Collision Detection for Deformable Objects

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Collision Detection for Deformable Objects

• Xin Huang
• huangxin_at_cs.unc.edu
• 16/10/2007

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Application
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Overview

• Deformable models
• deforming over time, cutting, breaking ..
• expensive to update the collision query structure
  such as BVH as model deforming

4
Overview

• Self- collision
• many adjacent or close primitives overlap
• result in a high number of false positives
• very challenging

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Outline

• Larsson 01 Collision detection for continuously
  deforming bodies
• Zhang 2007 Interactive Collision Detection for
  Deformable Models
• Govindaraju 03 CULLIDE Interactive Collision
  Detection between Complex Models in Large
  Environments using Graphics Hardware
• Govindaraju 05 Interactive Collision Detection
  between Deformable Models using Chromatic
  Decomposition

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Larsson 01

• Collision Detection for Continuously Deforming
  Bodies Larsson 01
• hybrid update an incremental bottom-up and a
  selective top-down update

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Larsson 01

• Broad phase sort and prune
• Narrow phase update, AABBs test, primitive test

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Larsson 01

• Bounding volume pre-processing
• Built 8-ary AABB tree in top-down manner
• A parent AABB is split along three principle
  axis to form 8 child sub-volumes
• Split planes center point of the box or average
  of all polygons midpoints

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Larsson 01

• Run-time AABB Updates
• Top-down traversing the faces under the node
  benefit if a few deep nodes
• Bottom-up Directly from AABBs of sub-node
  benefit if many deep nodes
• Trade-off

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Larsson 01

• Hybrid update
• For a tree with depth n, initially update the n /
  2 first levels bottom-up
• Non-updated nodes are updated top-down on the fly
  during collision traversal

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Larsson 01

1. reporting all intersecting triangle pairs (b)
   first arbitrary intersecting triangle pair

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Larsson 01

• Conclusion
• Fast to update during deformation
• Not consider Self-collision

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Zhang 2007

• Interactive Collision Detection for Deformable
  Models using Streaming AABBs---Zhang 2007
• Bound deformable objects as input streams
• Use GPU to perform parallel pairwise overlap test
• Compute in object space
• Previous GPU based method
• Depend on image resolution and view direction

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Zhang 2007
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Zhang 2007

• AABB tree building texture preparation

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Zhang 2007

• Streaming AABB Overlap Tests

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Zhang 2007

• Hierarchical Readback

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Zhang 2007

• Primitive Intersection Test on CPU
• Stream Update on GPU

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Zhang 2007

• Examples

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Zhang 2007

• Excluding texture download from CPU to GPU, 2-10
  times faster
• Including texture download, 1.4-2 times faster

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Zhang 2007
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Zhang 2007

• Conclusion
• Streaming AABB overlap tests and stream update
  using SIMD computations
• Stream reduction readback
• Collision detection in Object space

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Zhang 2007

• Limitation
• Pre-setup time to prepare AABB streams and map to
  textures in GPUs memory
• Need more texture memory
• Not report self-intersections

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CULLIDE---Govindaraju 03

• CULLIDE Interactive Collision Detection Between
  Complex Models in Large Environments using
  Graphics Hardware
• Compute potentially colliding set (PCS)
• Visibility query by graphics hardware

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CULLIDE---Govindaraju 03

• An object O does not collide with a set of
  objects S if O is fully-visible with respect to
  S.
• Compute PCS by two pass
• 1st pass, render the objects in the order O1,
  ..,On
• 2nd pass, render the objects in the reverse order
  On,On-1, ...O1
• test if an object is fully visible or not, if
  not, in PCS

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CULLIDE---Govindaraju 03

• Object level pruning
• perform object level pruning by computing the PCS
  of objects.
• Sub-Object Pruning
• identify potential regions of each object in PCS
• Exact Collision Detection
• Triangle-triangle intersection on the CPU

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CULLIDE---Govindaraju 03
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CULLIDE---Govindaraju 03

