Steven F' Ashby Center for Applied Scientific Computing Month DD, 1997

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R-LODs Fast LOD-based Ray Tracing of Massive
Models
Sung-Eui Yoon Lawrence Livermore National
Lab. Christian Lauterbach Dinesh Manocha Univ.
of North Carolina-Chapel Hill
2
Goal

• Perform an interactive ray tracing of massive
  models
• Handles various kinds of polygonal meshes
• (e.g., scanned data and CAD)

Double eagle tanker 82M triangles
St. Matthew 372M triangles
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Recent Advances for Interactive Ray Tracing

• Hardware improvements
• Exponential growth of computation power
• Multi-core architectures
• Algorithmic improvements
• Efficient ray coherence techniques Wald et al.
  01, Reshetov et al. 05

4
Hierarchical Acceleration Data Structures

• kd-trees for interactive ray tracing Wald 04
• Simplicity and efficiency
• Used for efficient object culling

Axis-aligned bounding box
kd-node
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Ray Tracing of Massive Models

• Logarithmic asymptotic behavior
• Very useful for dealing with massive models
• Due to the hierarchical data structures
• Observed only in in-core cases

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Performance of Ray Tracing with Different Model
Complexity

• Measured with 2GB main memory

Render time (log scale)
Memory thrashing!

Working set size
2GB
Model complexity (M tri) - log scale
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Low Growth Rate of Data Access Time
Growth rate during 1993 2004
47X
20X
2X
Courtesy http//www.hcibook.com/e3/online/moores
-law/
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Inefficient Memory Accesses and Temporal Aliasing

• St. Matthew (256M triangles)
• Around 100M visible triangles
• 1K by 1K image resolution
• 1M primary rays
• Hundreds of triangle per pixel
• Each triangle likely in differentarea of memory

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Main Contributions

• Propose an LOD (level-of-detail)-based ray
  tracing of massive models
• R-LOD, a novel LOD representation for Ray tracing
• Efficient LOD error metric for primary and
  secondary rays
• Integrate ray and cache coherent techniques

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Performance of Ray Tracing with Different Model
Complexity

• Measured with 2GB main memory

Render time (log scale)
Memory thrashing!

Working set size
2GB
Model complexity (M tri) - log scale
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Performance of LOD-based Ray Tracing
Achieved up to three order of magnitude speedup!

• Measured with 2GB main memory

Render time (log scale)
Working set size
Model complexity (M tri) - log scale
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Real-time Captured Video St. Matthew Model
512 by 512 and 2x2 super-sampling, 4 pixels of
LOD error in image space
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Related Work

• Interactive ray tracing
• LOD and out-of-core techniques
• LOD-based ray tracing

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Interactive Ray Tracing

• Ray coherences
• Heckbert and Hanrahan 84, Wald et al. 01,
  Reshetov et al. 05
• Parallel computing
• Parker et al. 99, DeMarle et al. 04, Dietrich et
  al. 05
• Hardware acceleration
• Purcell et al. 02, Schmittler et al. 04, Woop et
  al. 05
• Large dataset
• Pharr et al. 97, Wald et al. 04

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LOD and Out-of-Core Techniques

• Widely researched
• LOD book Luebke et al. 02
• Out-core algorithm course Chiang et al. 03
• LOD algorithms combined with out-of-core
  techniques
• Points clouds Rusinkiewicz and Levoy 00
• Regular meshes Hwa et al. 04, Losasso and Hoppe
  04
• General meshes Lindstrom 03, Cignoni et al. 04,
  Yoon et al. 04, Gobbetti and Marton 05

Not clear whether LOD techniques for
rasterization is applicable to ray tracing
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LOD-based Ray Tracing

• Ray differentials Igehy 99
• Subdivision meshes Christensen et al. 03, Stoll
  et al. 06
• Point clouds Wand and Straßer 03

Image plane
Footprint size of ray
Viewpoint
Ray beam for one pixel
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Outline

• R-LODs for ray tracing
• Results

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Outline

• R-LODs for ray tracing
• Results

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R-LOD Representation

• Tightly integrated with kd-nodes
• A plane, material attributes, and surface
  deviation

kd-node
Plane
Valid extent of the plane
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Properties of R-LODs

• Compact and efficient LOD representation
• Add only 4 bytes to (8 bytes) kd-node
• Drastic simplification
• Useful for performance improvement
• Error-controllable LOD rendering
• Error is measured in a screen-space in terms of
  pixels-of-error (PoE)
• Provides interactive rendering framework

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Two Main Design Criteria for LOD Metric

• Controllability of visual errors
• Efficiency
• Performed per ray (not per object)
• More than tens of million times evaluation

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Visual Artifacts
Surface deviation

• Visibility difference
• Illumination difference
• Path difference for secondary rays

Projected area
Curvature difference
View direction
Original mesh
LODs
Image plane
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R-LOD Error Metric

• Consider two factors
• Projected screen-space area of a kd-node
• Surface deviation

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Conservative Projection Method

• Measures the screen-space area affected by using
  an R-LOD

Image plane
R
Viewpoint
kd-node
B
PoE error bound
One ray beam
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R-LODs with Different PoE Values
PoE Original 1.85
5 10
(512x512, no anti-aliasing)
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LOD Metric for Secondary Rays

• Applicable to any linear transformation
• Shadow
• Planar reflection
• Not applicable to non-linear transformation
• Refraction
• Uses more general, but expensive ray
  differentials Igehy 99

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C0 Discontinuity between R-LODs

• Possible solutions
• Posing dependencies Lindstrom 03, Hwa et al. 04,
  Yoon et al. 04, Cignoni et al. 05
• Implicit surfaces Wald and Seidel 05

