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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.

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smooth view dependent lod control and its application to terrain rendering

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

Hugues Hoppe

Microsoft Research

IEEE Visualization 1998

terrain model
Terrain model

triangle mesh

texture image

complex terrain model
Complex terrain model

Grand Canyon data

4,097 x 2,049 vertices

~16.7 million triangles

rendering bottlenecks
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 << 17,000,000
locally adapt mesh complexity
Locally adapt mesh complexity
  • Given viewpoint, find coarse meshthat satisfies a screen-space projected error

e.g. maximum error is 3 pixels

view dependent lod control

coarser

finer

View-dependent LOD control

actual view

overhead view

related lod work
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
video
Video

Progressive meshes

[SIGGRAPH 96]

View-dependent refinement ofprogressive meshes

[SIGGRAPH 97]

view dependent progressive mesh

vspl0

vspl1

vspl2

vspl3

vspl4

vspl5

M0

v1

v2

v3

v10

v10

v11

v4

v5

v5

v8

v9

Mn

v12

v13

v6

v6

v7

v14

v15

View-dependent progressive mesh

[Hoppe96]

[Xia-Varshney96]

[Hoppe97]

M0

vspl0

vspl1

vspl2

vspl3

vspl4

vspl5

PM:

M0

v1

v2

v3

vsplit

runtime algorithm

v3

v9

v10

v10

v11

v11

v4

v4

v8

v8

v8

v9

v9

dependency

v12

v13

v6

v6

v7

v7

selectively refined mesh

new mesh

v14

v14

v15

v15

v15

Runtime algorithm

M0

v1

v2

v3

v10

v11

v4

v5

v8

v9

v12

v12

v13

v6

v7

v14

v15

contributions
Contributions
  • Runtime geomorphs
  • Compact data structures
  • Specialize for terrains:
    • accurate error during simplification
    • scalability
runtime geomorphs
Runtime geomorphs
  • Flythrough: temporal continuity (avoid “popping”)
  • When refining & coarsening, interpolate geometry over several frames
video13
Video

geomorphs

no geomorphs <> geomorphs

two cases
Two cases
  • Forward motion: geomorph refinement, easy
  • Backward motion: geomorph coarsening, more difficult
forward viewer motion

geomorphrefinement

instantaneousrefinement

instantaneouscoarsening

new view frustum

Forward viewer motion

prev. view frustum

model viewedfrom above

viewer motion path

geomorph refinement

v5

M0

v1

v2

v3

v6

v7

v7

v10

v11

v4

v5

v8

v9

v14

v15

v12

v13

v6

v7

v14

v15

Geomorph refinement
backward viewer motion

geomorphcoarsening

instantaneouscoarsening

instantaneousrefinement

new view frustum

Backward viewer motion

prev. view frustum

viewer motion path

geomorph coarsening
Geomorph coarsening
  • gradually interpolate vertex to parent’s position
  • when complete, modify mesh connectivity
  • no nesting of coarsening steps performed one layer at a time

(see paper for details)

accurate approximation error

0

2!

(0)

-2

2

1!

0

0

0

0

0

2

Accurate approximation error
  • Measuring error solely at grid points is insufficient:

-2

2

0

0

edgecollapse

elevationdata

0

2

surface can pop! measure surface-to-surface error

computing exact error
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)

scalability
Scalability
  • Original mesh: 16.7 million triangles; easily larger.
  • Hierarchical approach:
    • decompose into blocks
    • yet, preserve spatial continuity
hierarchical simplification
Hierarchical simplification

(off-line pre-processing)

apply bottom-up recursion

ecolA

ecolS

ecolB

simplify blocks& save ecol’s

simplifytop-level

stitch intolarger blocks

partition

pre-simplify

preserve boundary vertices

hierarchical block based repr
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

video24
Video

hierarchical construction

grand canyon

teapot

dragon

results
Results

Original: 16.7 million triangles

12,000 triangles @ 30fps, avg. 1.7 pixel error

5,000 triangles @ 60fps, avg. 3.5 pixel error

(SGI Octane, 195MHz R10K, MXI)

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