extending our previous work on simplicial complexes Our work: Our work: –Mathematical modeling of maps –Mathematical modeling of maps through abstract cell complexes (based on category theory) generalization operators –Minimal set of generalization operators for maps based on the above formalism ( Puppo and Viania Fernandez, 2001) –Multiresolution model –Multiresolution model and encoding data structure (on-going work) subtasks 8.3 8.1 Related to subtasks 8.3 and 8.1

15. MINGLE Mid-Term Meeting (June 26, 2002)15 Generalization operators for maps point abstraction region to point contraction line to point contraction line abstraction line merge region merge region to line contraction

16. MINGLE Mid-Term Meeting (June 26, 2002)16 Benefits from the Network Contributionyoung researchers Contribution to the research team of young researchers from other countries CollaborationsEuropean groups Collaborations with European groups working in multiresolution modeling Multidisciplinary character of the network: Multidisciplinary character of the network: exposure to research in geometric modeling from numerical analysis and approximation theory ParticipationMINGLE summer school Participation in the MINGLE summer school both for senior researchers and PhD students