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Expansion of R-LODs

• Expansion of the extent of the plane
• Inspired by hole-free point clouds rendering
  Kalaiah and Varshney 03
• A function of the surface deviation (20 of the
  surface deviation)

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Impact of Expansions of R-LODs
Hole
Before expansion
After expansion
PoE 5 at 512 by 512
Original model
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R-LOD Construction

• Principal component analysis (PCA)
• Compute the covariance matrix for the plane of
  R-LODs
• Hierarchical PCA computation
• Has linear time complexity
• Accesses the original data only one time with
  virtually no memory overhead

Normal
( Eigenvector)
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Utilizing Coherence

• Ray coherence
• Using LOD improve the utilization of SIMD
  traversal/intersection
• Cache coherence
• Use cache-oblivious layouts of bounding volume
  hierarchies Yoon and Manocha 06
• 10 60 performance improvement

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Outline

• R-LODs for ray tracing
• Results

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Implementation

• Uses common optimized kd-tree construction
  methods
• Based on surface-area heuristic MacDonald and
  Booth 90, Havran 00
• Out-of-core computation
• Decompose an input model into a set of clusters
  Yoon et al. 04

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Preprocessing

• Simplification computation speed
• Very fast due to its linear complexity
• (3M triangles per min)
• Memory overhead
• Requires 33 more storage over the optimized
  kd-tree representation Wald 04
• Runtime overhead
• 5 compared to non-LOD version of the same
  efficient ray tracer

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Impact of R-LODs
10X speedup
of intersected nodes per ray
Render time
Working set size
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Real-time Captured Video St. Matthew Model
512 x 512, 2 x 2 anti-aliasing, PoE 4
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Pros and Cons

• Limitations
• Does not handle advanced materials such as BRDF
• No guarantee there is no holes
• Advantages
• Simplicity
• Interactivity
• Efficiency

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Conclusion

• LOD-based ray tracing method
• R-LOD representation
• Efficient LOD error metric
• Hierarchical LOD construction method with a
  linear time complexity
• Reduce the working set size

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Ongoing and Future Work

• Investigate an efficient use of implicit surfaces
• Allow approximate visibility
• Extend to global illumination

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Acknowledgements

• Model contributors
• Funding agencies
• Army Research Office
• DARPA
• Lawrence Livermore National Laboratory
• National Science Foundation
• Office of Naval Research
• RDECOM
• Intel
• Microsoft

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Acknowledgements

• Eric Haines
• Martin Isenburg
• Dawoon Jung
• David Kasik
• Peter Lindstrom
• Matt Pharr
• Ingo Wald
• Anonymous reviewers

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Questions?

• Thanks!

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UCRL-PRES-223086
This work was performed under the auspices of the
U.S. Department of Energy by University of
California Lawrence Livermore National Laboratory
under contract No. W-7405-ENG-48.
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Additional slides
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Goal

• Perform an interactive ray tracing of massive
  models
• Handles various kinds of polygonal meshes
• (e.g., scanned data and CAD)

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Memory Hierarchies
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Hierarchical R-LOD Computation with Linear Time
Complexity
where , are x, y coordinates of kth
points
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Performance Comparison St. Matthew Model
2 20X improvements

Non-LOD
Render time (sec)
LOD
Approaching the model for every frame
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Image Quality Comparison St. Matthew Model
512 x 512, no anti-aliasing
LOD (PoE 4) Non-LOD
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Further Information

• R-LODs Fast LOD-based Ray Tracing of Massive
  Models
• S. Yoon, C. Lauterbach, and D. Manocha
• (To appear at) Pacific graphics (The Visual
  Computer) 2006

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Recent Advances for Interactive Ray Tracing

• Hardware improvements
• Exponential growth of computation power
• Multi-core architectures
• Algorithmic improvements
• Efficient ray coherence techniques Wald et al.
  01, Reshetov et al. 05

These improvements may not provide an efficient
solution to our problem!
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Ray Coherence Techniques

• Assume coherences between spatially coherent rays
• Works well with CAD or architectural models
• Highly-tessellated models
• There may not be much coherence between rays

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Ray Coherence Techniques

• Models with large primitives
• Group rays and test intersections between the
  group and a bounding box

Large triangles
Image plane
Viewpoint
Ray beams
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Ray Coherence Techniques

• Highly tessellated models
• Fall back to the normal ray tracing
• Causes incoherent memory accesses and temporal
  aliasing

Small triangles
Image plane
Viewpoint
Ray beams
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Runtime Traversal with R-LODs

• Built on top of the efficient kd-tree traversal
  algorithm Wald 04

Check whether the error is met?
Check whether there is an intersection?
kd-node w/ R-LOD
kd-node w/o R-LOD
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Two Main Design Criteria for LOD Metric

• Controllability of visual errors
• Efficiency
• Model complexity 100M (at least 27 deep kd-tree)
• Image resolution 1k by 1K ( 1M rays)
• 27M ( 1M x 27) times of LOD metric evaluation!

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Surface Deviation

• Combined with the previous projected-space error
  bound, R

Plane of R-LOD
Underlying geometry
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Properties of R-LODs

• Compact and efficient LOD representation
• Add only 4 bytes to (8 bytes) kd-node
• Drastic simplification
• Useful for performance improvement
• Recursively simplify 23 triangles into one R-LOD

kd-node w/ R-LOD
kd-node w/o R-LOD
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Image Quality Comparison Forest Model (32M
Triangles)
4 X speedup
PoE 0 (No LOD)
PoE 4 and cache-oblivious layout of kd-tree
Shading difference
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Image Quality Comparison Forest Model
PoE 0 (No LOD)
PoE 16
Shading difference
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R-LODs with Different PoE Values
PoE Original 40
80
512x512 image resolution