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

Hugues HoppeHugues HoppeMicrosoft ResearchMicrosoft Research

IEEE Visualization 1998IEEE Visualization 1998

Terrain modelTerrain model

triangle meshtriangle mesh texture imagetexture image

Complex terrain modelComplex terrain model

Grand Canyon dataGrand Canyon data

4,097 x 2,049 vertices4,097 x 2,049 vertices

~16.7 million triangles~16.7 million triangles

Rendering bottlenecksRendering bottlenecks

Rasterization:Rasterization: depth complexitydepth complexity

(~1-2 is OK) (~1-2 is OK) typically not a problemtypically not a problem

Geometric processing (transform, …):Geometric processing (transform, …): mesh complexitymesh complexity

(should be ~20,000 triangles) (should be ~20,000 triangles) bottleneck! bottleneck! e.g. 20,000 << 17,000,000e.g. 20,000 << 17,000,000

Locally adapt mesh complexityLocally adapt mesh complexity

Given viewpoint, find coarse meshGiven viewpoint, find coarse meshthat satisfies a that satisfies a screen-spacescreen-space projected error projected error

e.g. maximum error is 3 pixelse.g. maximum error is 3 pixels

View-dependent LOD controlView-dependent LOD control

actual viewactual view overhead viewoverhead view

finerfiner

coarsercoarser

Related LOD workRelated LOD work

Regular subdivisionRegular subdivision– [Lindstrom-etal96][Lindstrom-etal96]– [Duchaineau-etal97][Duchaineau-etal97] … …

Delaunay triangulationsDelaunay triangulations– [CohenOr-Levanoni96][CohenOr-Levanoni96]– [Cignoni-etal97][Cignoni-etal97] … …

Arbitrary triangulationsArbitrary triangulations– [Xia-Varshney96][Xia-Varshney96]– VDPMVDPM [Hoppe97] [Hoppe97]– [De Floriani-etal97][De Floriani-etal97]

• satisfies error tolerancesatisfies error tolerance with coarser mesh with coarser mesh

• generalizes togeneralizes to arbitrary meshes in 3D arbitrary meshes in 3D

VideoVideo

Progressive meshesProgressive meshes

View-dependent refinement ofView-dependent refinement ofprogressive meshesprogressive meshes

[SIGGRAPH 97][SIGGRAPH 97]

[SIGGRAPH 96][SIGGRAPH 96]

View-dependent progressive meshView-dependent progressive mesh

[Xia-Varshney96][Xia-Varshney96]

vsplitvsplit

vv22

vsplvspl00MM00 vsplvspl11 vsplvspl22 vsplvspl33 vsplvspl44 vsplvspl55

vv11 vv33MM00

vv1010 vv1111

vsplvspl33

vv11 vv22

vv44 vv55

vsplvspl00

vv88 vv99

vsplvspl22

vv33

vv66 vv77

vsplvspl11

vv55

vv1212 vv1313

vsplvspl44

vv1010

vsplvspl55

vv1414 vv1515

vv66

PM:PM:

MMnn

MM00

[Hoppe97][Hoppe97]

[Hoppe96][Hoppe96]

Runtime algorithmRuntime algorithm

selectively selectively refined meshrefined mesh

vv55vv1010 vv1111 vv44 vv88 vv99

vv77vv1212 vv1313

vv11 vv22 vv33MM00

vv66

vv1414 vv1515

vv1212 vv1313vv1212

vv1010 vv1111vv1010 vv1111 vv44vv44

vv66

vv1414 vv1515

vv66

vv1414 vv1515

vv88 vv99

vv33

vv1515

vv77vv77

vv88vv88 vv99vv99

new meshnew mesh

dependencydependency

ContributionsContributions

Runtime geomorphsRuntime geomorphs

Compact data structuresCompact data structures

Specialize for terrains:Specialize for terrains: accurate error during simplificationaccurate error during simplification scalabilityscalability

Runtime geomorphsRuntime geomorphs

Flythrough: temporal continuityFlythrough: temporal continuity (avoid “popping”) (avoid “popping”)

When refining & coarsening,When refining & coarsening, interpolate geometry over several frames interpolate geometry over several frames

