Physically-Based Interactive Sand SimulationMarta Pla-Castells, Ignacio Garcı́a-Fernández and Rafael J. Martı́nez-Durá

Instituto de Robótica, Universidad de Valencia, Spain

Introduction

I Interactive terrain simulation is necessary insome Virtual Reality applications. It is acomplex modeling problem.

I In simulation for training realism is a must,because the trainee has to acquire skills basedon the behavior of the environment.

I For this reason, when the simulation involvesterrain manipulation the soil model must bephysically-based.

I Terrain is usually represented as a grid orheight field.

I In the Computer Graphics literature, modelshave been proposed mainly for terrainanimation purposes [1, 2].

Main Goal

I Our main goal is to provide a model of sand:I that is physically-based;I that considers collisions and horizontal

displacement of sand;I with reaction forces;I and that can be used in real-time, interactive

applications.

Physically-Based Sand Model

I We adapt a classical model from the physicsliterature [3] to be used over the discreterepresentation of terrain used in ComputerGraphics

I This model was previously presented in atheoretical work [4], and here we propose itsapplication to Computer Graphics.

I A local rule checks for steep regions, andcauses avalanches that reduce the slope, likein cellular automata formulation of sandpiles.

I The model is interactive: contact forces can becomputed and applied both to the sandpile andto the object in contact.

Horizontal Sand Displacement

Terramechanics

When a portion of soil is displaced, it is consideredas a solid that slides along a pre-defined interface,causing what is called a fracture [5].

Soil displacement

SoilTool

during fracture

⇓

Discrete Model

I The variables of the terramechanics model arecomputed using the the discrete model of sand.

I The fracture region and the horizontal force on thetool are computed.

I If the tool advancesthe material ispushed, slidingalong the fracture.

I Every cell’s heightabove the fractureincreasesaccordingly.

i0

i1

iN

iN+1

i0

i1

iN

iN+1

Fracture

Tool Soil

Tool

Fracture

Soil

Numerical Experiments

I We have implemented two tests, T1 and T2:I T1 corresponds to a cube with unit edges falling

on a flat ground,I T2 corresponds to the same cube pushing

material horizontally.

I The tests have been repeated for different griddensities, recording the time necessary to run10000 steps.

I To use an scenario easy to reproduce, the physicslibrary Open Dynamics Engine (ODE) has beenused.

I Collision detection has been done by means of raycasting.

EUROGRAPHICS’08 ConferenceCrete, GreeceApril 14 – 18

Results

Results for Test T1 (Only Vertical Forces Appear)

I All times are below 0.2ms.I Although the increase of the

cost is not linear, results arevery good even for densegrids.

I This results indicate that thesand model is suitable forreal-time applications.

Average time per step in T1

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

10 20 30 40 50 60

Number of divisions

Time (ms)

Results for Test T2 (Case with Lateral Displacements)

I All times are below 2ms.I Again, te results are good

even for dense grids.I In this case, scalability of the

model is not so good as in T1.

I The CPU cost of the collisiondetection and horizontalmaterial displacement hasbeen obtained (in %)

I The code corresponding tothese two tasks is notoptimized, and it takes60%–80% of the CPU⇒ Results are good. But evenbetter results are possible,with optimization

Average time per step in T2

0

0,5

1

1,5

2

2,5

10 20 30 40 50 60

Number of divisions

Time (ms)

Average CPU usageof the three main tasks

Collision Detection

33%

Sand Model25%

Material Displacement

42%

Conclusion

I The model is physically-based.I It considers sand pile evolution, interaction and horizontal

material displacement.I The situations where horizontal displacement happens are

more CPU demanding, but still the model can be run inreal-time in complex applications.

I Optimization strategies have to be investigated:I Parallelism,I Multi-scale analysis of the grid,I Hardware accelerated collision detection,I Implementation of the model on GPU.

References

[1] R. W. Sumner et al.Computer Graphic Forum, 18, 1999.

[2] K. Onoue and T. Nishita.Computer Graphics Forum, 24(1):51–60, 2005.

[3] J. P. Bouchaud et al.Journal de Physique I France, 4:1383–1410, 1994.

[4] M. Pla-Castells et al.In Proc. of Cellular Automata, pages 392–401, 2006.

[5] J. Shen and R. L. Kushwaha. Soil-Machine Interactions.Marcel Dekker, New York, 1998.

LSYM - Instituto de Robtica. Universidad de Valencia Mail: Marta.Pla@uv.es URL: http://robotica.uv.es/LSYMP.O. Box 2085 – 46071, Valencia, Spain