Transcript Steven F. Ashby Center for Applied Scientific Computing

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
Goal
● Perform an interactive ray tracing of
massive models
● Handles various kinds of polygonal meshes
(e.g., scanned data and CAD)
Double eagle tanker
St. Matthew
82M triangles
372M triangles
Forest model (32M)
2
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]
3
Hierarchical Acceleration Data
Structures
● kd-trees for interactive ray tracing [Wald
04]
● Simplicity and efficiency
● Used for efficient object culling
kd-node
Axis-aligned
bounding box
4
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
5
Performance of Ray Tracing with
Different Model Complexity
● Measured with 2GB main memory
Render time
(log scale)
Working set
size
Memory
thrashing!
2GB
Model complexity (M tri) - log scale
6
Low Growth Rate of
Data Access Time
Growth rate
during 1993 – 2004
50
45
40
35
30
25
20
15
10
5
0
47X
2X
20X
Disk
access
speed
RAM
access
speed
CPU
speed
Courtesy: http://www.hcibook.com/e3/online/moores-law/
7
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 different
area of memory
8
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
9
Performance of Ray Tracing with
Different Model Complexity
● Measured with 2GB main memory
Render time
(log scale)
Working set
size
Memory
thrashing!
2GB
Model complexity (M tri) - log scale
10
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
11
Real-time Captured Video – St.
Matthew Model
512 by 512 and 2x2 super-sampling,
4 pixels of LOD error in image space
12
Related Work
● Interactive ray tracing
● LOD and out-of-core techniques
● LOD-based ray tracing
13
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]
14
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
15
LOD-based Ray Tracing
● Ray differentials [Igehy 99]
● Subdivision meshes [Christensen et al. 03, Stoll
et al. 06]
● Point clouds [Wand and Straβer 03]
Image plane
Viewpoint
Footprint size
of ray
Ray beam for one pixel
16
Outline
● R-LODs for ray tracing
● Results
17
Outline
● R-LODs for ray tracing
● Results
18
R-LOD Representation
● Tightly integrated with kd-nodes
● A plane, material attributes, and surface
deviation
Rays
kd-node
Plane
No
intersection
Normal
Intersection
Valid extent
of the plane
19
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
20
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
21
Visual Artifacts
Surface deviation
● Visibility difference
● Illumination difference Projected area
Curvature
● Path difference for secondary rays
difference
View direction
Original mesh
Ray with original mesh
Ray with LODs
LODs
Image plane
22
R-LOD Error Metric
● Consider two factors
● Projected screen-space area of a kd-node
● Surface deviation
23
Conservative Projection Method
● Measures the screen-space area affected by
using an R-LOD
?
LOD metric: C (B) dmin > R
Image plane
dmin
Viewpoint
B{
R
kd-node
PoE error bound
One ray beam
24
R-LODs with Different PoE
Values
PoE: Original
1.85
5
(512x512, no anti-aliasing)
10
25
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]
26
C0 Discontinuity between R-LODs
Ray
● Possible solutions
● Posing dependencies [Lindstrom 03, Hwa et al.
04, Yoon et al. 04, Cignoni et al. 05]
● Implicit surfaces [Wald and Seidel 05]
27
Expansion of R-LODs
Ray
● 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)
28
Impact of Expansions of R-LODs
Hole
Before
expansion
After
expansion
Original model
PoE = 5
at 512 by 512
29
R-LOD Construction
● Principal component analysis (PCA)
● Compute the covariance matrix for the plane of
R-LODs
Normal (= Eigenvector)
● Hierarchical PCA computation
● Has linear time complexity
● Accesses the original data only one time with
virtually no memory overhead
30
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
31
Outline
● R-LODs for ray tracing
● Results
32
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]
33
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
34
Impact of R-LODs
10X speedup
# of intersected
nodes per ray
Render time
Working set
size
PoE = 0
(No LOD)
PoE = 2.5
35
Real-time Captured Video – St.
Matthew Model
512 x 512, 2 x 2 anti-aliasing, PoE = 4
36
Pros and Cons
● Limitations
● Does not handle advanced materials such as
BRDF
● No guarantee there is no holes
● Advantages
● Simplicity
● Interactivity
● Efficiency
37
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
38
Ongoing and Future Work
● Investigate an efficient use of implicit
surfaces
● Allow approximate visibility
● Extend to global illumination
39
Acknowledgements
● Model contributors
● Funding agencies
●
●
●
●
●
●
●
●
Army Research Office
DARPA
Lawrence Livermore National Laboratory
National Science Foundation
Office of Naval Research
RDECOM
Intel
Microsoft
40
Acknowledgements
● Eric Haines
● Martin Isenburg
● Dawoon Jung
● David Kasik
● Peter Lindstrom
● Matt Pharr
● Ingo Wald
● Anonymous reviewers
41
Questions?
Thanks!
42
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.
43
Additional slides
44
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
Isosurface (472M)
45
Memory Hierarchies
Speed
Size
1KB
100 ns
Register
1MB
Caches
101 ns
1GB
Main memory
102ns
> 1GB
Disk storage
104ns
46
Hierarchical R-LOD Computation
with Linear Time Complexity
n
 xy   ( xk   x )( yk   x ),
where
xk
,
yk
k 1
are x, y coordinates of kth points
n
n
2 n
2
 xy   xk yk   xk  yk  2
n k 1 k 1
n
k 1
n
n
x  y
k 1
k
k 1
k
+
47
Performance Comparison – St.
Matthew Model
2 ~ 20X
improvements
Non-LOD
Render time
(sec)
LOD
Approaching the model for every frame
48
Image Quality Comparison – St.
Matthew Model
512 x 512, no anti-aliasing
LOD (PoE = 4)
Non-LOD
49
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
50
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!
51
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
Image plane
Small
triangles
Viewpoint
Rays per each pixel
52
Ray Coherence Techniques
● Models with large primitives
● Group rays and test intersections between the
group and a bounding box
Image plane
Large
triangles
Viewpoint
Ray beams
53
Ray Coherence Techniques
● Highly tessellated models
● Fall back to the normal ray tracing
● Causes incoherent memory accesses and
temporal aliasing
Small
Image plane
triangles
Viewpoint
Ray beams
54
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?
If intersected,
return shading info
Otherwise,
stop traversal
: kd-node w/ R-LOD
: kd-node w/o R-LOD
55
Two Main Design Criteria for LOD
Metric
● Controllability of visual errors
● Efficiency
● Model complexity: 100M (at least 27 deep kdtree)
● Image resolution: 1k by 1K (= 1M rays)
● 27M (= 1M x 27) times of LOD metric
evaluation!
56
Surface Deviation
● Combined with the previous projectedspace error bound, R
New R
Plane of R-LOD
Underlying
geometry
57
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
Simplify
58
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
59
Image Quality Comparison –
Forest Model
PoE = 0 (No LOD)
PoE = 16
Shading
difference
60
R-LODs with Different PoE
Values
PoE: Original
40
512x512 image resolution
80
61