VideoVideo

geomorphsgeomorphsno geomorphs <> geomorphsno geomorphs <> geomorphs

Two casesTwo cases

Forward motion: geomorph refinement,Forward motion: geomorph refinement, easy easy

Backward motion: geomorph coarsening,Backward motion: geomorph coarsening, more difficult more difficult

Forward viewer motionForward viewer motion

model viewedfrom above viewer motion path

prev. view frustumnew view frustum

geomorphrefinement instantaneous

coarseninginstantaneous

refinement

Geomorph refinementGeomorph refinement

vv77vv66

vv55vv1010 vv1111 vv44 vv88 vv99

vv1212 vv1313

vv11 vv22 vv33MM00

vv1414 vv1515

vv77vv66

vv55

vv1515vv1414

vv77

Backward viewer motionBackward viewer motion

viewer motion path

prev. view frustumnew view frustum

geomorphcoarsening instantaneous

refinementinstantaneous

coarsening

Geomorph coarseningGeomorph coarsening

gradually interpolate vertex to parent’s positiongradually interpolate vertex to parent’s position when complete, modify mesh connectivitywhen complete, modify mesh connectivity

no nesting of coarsening stepsno nesting of coarsening steps performed one layer at a time performed one layer at a time

(see paper for details)(see paper for details)

Accurate approximation errorAccurate approximation error

Measuring error solely at grid pointsMeasuring error solely at grid points is insufficient: is insufficient:

edgecollapse

2-2

2

0

0

0 0

2-2

2

0

0

0elevation

data

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

(0)1!

2!

0

0

Computing exact errorComputing exact error

edgecollapse

grid line interior to an edgegrid point interior to a facecenter vertex (no error)

(pre-processing computation (pre-processing computation not time-critical) not time-critical)

ScalabilityScalability

Original mesh:Original mesh: 16.7 million triangles; easily larger. 16.7 million triangles; easily larger.

Hierarchical approach:Hierarchical approach: decompose into blocksdecompose into blocks yet, preserve spatial continuityyet, preserve spatial continuity

Hierarchical simplificationHierarchical simplification

partition pre-simplifysimplify blocks& save ecol’s

stitch intolarger blocks

simplifytop-level

ecolA

ecolB

ecolS

apply bottom-up recursion

preserve boundary verticespreserve boundary vertices

(off-line pre-processing)(off-line pre-processing)

Hierarchical block-based repr.Hierarchical block-based repr.

basemesh

pre-simplifiedterrain

vsplitS vsplitA vsplitB

block refinements

2.8%

0.1%

0.04%

0.03%

0.0%

maximumerror

blockrefinements

LOD

leve

l

LOD

leve

l

spatial localityspatial locality

VideoVideo

hierarchical constructionhierarchical constructiongrand canyongrand canyon

teapotteapotdragondragon

ResultsResults

Original: 16.7 million trianglesOriginal: 16.7 million triangles

12,000 triangles @ 30fps, avg. 1.7 pixel error12,000 triangles @ 30fps, avg. 1.7 pixel error 5,000 triangles @ 60fps, avg. 3.5 pixel error5,000 triangles @ 60fps, avg. 3.5 pixel error

(SGI Octane, 195MHz R10K, MXI)(SGI Octane, 195MHz R10K, MXI)

SummarySummary

VDPM: irregular meshesVDPM: irregular meshes accuracy accuracy reduce geometry bottleneck reduce geometry bottleneck

easy generalization to arbitrary surfaceseasy generalization to arbitrary surfaces

Temporal coherence: runtime geomorphsTemporal coherence: runtime geomorphs

Approximation error: surface-basedApproximation error: surface-based

Scalability: block-based hierarchyScalability: block-based hierarchy

Future workFuture work

Generalize to arbitrary meshes:Generalize to arbitrary meshes: Use simplification metric from Use simplification metric from

“Appearance-preserving simplification”“Appearance-preserving simplification” [Cohen-etal98][Cohen-etal98]

Region-based hierarchyRegion-based hierarchy

Non-static geometryNon-static geometry

Stochastic geometric detailStochastic geometric detail