Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

RLE Sparse Level Sets

Ben Houston

Mark WiebeChristopher Batty

Fluids and Level Sets Session

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Level Sets

A level set represents a shape or form implicitly via a scalar function, Φ(x), defined over a region, Ω.

Inside: Ω- = { x | Φ(x) < 0, x elementOf Ω }

Interface: Γ = { x | Φ(x) = 0, x elementOf Ω }

Outside: Ω+ = { x | Φ(x) > 0, x elementOf Ω }

Useful for many things including:Shape Metamorphosis [Breen & Whitaker 2001]Surface Editing [Museth et al. 2002]Fluid Simulation

Fluid Surface [Foster/Fedkiw. 2001, Enright et al. 2002]

Occlusions [Houston et al. 2003]Rigid Bodies [Guendelman et al. 2003]

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Scaleable Level Sets (1)

“Sparse Field” Level Set [Whitaker 1998]

• Set of linked lists corresponding to isocontours around the interface allow fast access to narrow band interface.

• Interface is isolated within a dense field – thus in terms of space the field is not that scalable.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Scaleable Level Sets (2)

Sparse Block Level Sets [Bridson 2003, Whitaker 2003]• Have two grids, one at a lower

resolution that contains pointers to optionally allocated high resolution grids. Just allocate around level set interface.

• O(n2.25) storage, O(>1) sequential, O(1) random access.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Scaleable Level Sets (3)

• O(n2) storage, O(log n) random access, O(log n) sequential,.

• Random access is a slow (log n) because each level is a pointer dereference in most implementations. [Bridson 2003]

• If voxel values are no longer regularly spaced then many standard level set algorithms (i.e. WENO) need to be reformulated.

Octree Level Sets [Strain 1999, Frisken 2000]

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

The Basic IdeaCompress regions of level set volume using run-length encoding

(RLE). Thus achieve scalability without having to re-implement our existing level set algorithms.

Previous related work:

[Curless & Levoy 1996] Compressed scalar field volumes (not level sets) using RLE to scale upwards of 500 Mv.

[Bridson 2003] Theorized that RLE compressed level sets, based on [Curless & Levoy 1996] would be useful and scalable, even if random access was painfully slow.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Compress using 3 runs types based on their respective distance values.

Basic RLE Level Sets (1)

+ ∞ Outside of region: Φ > d.Only voxel sign is stored.

Defined Within narrow interface band: | Φ | ≤ d. Voxel values are stored explicitly.

- ∞ Inside of region: Φ < -d.Only voxel sign is stored.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Fast Random Access

Basic Fast Random Access• Associate each run with it’s voxel coordinate.

• Binary search for run containing voxel of interest is possible. O( log R )

Faster Fast Random Access• Create a lookup table for each line of RLE volume and restart

RLE encoding on each line.

• Using lookup reduces region of interest for binary search. O( log r )

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Ray Traced Scan Conversion

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Buddha Rotation

Scan Resolution 600x600x600 4 Minutes a Frame.Down-sampled to 300x300x300Buddha model was optimized prior to transformation – reduced to ~150,000 faces.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Simple Tar Monster

380,835 runs

1,132,146 defined scalar values

7.38 MB of storage

IsosurfaceDefined Voxels

55.9 million voxels

477 x 364 x 344 voxels

213.5 MB of storage

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Surface / Shape Editing• Implementing CSG Booleans and more complex editing

operations (similar to [Museth et al. 2002]) is pretty trivial & can be very efficient.

• See [Wiebe & Houston 2004] for more details.

Low Res. Fluid Simulation Results Results After Selective “Morph Targeting”

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Metamorphosis• Level set shape metamorphosis similar to [Breen & Whitaker 2001] is

also easy to implement.• Was used on two shots in Scooby-Doo 2 – see [Wiebe & Houston

2004] for details.

Final Shot using Morphed RLE Sparse Level as Facial “Morph Target”

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Fluid Simulation• We’ve converted our level set based fluid simulator to use RLE sparse

level sets. Details: Batty et al (2004) “RLE Sparse Fluid Simulation”.• RLE sparse level set fluid simulator is faster than our original fluid

simulator.• If one constructs the RLE sparse field structure appropriately there is

no need for a fixed bounding box.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

Results: Soft & Rigid Body Simulation• RLE sparse level sets appear to be useful in simulators that use a dual

tetrahedral-level set representation such as [Guendelman et al. 2003].

• In/out hit tests are quicker with RLE sparse level sets than with octrees and require less storage space.

• Also useful in soft body FEM simulations (i.e. [Irving et al. 2004] in regards to representing non-soft body actors.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

SummaryRLE Sparse Level Sets:

Highly scalable - 130 Mv ≈ 10 MB

Fast random access - a fast O( log r )

Optimal sequential interface traversal - O(1) / element

f(x) is approx. defined throughout bounding volume.

Compatible with most standard level set algorithms.

Fairly easy to work with.

Houston, Wiebe & Batty. (2004) RLE Sparse Level Sets.

http://software.franticfilms.com

AcknowledgementsFrantic Films

National Research Council of Canada

Prof. Fedkiw’s Stanford Group

NVIDIA Film Group

Microsoft