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) St. Matthew 372M triangles Double eagle tanker 82M triangles Forest model (32M)

3 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 kd-node Axis-aligned bounding box

5 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

6 Performance of Ray Tracing with Different Model Complexity ● Measured with 2GB main memory Memory thrashing! Render time (log scale) Model complexity (M tri) - log scale Working set size 2GB

7 Low Growth Rate of Data Access Time Growth rate during 1993 – 2004 Courtesy: 47X 20X 2X

8 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

9 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

10 Performance of Ray Tracing with Different Model Complexity ● Measured with 2GB main memory Memory thrashing! Render time (log scale) Model complexity (M tri) - log scale Working set size 2GB

11 Performance of LOD-based Ray Tracing ● Measured with 2GB main memory Model complexity (M tri) - log scale Achieved up to three order of magnitude speedup! Render time (log scale) Working set size

12 Real-time Captured Video – St. Matthew Model 512 by 512 and 2x2 super-sampling, 4 pixels of LOD error in image space

13 Related Work ● Interactive ray tracing ● LOD and out-of-core techniques ● LOD-based ray tracing

14 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]

15 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

16 LOD-based Ray Tracing ● Ray differentials [Igehy 99] ● Subdivision meshes [Christensen et al. 03, Stoll et al. 06] ● Point clouds [Wand and Straβer 03] Viewpoint Image plane Ray beam for one pixel Footprint size of ray

17 Outline ● R-LODs for ray tracing ● Results

18 Outline ● R-LODs for ray tracing ● Results

19 R-LOD Representation ● Tightly integrated with kd-nodes ● A plane, material attributes, and surface deviation Plane Normal kd-node Valid extent of the plane Intersection No intersection Rays

20 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

21 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

22 Visual Artifacts ● Visibility difference ● Illumination difference ● Path difference for secondary rays Surface deviation Projected area Curvature difference View direction Image plane Ray with original mesh Ray with LODs Original mesh LODs

23 R-LOD Error Metric ● Consider two factors ● Projected screen-space area of a kd-node ● Surface deviation

24 Conservative Projection Method ● Measures the screen-space area affected by using an R-LOD Viewpoint Image plane PoE error bound B { R d min C (B) d min > R ? LOD metric: One ray beam kd-node

25 R-LODs with Different PoE Values PoE: Original (512x512, no anti-aliasing)

26 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]

27 C 0 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] Ray

28 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) Ray

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

30 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)

31 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

32 Outline ● R-LODs for ray tracing ● Results

33 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]

34 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

35 Impact of R-LODs PoE = 0 (No LOD) PoE = 2.5 # of intersected nodes per ray Render time Working set size 10X speedup

36 Real-time Captured Video – St. Matthew Model 512 x 512, 2 x 2 anti-aliasing, PoE = 4

37 Pros and Cons ● Limitations ● Does not handle advanced materials such as BRDF ● No guarantee there is no holes ● Advantages ● Simplicity ● Interactivity ● Efficiency

38 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

39 Ongoing and Future Work ● Investigate an efficient use of implicit surfaces ● Allow approximate visibility ● Extend to global illumination

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

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

42 Questions? Thanks!

43 UCRL-PRES 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.

44 Additional slides

45 Goal ● Perform an interactive ray tracing of massive models ● Handles various kinds of polygonal meshes (e.g., scanned data and CAD) St. Matthew 372M triangles Double eagle tanker 82M triangles Isosurface (472M)

46 Memory Hierarchies Register Caches Main memory Disk storage Size 1KB 1MB 1GB > 1GB Speed 10 0 ns 10 1 ns 10 2 ns 10 4 ns

47 Hierarchical R-LOD Computation with Linear Time Complexity where, are x, y coordinates of kth points +

48 Performance Comparison – St. Matthew Model Render time (sec) Non-LOD LOD 2 ~ 20X improvements Approaching the model for every frame

49 LOD (PoE = 4) Non-LOD Image Quality Comparison – St. Matthew Model 512 x 512, no anti-aliasing

50 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

51 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!

52 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 Viewpoint Image plane Small triangles Rays per each pixel

53 Ray Coherence Techniques ● Models with large primitives ● Group rays and test intersections between the group and a bounding box Viewpoint Image plane Large triangles Ray beams

54 Ray Coherence Techniques ● Highly tessellated models ● Fall back to the normal ray tracing ● Causes incoherent memory accesses and temporal aliasing Viewpoint Image plane Small triangles Ray beams

55 Runtime Traversal with R-LODs ● Built on top of the efficient kd-tree traversal algorithm [Wald 04] : kd-node w/ R-LOD: kd-node w/o R-LOD Check whether the error is met? Check whether there is an intersection? If intersected, return shading info Otherwise, stop traversal

56 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!

57 Surface Deviation ● Combined with the previous projected- space error bound, R Underlying geometry Plane of R-LOD New R

58 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 2 3 triangles into one R-LOD kd-node w/o R-LOD kd-node w/ R-LOD Simplify

59 Image Quality Comparison – Forest Model (32M Triangles) PoE = 0 (No LOD)PoE = 4 and cache-oblivious layout of kd-tree 4 X speedup Shading difference

60 Image Quality Comparison – Forest Model PoE = 0 (No LOD)PoE = 16Shading difference

61 R-LODs with Different PoE Values PoE: Original x512 image resolution