Smooth view-dependent LOD control and its application to terrain rendering

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Smooth view-dependent LOD control and its
application to terrain rendering

• Hugues Hoppe
• Microsoft Research
• IEEE Visualization 1998

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Terrain model
triangle mesh
texture image
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Complex terrain model
Grand Canyon data 4,097 x 2,049 vertices 16.7
million triangles
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Rendering bottlenecks

• Rasterization
• ? depth complexity (1-2 is OK)
• typically not a problem
• Geometric processing (transform, )
• ? mesh complexity (should be 20,000 triangles)
• bottleneck! e.g. 20,000 ltlt 17,000,000

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Locally adapt mesh complexity

• Given viewpoint, find coarse meshthat satisfies
  a screen-space projected error

e.g. maximum error is 3 pixels
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View-dependent LOD control
actual view
overhead view
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Related LOD work

• Regular subdivision
• Lindstrom-etal96
• Duchaineau-etal97
• Delaunay triangulations
• CohenOr-Levanoni96
• Cignoni-etal97
• Arbitrary triangulations
• Xia-Varshney96
• VDPM Hoppe97
• De Floriani-etal97

• satisfies error tolerance with coarser mesh
• generalizes to arbitrary meshes in 3D

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Video
Progressive meshes
SIGGRAPH 96
View-dependent refinement ofprogressive meshes
SIGGRAPH 97
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View-dependent progressive mesh
Hoppe96
Xia-Varshney96
Hoppe97
vspl0
M0
vspl1
vspl2
vspl3
vspl4
vspl5
PM
M0
v2
v1
v3
vsplit
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Runtime algorithm
v1
v2
v3
M0
v5
v10
v11
v4
v8
v9
v7
v12
v13
v6
v12
v14
v15
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Contributions

• Runtime geomorphs
• Compact data structures
• Specialize for terrains
• accurate error during simplification
• scalability

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Runtime geomorphs

• Flythrough temporal continuity (avoid
  popping)
• When refining coarsening, interpolate
  geometry over several frames

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Video
geomorphs no geomorphs ltgt geomorphs
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Two cases

• Forward motion geomorph refinement, easy
• Backward motion geomorph coarsening, more
  difficult

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Forward viewer motion
prev. view frustum
model viewedfrom above
viewer motion path
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Geomorph refinement
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Backward viewer motion
prev. view frustum
viewer motion path
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Geomorph coarsening

• gradually interpolate vertex to parents position
• when complete, modify mesh connectivity

• no nesting of coarsening steps ? performed one
  layer at a time

(see paper for details)
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Accurate approximation error

• Measuring error solely at grid points is
  insufficient

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-2
0
0
edgecollapse
elevationdata
2
0
surface can pop!? measure surface-to-surface
error
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Computing exact error
edgecollapse
center vertex (no error)
grid point interior to a face
grid line interior to an edge
(pre-processing computation ? not time-critical)
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Scalability

• Original mesh 16.7 million triangles easily
  larger.
• Hierarchical approach
• decompose into blocks
• yet, preserve spatial continuity

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Hierarchical simplification
(off-line pre-processing)
apply bottom-up recursion
ecolA
ecolS
ecolB
simplify blocks save ecols
stitch intolarger blocks
simplifytop-level
partition
pre-simplify
preserve boundary vertices
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Hierarchical block-based repr.
basemesh
pre-simplifiedterrain
block refinements
vsplitS
vsplitA
vsplitB
2.8
blockrefinements
0.1
maximumerror
LOD level
0.04
0.03
0.0
spatial locality
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Video
hierarchical construction grand
canyon teapot dragon
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Results
Original 16.7 million triangles 12,000 triangles
_at_ 30fps, avg. 1.7 pixel error 5,000 triangles
_at_ 60fps, avg. 3.5 pixel error (SGI Octane,
195MHz R10K, MXI)
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Summary

• VDPM irregular meshes
• accuracy ? reduce geometry bottleneck
• easy generalization to arbitrary surfaces
• Temporal coherence runtime geomorphs
• Approximation error surface-based
• Scalability block-based hierarchy

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Future work

• Generalize to arbitrary meshes
• Use simplification metric from Appearance-preserv
  ing simplification Cohen-etal98
• Region-based hierarchy
• Non-static geometry
• Stochastic geometric detail