1. Smooth view-dependent LOD control and its application to terrain rendering Hugues Hoppe Microsoft Research IEEE Visualization 1998

2. Terrain model triangle mesh texture image

3. Complex terrain model Grand Canyon data 4,097 x 2,049 vertices ~16.7 million triangles

4. Rendering bottlenecks l Rasterization: n  depth complexity (~1-2 is OK) n typically not a problem l Geometric processing (transform, …): n  mesh complexity (should be ~20,000 triangles) n bottleneck! e.g. 20,000 << 17,000,000

5. Locally adapt mesh complexity l Given viewpoint, find coarse mesh that satisfies a screen-space projected error e.g. maximum error is 3 pixels

6. View-dependent LOD control actual view overhead view finer coarser

7. Related LOD work n Regular subdivision –[Lindstrom-etal96] –[Duchaineau-etal97] … n Delaunay triangulations –[CohenOr-Levanoni96] –[Cignoni-etal97] … n Arbitrary triangulations –[Xia-Varshney96] –VDPM [Hoppe97] –[De Floriani-etal97] satisfies error tolerance with coarser meshsatisfies error tolerance with coarser mesh generalizes to arbitrary meshes in 3Dgeneralizes to arbitrary meshes in 3D

8. Video Progressive meshes View-dependent refinement of progressive meshes [SIGGRAPH 97] [SIGGRAPH 96]

9. View-dependent progressive mesh [Xia-Varshney96] vsplit v2v2v2v2 vspl 0 M0M0M0M0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 vspl 5 v 14 v 15 v6v6v6v6 PM: MnMnMnMn M0M0M0M0 [Hoppe97] [Hoppe96]

10. Runtime algorithm selectively refined mesh v5v5v5v5 v 10 v 11 v4v4v4v4 v8v8v8v8 v9v9v9v9 v7v7v7v7 v 12 v 13 v1v1v1v1 v2v2v2v2 v3v3v3v3 M0M0M0M0 v6v6v6v6 v 14 v 15 v 12 v 13 v 12 v 10 v 11 v 10 v 11 v4v4v4v4 v4v4v4v4 v6v6v6v6 v 14 v 15 v6v6v6v6 v 14 v 15 v8v8v8v8 v9v9v9v9 v3v3v3v3 v7v7v7v7 v7v7v7v7 v8v8v8v8 v8v8v8v8 v9v9v9v9 v9v9v9v9 new mesh dependency

11. Contributions l Runtime geomorphs l Compact data structures l Specialize for terrains: n accurate error during simplification n scalability

12. Runtime geomorphs l Flythrough: temporal continuity (avoid “popping”) l When refining & coarsening, interpolate geometry over several frames

13. Video geomorphs no geomorphs <> geomorphs

14. Two cases l Forward motion: geomorph refinement, easy l Backward motion: geomorph coarsening, more difficult

15. Forward viewer motion model viewed from above viewer motion path prev. view frustum new view frustum geomorph refinement instantaneous coarsening instantaneous refinement

16. Geomorph refinement v7v7v7v7 v6v6v6v6 v5v5v5v5 v 10 v 11 v4v4v4v4 v8v8v8v8 v9v9v9v9 v 12 v 13 v1v1v1v1 v2v2v2v2 v3v3v3v3 M0M0M0M0 v 14 v 15 v7v7v7v7 v6v6v6v6 v5v5v5v5 v 14 v7v7v7v7

17. Backward viewer motion viewer motion path prev. view frustum new view frustum geomorph coarsening instantaneous refinement instantaneous coarsening

18. Geomorph coarsening n gradually interpolate vertex to parent’s position n when complete, modify mesh connectivity n no nesting of coarsening steps  performed one layer at a time (see paper for details)

19. Accurate approximation error l Measuring error solely at grid points is insufficient: edge collapse 2-2 2 0 0 0 0 2 2 0 0 0 elevation data surface can pop!  measure surface-to-surface error (0) 1! 2! 0 0

20. Computing exact error edge collapse grid line interior to an edge grid point interior to a face center vertex (no error) (pre-processing computation not time-critical) (pre-processing computation  not time-critical)

21. Scalability l Original mesh: 16.7 million triangles; easily larger. l Hierarchical approach: n decompose into blocks n yet, preserve spatial continuity

22. Hierarchical simplification partitionpre-simplify simplify blocks & save ecol’s stitch into larger blocks simplify top-level ecol A ecol B ecol S apply bottom-up recursion preserve boundary vertices (off-line pre-processing)

23. Hierarchical block-based repr. base mesh pre-simplified terrain vsplit S vsplit A vsplit B block refinements 2.8% 0.1% 0.04% 0.03% 0.0% maximum error block refinements LOD level spatial locality

24. Video hierarchical construction grand canyon teapotdragon

25. Results Original: 16.7 million triangles 12,000 triangles @ 30fps, avg. 1.7 pixel error 5,000 triangles @ 60fps, avg. 3.5 pixel error 5,000 triangles @ 60fps, avg. 3.5 pixel error (SGI Octane, 195MHz R10K, MXI)

26. Summary l VDPM: irregular meshes n accuracy  reduce geometry bottleneck n easy generalization to arbitrary surfaces l Temporal coherence: runtime geomorphs l Approximation error: surface-based l Scalability: block-based hierarchy

27. Future work l Generalize to arbitrary meshes: n Use simplification metric from “Appearance-preserving simplification” [Cohen-etal98] n Region-based hierarchy l Non-static geometry l Stochastic geometric detail