Fast Hydraulic Erosion Simulation and Visualization on GPU

Fast Hydraulic Erosion Simulation and Visualization on GPU

Xing Mei1 Philippe Decaudin2 Bao-Gang Hu1

1. CASIA (China) 2. INRIA (France)

Pacific Graphics’07

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Outline

■ Introduction■ Hydraulic Erosion■ Existing Methods

■ Hydraulic Erosion on GPU■ Method Overview■ Simulation Steps■ Multi-pass Implementation on GPU

■ Results

■ Conclusion & Future Work

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Introduction- Hydraulic Erosion

■ ProcessWater flow takes away (dissolves) the soil

and relocates (deposits) it somewhere else

■ EffectChanges terrain appearance

Creates interesting geo-morphological structures

Gullies Eroded landscape on Maui Island

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■ Enhance realism

■ A useful complement to fluid simulation

Topographical changes affect the water flow

[Chiba’98]

Introduction- Erosion Simulation (Why?)

[Beneš’06]

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■ Procedural [Kelly’88, Prusinkiewicz’93] Ad hoc rules with fractal terrain generation Fast and efficient; No water flow involved

Limited control on the erosion results

■ Physically Based Simulation

[Musgrave’89, Chiba’98, Neidhold’05…] Simulation on already-existing terrains Controllable Erosion Process, but computationally expensive

4 fps on 256x256 grids [Neidhold’05]

5 fps on 300x300 grids [Beneš’07]

Limited for interactive applications

Introduction- Existing Methods

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■ A novel hydraulic erosion simulation method

Effectiveproduces the important features in the erosion process Gullies, water catchments, deposited sediment…

EfficientWell mapped to GPU

Interactive frame rates for large size terrains

Erosion on GPU- Motivation

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■ 5 steps in one cycle of the simulation

Terrain

water

Rainfall & River Source Water Movement

Erosion

Deposition

Sediment Transportation

DepositedSediment

Catchment

Evaporation

(1) Water Increment(2) Water Movement (flow simulation)

(3) Erosion or Deposition(4) Sediment Transportation

(5) Evaporation

Erosion on GPU- Method Overview

Water Height -

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■ Layers of 2D arrays

■ Each step should update the cell data in parallel

No scattering operations on the data array involved

cell

Erosion on GPU- Data Structure

Arrays

Terrain Height -

d

b

Suspended Sediment s Outflow flux

Velocity

),,,( BTRL fffff

),( yx VVV

cell

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■ Two kinds of sources

River sources – fixed location, radius, intensity

Raindrops – random location, radius, intensity

Erosion on GPU(1) Water Increment

tKd r Water increment

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■ Possible Models? GPU friendly

Grid-based methods > Lagrangian methods Efficient

Shallow water model > 3D Navier-Stokes Equation Suitable for Erosion-Deposition

Velocity field is necessary

■ Previous models on shallow water framework Simplified Newtonian physics model [Neidhold’05]

hard to parallelize Kass&Miller’s implicit method [Beneš’07]

many iterations over the grid, not efficient for large size terrain

■ Our choiceThe Virtual Pipe model [O’Brien’95]

Erosion on GPU(2) Water Movement (Flow Simulation)

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■ Virtual Pipe Model■ Water is exchanged between cells through virtual pipes

■ How much water exchanged through each pipe?

Flux – accelerated by the hydrostatic pressure difference

P0

P0

Cell

Erosion on GPU(2) Water Movement (Flow Simulation)

LF

BF

RF

TF

P1 P2

Two-Step Process1.Update Flux2.Update Water Height

A simple explicit method

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■ Two “problems” about the original model

Erosion on GPU(2) Water Movement (Flow Simulation)

Cell LF

BF

RF

TF 1. Staggered gridwater height (d) – cell centerflux (F) – cell border

2. Non-negative water updateA scaling back processscattering operations are involved

Both are not GPU-friendly

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■ Adaptation to the original model ■ the outflow flux for each cell

■ Flux (F) and outflow flux (f)

■ Water height update (d)

- send away the outflow flux

- collect inflow flux from neighbours

Outflow flux

Cell(x,y)

Inflow flux

Erosion on GPU(2) Water Movement (Flow Simulation)

