Efficient Storage, Compression and Transmission of Complex 3D Models context & problem definition general framework & classification our new algorithm applications for digital documents
Mesh Decimation highly detailed meshes laser scanners iso surfaces from CT automatic meshing of CAD models transmit, render, store data reduction without quality reduction efficiency graphics hardware global system performance
/ 286578 / 30392 / 3774 Leif Kobbelt Erlangen Nu rnberg 1087716 Mesh Decimation
State of the Art Vertex Removal (remove + triangulate) Re Tiling (redistribute new vertices on the old mesh) Vertex Clustering (quantize space: R 3 > N 3 ) Wavelet Representations (special connectivity)
General Framework for Incremental Mesh Decimation topological operation(s) (complexity, flexibility) distance / error measure (conservative, economical) quality criterion performance
Schroeder s Mesh Decimation vertex removal error accumulation ordering (?) 500 5000 tri / sec
Hoppe s Progressive Meshes edge collapse Hausdorff distance ordering by distance + fairness 10 30 tri / sec
Invertible Topological Operation v l t a v a e v b t b Vertex Split v l v c v r Edge Collapse v r Progressive Meshes Multi Resolution (continuous resolution, discrete resolution)
Garland / Heckbert s Mesh Simplification vertex contraction error quadrics ordering by distance 4500 tri / sec
The general framework topological operators vertex removal (free triangulation) edge collapse (free position) half edge collapse distance measures local accumulation (over estimate) error quadrics (over/under estimate) one/two sided Hausdorff distance (complex) quality criterion implicit (error tolerance) explicit (curvature energy)
A Knapsack Approach half edge collapse cost (binary operation) global error control capacity (one sided (!) Hausdorff distance) > candidate set fairness criteria guidance > priority queue > greedy algorithm
Why??? separate topology from geometry exact error tolerances (cf. scattered data interpolation) intuivite handling global error tolerance application dependent fairness smoothness for display roundness for finite elements distance for detail preservation...
Discrete Fairness discrete fundamental forms > discrete energy functionals optimal smoothness > minimum bending optimal stability > minimum aspect ratio equal edge length > minimum distorsion maximum detail (with fixed number of triangles) > minimum approx. error color attributes topological distance (independent set)
Computing the Hausdorff Distance maximum minimum distance (original points to current mesh) assign removed vertices to coarse triangles redistribute vertices by local sweep
Applications efficient storage progressive transmission (quick previews) finite elemente analysis (mesh generation, local refinement)
871K 6.5K 3.5K
continuous transmission of images: continuous transmission of 3d objects:
progressive transmission of images: interactive progressive transmission of 3d objects:
load adaptive / view dependent display: 316.498 49.279
Reverse Finite Element Mesh Generation...
operation planing system / numerical algorithms: 188.260 43.273
... trade geometry for texture attributes...
3D Models in Interactive Applications and Digital Documents games electronic catalogs architectural walk throughs digital mock up the virtual museum electronic clinical records geometric design log books
G A M E S! image: courtesy Eidos
Electronic catalogue / commerce image: courtesy PC Chips Electronic museum Architectural walk throughs 3d object: courtesy Cytberware
Electronic clinical record with 3d objects
Car body design log book
Conclusion general purpose mesh decimation intuitive parameters (tolerance + fairness) exact global error control (Hausdorff) fast (> 1 K tri / sec) level of detail for arbitrary meshes efficient algorithms mesh hierarchy > interactive multi resolution modeling