Gigantic Deformable SurfacesHierarhical RLE Level Sets

Ben Houston, Neuralsoft, Frantic FilmsMichael B. Nielsen, University of AarhusChristopher Batty, Frantic FilmsOla Nilsson, Linköping Institute of TechnologyKen Museth, Linköping Institute of Technology

Part 1 - Data StructurePart 1 - Data Structure

Michael Bang Nielsen

An Implicit Representation for Deformable Surfaces:Level SetsAn Implicit Representation for Deformable Surfaces:Level Sets

}0),,(|),,{( zyxfzyxSSurface deformation governed by PDE.

Problem StatementProblem Statement

• What?

– 1) Memory efficient 2) Computationally efficient 3) ”Out-Of-The-Box” 4) Versatile 5) Compatible representation of high resolution deforming surfaces.

• Why?

– Deforming surfaces have wide applicability in computer graphics and simulation: Fluids, Geometric Modelling, Morphing...

• How?

– The Hierarchical-RLE (H-RLE) datastructure: Combine best features of the RLE Sparse Level Set [Houston,Batty,Wiebe 2004] and the DT-Grid [Nielsen and Museth 2004].

1D Run Length Encoding1D Run Length Encoding

Run Length Encoding (RLE) partitions a sequence of data into runs, each associated with a specific runcode.

2D Hierarchical RLE2D Hierarchical RLE

YRLE Block

RLE Segment

XRLE Block

Toolbox of AlgorithmsToolbox of Algorithms

The algorithms are recursive in the dimension of the H-RLE.

• Construction time is optimal: O(D).

• Rebuilding the narrow band: O(D).

• Sequential and stencil access times are optimal: O(1) per grid point.

• Axis aligned CSG operations are optimal: O(D1+D2).

• Random and neighbor access times are logarithmic in the number of runs in at most k RLE segments, where k is the dimension.

Features of H-RLEFeatures of H-RLE

• Data structure and algorithms are fast in practice: Accomodate the cache hierarchies of modern computers.

• Asymptotically optimal memory footprint, O(D), and near-optimal memory footprint in practice.

• Level set simulations can go ”out-of-the-box”

• Generalizes to N dimensions.

Part 2 - ApplicationsPart 2 - Applications

Ben Houston

Unified Implicit Object RepresentationUnified Implicit Object Representation

• The “Augmented Level Set”– Combined level set with any number of auxiliary subordinate

fields.

• UVW texture coords, alpha channels, interface velocities…

– Abstraction layer for operations that modify both the level set and subordination fields:

• mesh to level set, boolean operations, fluid advection, level set rendering, etc

– H-RLE level set is suited since H-RLE grid can be shared between multiple fields.

Efficient ClippingEfficient Clipping

• Since we classify non-narrow band space we can use store “unclosed level sets.”

Fast Scan ConversionFast Scan Conversion

Fast Scan Conversion of Large Meshes– Input mesh must be closed and non-self

intersecting.

– MAUCH, S. 2000. A fast algorithm for computing the closest point and distance transform.

Happy Buddha

600x1445x600 = 520 million voxels6 voxel narrow band59 sec on 1.5GHz Pentium Mobile.

Robust Scan ConversionRobust Scan Conversion

Scan Conversion of Open & Intersecting Meshes

– We thus take a visibility-testing approach via the use of ray tracing.

– Conceptually, for each point we cast a number of rays to sample the world around and if the majority of the rays hit back faces, that location is interior, otherwise it is exterior.

Robust Scan ConversionRobust Scan Conversion

– This robust method can be applied to H-RLE level set scan conversion such that less than O (n^3) space or time is required.

– Robustness has been production tested.

Direct Ray TracingDirect Ray Tracing

• Computational equivalent to ray tracing large non-compressed narrow band level sets because of the cache coherent nature of the H-RLE level set.

Surface DeformationSurface Deformation

Fluid SimulationFluid Simulation

• It is easy to encoding whole fluid volumes, as opposed to just the interface, using the H-RLE grid structure.

Fluid Augmented Level Set

– Interface Level Set, Volume Staggered Velocities.

Occlusions Augmented Level Set:

– Interface Level Set, Centered SurfaceVelocities, Surface Slip Conditions

Computation and storage scales in terms fluid volume.

Fluid SimulationFluid Simulation

• We encountered the mass conversation pressure projection as the main storage bottleneck.

• Our solution was to apply RLE compression to both the matrix and vector representations. – Compress the 4 unique diagonals using 4 RLE streams.

– Requires at most O( v ) storage and computation for matrix and vector representations.

– Matrix and vector operations used in the conjugate gradient algorithm all require near sequential access thus computation scales in terms of storage.

• Level Set Propagation Comparison

• Curvature-based flow (i.e. Heat equation)

Performance EvaluationPerformance Evaluation

• Model Storage Comparison

Thank You!Thank You!

More information online:

http://www.exocortex.org/hrle2005/

“Hierarchical RLE Level Sets” (in review)

Conditionally Accepted to ACM TOG.

Provides all details of the data structure and uses described today.

“The Visual Simulation of Wispy Smoke”,

Today @ 1:30 in room West Hall B.