Lf

Bf

Rf

Tf0,,,

),,,(

BTRL

BTRL

ffff

fffff

)( outin fftd

),1(),( yxfyxfF RLL

LF

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■ Non-negative water update

Erosion on GPU(2) Water Movement (Flow Simulation)

Outflow flux

Cell

Inflow flux

Lf

Bf

Rf

Tf

dftK out

)( outin fftd

0 outin ftftddd

omitted, strengthened condition inft

0 outftd

a scaling factor K limiting the outflow flux

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■ 3-step process Update outflow flux Update water height Update (horizontal) velocity field

From Flux (f) to Velocity (V)

■ No-Slip Boundaries

set outflow flux to 0 for boundary cells

■ Limitation for time step ]1,0[,),max(

y

V

x

Vt

yx

Erosion on GPU(2) Water Movement (Flow Simulation)

fdAtV xx Cell

X

Boundarycell

0Lf

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Sediment transport capacity

Current suspended sediment

How to compute for each cell ?

We adapt a classic model from soil science [Julien’85]

CS

S

CS CS ErosionDeposition

C

Erosion on GPU(3) Erosion & Deposition

)sin( VKC c

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■ Suspended sediment (S) is advected by the velocity field

■ Many GPU-friendly schemes to solve the equation Stable semi-Lagrangian method [Stam’99]

Upwind differencing scheme

More mass-conservative methods such as BFECC [Kim’05, Selle’07]

0

SVt

S

),(),( tvytuxSyxS ttt

Erosion on GPU(4) Sediment Transportation

(advection dominated, no diffusion considered)

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■ General computation framework on GPU [Harris’03, Owens’07]To update a 2D array in parallel:

■ Multi-pass process

Initialization

3

2

1

),(

),,,(

,,

TVVV

Tfffff

Tsdb

yx

BTRL

(1) Water Increment

(2) Flow Simulation

(3) Erosion-Deposition

(4) Sediment transport

(5) Evaporation

Outflow

Water Height

Velocity

Simulation

Visualization

VS: Vertex TexturePS: Phong Lighting

Erosion on GPU- Multi-pass Implementation on GPU

pack datainto textures

draw a screen-aligned quad

update texture in pixel shader

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Results

■ Platform: Pentium IV 2.4GHz + 2Gb RAM + Nvidia 8800 GTX

512x512 grids for video demos

water

suspended sediment in the flow

deposited sediment

“PG scene” in the rainVideo

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Results

■ Deposited sediment in a basin

The bottom of the basin is flattened by the deposited sediment

Video

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Results

■ River flow in a drained channel

Part of the original river bank get eroded

Video

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Results

■ Mountain scene eroded by rainfall

Video

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Results

■ Final example:

the combination of the rainfall and the river source

Video

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Results

■ Performance results for the final example at different grid size

403

186

59

16 40

50

100

150

200

250

300

350

400

450

256x256 512x512 1024x1024 2048x2048 4096x4096

Cycles per second

Cycles per second

Interactive frame rates for terrain up to 1024x1024!

1 cycle = 1 simulation + 1 visualization

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Results

■ ST, VT, CT at different grid size

2.48 5.3816.95

62.5

248.47

1.28 2.9710.31

40

155.89

1.29 2.38 6.6522.88

91.22

0

50

100

150

200

250

300

256x256 512x512 1024x1024 2048x2048 4096x4096

ST(ms)

VT(ms)

CT(ms)

ST : Simulation TimeVT : Visualization TimeCT : Cycle Time = ST + VT

1. ST, VT, CT scales well with grid size ~ linear with # of cells

2. VT takes more time for large size terrain

3. Further Improvements

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Conclusion & Future Work■ A novel simulation method for hydraulic erosion

■ Effective – proper model selection and adaptation for each step

Produces dynamic erosion process and realistic results■ Efficient - well designed for complete GPU implementation

Interactive frame rates for large size terrain

■ Future work■ Further improvements on models:

Fluid solver - Limitation for time step

Erosion Model - Little erosion on flat terrain■ Extension to non-height-field scene

(general 3D objects, structures with caves)■ More erosion process – thermal weathering, wind erosion…

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Thanks!

More info on

http://evasion.imag.fr/Publications/2007/MDH07/