ray tracing animated scenes using motion decomposition johannes günther, heiko friedrich, ingo...
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![Page 1: Ray Tracing Animated Scenes using Motion Decomposition Johannes Günther, Heiko Friedrich, Ingo Wald, Hans-Peter Seidel, and Philipp Slusallek](https://reader035.vdocument.in/reader035/viewer/2022070412/5697bf871a28abf838c88b92/html5/thumbnails/1.jpg)
Ray Tracing Animated Scenes using Motion Decomposition
Johannes Günther, Heiko Friedrich, Ingo Wald, Hans-Peter Seidel,
and Philipp Slusallek
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September 7, 2006 Eurographics, Vienna 2
Introduction
Nowadays realtime ray tracing on single PC– Packet tracing [Wald PhD04, Reshetov SIG05]
– Clever acceleration structures (SAH [McDonald GI89])
Best known method: kd-trees [Havran PhD01]
BUT, so far only static scenes– Walkthrough– Rigid-body animations [Wald PVG03]
Reason: high kd-tree build time
preprocessing
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Related Work – Dynamic Scenes
Three approaches:
Alternative acceleration structures– BVHs [Wald TOG06, Lauterbach RT06]
– Grids [Wald SIG06]
– Hybrid data structures [Woop GH06, Havran RT06, Wächter EGSR06]
Faster construction of kd-trees– [Popov RT06, Hunt RT06]
Avoid the (re)construction of kd-trees
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Avoid Updating the KD-Tree
IDEA: “make dynamic scenes static”
Assumptions:– Deformation of a base mesh (constant connectivity)
– All frames of animation known in advance– Local coherent motion
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Method Overview
Motion decomposition– Affine transformations
+ residual motion
Fuzzy kd-tree– Handles residual motion
Clustering– Exploit local coherent motion
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Motion Decomposition
Dynamic scene: ball thrown onto floor
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Motion Decomposition
Affine transformations– Approximate deformations– Include shearing (3rd frame)
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Motion Decomposition
residual motion
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Motion Decomposition
fuzzy boxes
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Fuzzy KD-Tree
Handles residual motion KD-Tree over the fuzzy boxes of triangles
Valid over complete animation
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Illustration
transformation
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Illustration
affine transformations only adding residual motion
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Details: Clustering
Efficient ray tracing:– Small fuzzy boxes
Minimize residual motion
Cluster coherently moving triangles
Many clustering algorithms– But mostly for static meshes– Not designed for ray tracing
Develop new one– based on Lloyd relaxation
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Clustering Algorithm
Start with one cluster (all triangles) Lloyd relaxation:
– Find transformations for clusters Linear least squares problem
– Recluster triangles– Until convergence
Insert new cluster– Seeded by triangle with highest
residual motion
Until improvement below threshold
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Ray Tracing: Two-level Approach
Build top-level kd-tree over current cluster bounds Transform rays into local coordinate system
– Inverse affine transformation of cluster
from motion decomposition
Traverse fuzzy kd-tree of cluster
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Results
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Video
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Ray Tracing Performance
Single CPU(Opteron 2.8 GHz)
1024×1024 px
Incl. shading
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More Complex Shading
With texturing, lighting, shadows: 2.2 fps(static kd-tree: 4.1 fps)
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September 7, 2006 Eurographics, Vienna 20
Comparison to Static KD-Tree
Baseline: separate static kd-tree per frame
Traversal steps– Factor 1.5 - 2
Intersections– Factor 1.2 – 2, Cow 4, Chicken 6
Average fps– Factor 1.2 – 2.6, alone two-level kd-tree costs ca. 30%
Memory– only one fuzzy kd-tree (+ transformation matrices)
– vs. #frames static kd-trees
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Clustering ProcessResidual Motion
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Clustering also in time domain– Better adaptation to separated animation sequences– E.g. with the chicken: walking, being scared, flying
Handle interpolation between key frames– By interpolation of the computed transformations?
Interaction with dynamic scenes– So far all poses known in advanceHarnessing more information from application– Skinning operators, skeleton, joint angles with limits– See also [TVC/PG06]
Future Work
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Summary
Animated scenes at interactive frame rates– Motion decomposition and fuzzy kd-trees
Automatic clustering into coherently moving sub-meshes
Integrates nicely into existing ray tracing systems
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Questions?
Thank You
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Transformation X of vertex v
Solve linear least squares problem
Finding “Good” Transformations
'vvX
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Clustering Process
Residual Motion Surface Area