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

Terrain model triangle mesh texture image

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

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

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

View-dependent LOD control actual view overhead view finer coarser

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

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

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]

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

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

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

Video geomorphs no geomorphs <> geomorphs

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

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

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

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

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)

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

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)

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

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)

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

Video hierarchical construction grand canyon teapotdragon

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

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

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