• Limitation
• No distance and penetration information
• Image-space resolution
• Cannot handle self-collision

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Self-collision

• Challenge
• Non-interactive rates
• Many adjacent or nearby primitives in close
  proximity
• A high number of false positives

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Govindaraju 05

• Interactive Collision Detection between
  Deformable Models using Chromatic Decomposition
• Chromatic Mesh Decomposition
• Set-based Self-Collision Detection

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Govindaraju 05

• Non-Adjacent Collision Detection (NACD) AABB and
  2.5D overlap test
• Adjacent Collision Detection (ACD) exact VF
  and EE elementary tests

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Govindaraju 05

• Chromatic Mesh Decomposition
• Independent Sets
• Graph Coloring
• Construct an extended-dual graph G (V, E)
• Each primitive pi correspond to a vertex V(pi) in
  V
• Add an edge (V(pl), V(pm)) to E if and only if
• pl and pm are vertex-adjacent
• There exists a primitive p in the mesh that both
  (pl, p) and (p, pm) are adjacent

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Govindaraju 05

• AABB Hierarchy Culling
• Test the Hierarchy against itself
• Compute non-adjacent primitive colliding
• 2.5D Overlap Tests
• Extend CULLIDE

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Govindaraju 05

• 2.5D Overlap Tests
• First pass Traverse the primitives in Si from
  the last to the first. Test if pim is
  fully-visible against previously rendered
  primitives in Sj, i.e. S jgtm
• Second pass Traverse the primitives in Si from
  the first to the last. Only test the primitive
  pim which was fully visible in the first pass for
  potential overlap with the PCS Sj, i.e. Sjltm

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Govindaraju 05

• Exact Tests Non-Adjacent Primitives
• Merge the PCS of all independent sets
• Use AABB hierarchy to compute intersecting pairs
• Perform EE and VF tests between pairs
• Exact Tests Adjacent Primitives
• Check all adjacent primitives for intersection
• Do not test the shared edge or vertex

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Govindaraju 05
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Govindaraju 05

• Limitation
• Mesh with fixed connectivity
• Work well with a small number of overlapping
  pairs
• Chromatic decomposition may produce a high number
  of independent sets

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Conclusion

• No general or optimal method existed
• Approaches based on BVH have shown to be
  efficient
• Image-space techniques can achieve highly culling
  rate, however, is limited by discretization
  accuracy
• Self-collision still remains challenging

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Some other approaches

• Distance Fields
• Spatial Subdivision
• Stochastic Methods
• (Refer to Teschner 2005, a State of the Art
  review)

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References

• Survey LIN M., MANOCHA D. Collision and
  proximity queries. In Handbook of Discrete and
  Computational Geometry, 2003
• Collision detection for deformable objects.
  Teschner, M., Kimmerle, S., Heidelberger, B.,
  Zachmann, G., Raghupathi, L., Fuhrmann, A., Cani,
  M.-P., Faure, F., Magnenat-Thalmann, N.,
  Strasser, W., and Volino, P. 2005. Computer
  Graphics Forum
• Larsson T., Akenine-Möller T. 2001. Collision
  detection for continuously deforming bodies. In
  Eurographics, pp. 325333. short presentation.
• Interactive Collision Detection for Deformable
  Models Using Streaming AABBs, Xinyu Zhang, Young
  J. Kim, IEEE Trans Visualization Computer
  Graphics, 2007
• Govindaraju, N., Redon, S., Lin, M. C., and
  Manocha, D. 2003. CULLIDE Interactive Collision
  Detection between Complex Models in Large
  Environments using Graphics Hardware. Proc. of
  Eurographics/SIGGRAPH Workshop on Graphics
  Hardware
• Interactive Collision Detection between
  Deformable Models using Chromatic Decomposition,
  Naga K. Govindaraju, David Knott, Nitin Jain,
  Ilknur Kabul, Rasmus Tamstorf, Russel Gayle, Ming
  C. Lin, Dinesh Manocha in ACM SIGGRAPH 2005