Geometric Modeling and Computer Graphics Group

1. Geometric Modeling and Computer Graphics Group DISI University of Genova http://www.disi.unige.it/research/Geometric_modeling/

2. Group People • Faculty members • Leila De Floriani • Paola Magillo • Enrico Puppo • PhD students • Emanuele Danovaro • Franco Morando • Laura Papaleo • Raquel Viania Fernandez (MINGLE training network) • Post-doc • Mesmoudi Mohammed Mostefa (MINGLE training network)

3. Research Activity • Fields of activity • Geometric modeling • Computational geometry • Reference applications • visualization • geographic data processing • computer aided design • computer vision • virtual reality

4. Research Activity • Current activity Modeling and computational issues concerning representation and manipulation of spatial objects • multiresolution geometric modeling • for surfaces, two- and three-dimensional scalar fields • applications: GIS, virtual reality, volume data visualization • emphasis: geometric algorithms and data structures • shape reconstruction • multiresolution modeling of geographic maps

5. MINGLE: Multiresolution in Geometric Modeling • European Training Network • Partners: • SINTEF Applied Mathematics, Norway (coordinator) • Tel Aviv University (TAU), Israel • Munich University of Technology (TUM), Germany • Israel Institute of Technology (TECHNION), Israel • Max Planck Institute (MPII), Germany • Laboratoire de Modelisation et Calcul (UJF), France • University of Cambridge Computer Laboratory (UCAM-CLAB), UK • Department of Computer and Information Sciences, University of Genova (DISI), Italy • Systems in Motion AS (SIM), Norway

6. ARROV: Augmented Reality for Remotely Operated Vehicles • EEC Project • Partners: • OmniTech AS, Norway • General Robotics Limited (GRL), UK • Department of Science and Technology, University of Verona • Department of Computer and Information Sciences, University of Genova (DISI), Italy • Centro Elettrotecnico Sperimentale Italiano (CESI), Italy • Racal Survey Norge AS, Norway

7. ARROV: Augmented Reality for Remotely Operated Vehicles • Advanced technologies for multifunctional Remotely Operated Vehicles (ROV) for the inspection, monitoring and survey of underwater environments and man-made installations • a novel integrated sensorial system (optical and acoustical data) • augmented reality representation of the scene to help the ROV pilot • synthesis of a 3D model of the scene from sensorial data • unified man machine interface

8. Cultural Heritage: Advanced methods for acquisition and restitution • Italian national project • Partners: • Universities: Roma, Milano, Torino, Bologna • CNR Institutes: Roma, Torino • Industries: CM-Sistemi (Roma), EIDOCOM (Milano) • Develop a system for the interactive navigation and exploration of and archeological site and related data • multimedial data bases • advanced methods for acquisition and restitution • interface for the tourist and for the expert • case-of-study: the roman theatre of Aosta

9. SPADA: Representation and Processing of Spatial Data in Geographic Information Systems • Project funded by the Italian Ministry of University and Scientific and Technological Research (MURST) • Coordinated by DISI • Aim of the Project: • Efficient and intelligent access and manipulation of spatial data: • different levels of detail • constraint databases for geometrical data • integrate the spatial and descriptive components • indexing and query optimization • an extended query language for spatial databases • user interface • scalar fields and maps • vector and raster formats

10. SPADA: Representation and Processing of Spatial Data in Geographic Information Systems • Partners: • Department of Computer and Information Science, University of Genova • Department of Computer Science, University of Milano, • Department of Electric Engineering, University of L'Aquila • Scientific and Technological Department, University of Verona, • Department of Systems and Information, University of Firenze

11. Multiresolution Geometric Models: Motivations • Spatial object (surface, graph of a scalar field) modeled as a mesh of simplices (triangle mesh, tetrahedral mesh) • Applications: • virtual reality, CAD • GISs (terrains) • scientific data visualization • Availability of meshes of large size

12. High uniform resolution 12701 triangles • Variable resolution • based on distance • 3065 triangles

13. Variable resolution (high only on isosurface) 80,493 tetrahedra 16,272 isosurface faces High uniform resolution 163,831 tetrahedra 16,272 isosurface faces

14. Multiresolution Geometric Models: Motivations • Objective: • Dealing with models of reduced size whose accuracy in describing the spatial object satisfies some requirements • Examples: • Transmission of a geometric model: send a coarse representation first, then add details when needed progressive mesh transmission • Real-time rendering: on-line retrieval of a model whose size and accuracy best fit the requirements of an application task selective refinement

15. Progressive transmission 1740 triangles 100% error 2156 triangles 25% error 5459 triangles 6% error 69451 triangles 0% error

16. Application to Free-Form Surface Rendering 1.6% error 21663 triangles 6% error 5459 triangles 1.6% error inside box 5101 triangles (2741 in box)

17. Application to Terrain Rendering Error=24.5 1999 triangles Error=0.5 inside box 2001 triangles (1179 in box) Error=0.5 28995 triangles

18. Application to Volume Data Visualization Error=0 in box 35,605 tetrahedra 9,404 iso. faces Error=0 163,831 tetrahedra 16,272 iso. faces Error=0 on isosurface 80,493 tetrahedra 16,272 iso. faces

19. The Multi-Tesselation • A unified framework for multiresolution geometric modeling based on simplicial complexes • Efficient data structures and algorithms for representing and accessing MTs • general-purpose data structures • compressed data structures • algorithms for selective refinement • Applications • terrain modeling • free-form surfaces and solids • volume data modeling and visualization

20. A software library based on the MT • Supports the design of applications exploiting multiresolution on geometric objects • Fully parametric on: • the dimensions of the mesh and of the embedding space • attribute associated with mesh vertices and cells • criteria to extract meshes at variable resolution • Allows using any simplification code to build the MT • Ready-to-use MT constructors: • for terrains from either scattered points, DEM grids, or TINs • for free-form surfaces from generic triangle meshes • Demos: • A program to fly over a terrain, • A program to analyze an object by interactively using a magic lens • Written in C++

21. The TAn2 System • Efficient scientific visualization of large irregular volume data sets • Based on a Multi-Tetrahedralization (3D MT) • Construction through edge collapse (CUTE) • Compressed data structure • Selective refinement to support isosurfaces, cut planes, windowing, and direct volume rendering • Collaboration with CNUCE-CNR, Pisa

22. Hierarchy of Tetrahedra (HT) • Multiresolution modeling of regular volume data sets • Model based on a recursive tetrahedron bisection • Efficient data structure based on a location code • Selective refinement and surface extraction based on constant-time neighbor finding • Collaboration with the University of Maryland, USA

23. Multiresolution Geometric Modeling • Training Activity in MINGLE • Multiresolution modeling of terrains (SPADA) • Multiresolution modeling of surfaces for virtual reality applications (Cultural Heritage Project) • Multiresolution modeling of volume data for visualization • cooperation with Visual Computing Group, National Research Council, Pisa • cooperation with Department of Computer Science, University of Maryland, USA