Collision Detection for Deformable Models

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Collision Detection for Deformable Models

• Huai-Ping Lee
• lhp_at_cs.unc.edu

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Differences in Deformable Models

• Collision and self-collisions
• Self collisions are often neglected for rigid
  bodies
• Preprocessing
• Data structure need to be updated frequently
• Performance
• Efficiency is very important

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Hybrid Approach LAM01

• Goal adapt BVHs to handle deformable models
  efficiently
• Some modification in building and updating the
  tree
• Efficiency of updating hierarchies is more
  important than the tightness of BVs
• AABBs are preferred

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Hybrid Approach LAM01

• For a bottom-up update strategy using AABBs
  vdB97, 8-ary tree version is 10 to 20 percent
  faster than binary version
• Fewer nodes need to be updated (if using top-down
  approach)
• Recursion depth during collision tests is lower

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Hybrid Approach LAM01

• Bounding volume pre-processing
• 8-ary AABB tree built in top-down manner
• A parent AABB is split along three axis to form
  eight child sub-volumes
• No significant difference between ways of
  choosing split planes
• Center of the box or average point of all polygons

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Hybrid Approach LAM01

• Run-time update
• Hybrid of top-down and bottom-up updates
• For a tree with depth n, initially update the n/2
  first levels bottom-up.
• During a collision traversal, update those
  non-updated nodes top-down as needed

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Hybrid Approach LAM01

• Results for hard cases
• All intersecting face pairs are reported

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Hybrid Approach LAM01

• Results for simple cases
• Only the first intersecting face pair is reported

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Hybrid Approach LAM01

• Improved bounding volume hierarchies for
  deformable models
• More efficient update
• Self-collisions are not considered

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Lazy Update MKE03

• Another improvement to BVHs
• Using k-DOPs
• Build the tree top-down
• Also reported that 4-ary and 8-ary trees are
  better
• Lazy update
• Re-inserts the vertices into the leaf k-DOPs and
  build internal nodes bottom-up
• Also want to detect self-collision

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Lazy Update MKE03

• Knowing maximum velocity of the vertices, some
  BVs need not be updated
• Parts of the hierarchy where vertices do not
  travel more than a distance b can be omitted
  during the hierarchy update for a time t b / v,
  if proximities smaller than eclose 2b is to be
  detected
• The BVs have been fattened by eclose / 2

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Lazy Update MKE03

• BVHs are still inappropriate when detecting
  self-collisions
• bounding boxes will always find contacts between
  adjacent sub-objects
• Test the BVH against itself?
• Need to skip some tests between adjacent
  sub-surfaces
• Previous solutions VMT94 and Pro97
• This paper uses method in Pro97

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Curvature Criterion VMT94

• If There exists a vector V for which N.V gt 0 at
  every point of S
• And The projection of C on a plane orthogonal to
  V along the direction of V has no
  self-intersections
• Then There are no self-collisions on the surface
  S.

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Curvature Criterion VMT94

• For each sub-surface
• Search for V
• If V exists, test the projected region for
  self-intersection
• If both succeeded, there is no self-intersection
• Otherwise, check for self intersections in the
  sub-surface

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Curvature Criterion VMT94

• V can be propagated bottom-up in the tree
• Divide a sphere into 14 unit vectors
• In each node, keep those vectors that have
  positive dot products with all the normals in the
  BV

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Normal Cones Pro97

• In each BV, keep a cone representing a super set
  of normal directions
• Parent cones are easily computed from child cones
• a ß/2 max(a1, a2)
• If a?p, check for self-intersection

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Lazy Update MKE03

• Another way to improve hierarchy update
• Also detects self-intersection using normal cones
• Results
• HUHierarchy Update, CTCollision Test

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Morphing of Tree LAM03

• Accelerate the special case in which models are
  deformed by mesh morphing
• First establish the correspondence between
  geometric parts in reference models, assuming all
  models have the same number of vertices and mesh
  connectivity
• Interpolate between these parts
• The models in each frame are formed by linear
  blending the n reference models

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Morphing of Tree LAM03

• Tree building (top-down)
• Add one BV per node in the tree for each
  reference model
• Namely, each node in the tree contain n BVs
• BVs are updated by blending the bounding volumes
  of corresponding sub-models
• using the same weights for linear blending

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Morphing of Tree LAM03

• Experimentthree reference models

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Morphing of Tree LAM03

• Compared with hybrid method LAM01

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Image-Space Techniques

• Work with 2D or 3D discretized representation of
  objects
• Do not perform exact collision detection due to
  discretization error
• Make use of graphics hardware
• Have to worry about bandwidth to and from
  graphics card
• Too many read-backs of buffers (depth, color,
  stencil) will make it slower than using only CPU

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Layered Depth Image (LDI) Decomposition HTG03

• Use discretized 3D representation to accelerate
  collision detection
• Look like this

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Layered Depth Image (LDI) Decomposition HTG03

• Stage 1 Compute AABB intersection for a pair of
  objects (Volume-of-Intersect, VoI)
• Stage 2 Compute the two LDIs restricted to the
  VoI
• like scan-line conversions

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Layered Depth Image (LDI) Decomposition HTG03

• How to compute LDIs?
• Render a 2D projection for each depth value
• Like scan-conversions
• Need to read back the rendered image from frame
  buffer
• For simple environment, graphics hardware version
  runs slower than CPU version

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Layered Depth Image (LDI) Decomposition HTG03

• Stage 3 Perform the actual collision detection
• (3a) Count the overlapping pixels
• (3b) Check if vertices of an object are in
  another objects volume

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Layered Depth Image (LDI) Decomposition HTG03

• Resultsusing intersection volume (3a)
• Depth complexity is the number of layers in LDI

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Layered Depth Image (LDI) Decomposition HTG03

• Resultsusing vertex-in-volume
• Times for LDI generation for entire objects

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Layered Depth Image (LDI) Decomposition HTG03

• Does not need much pre-computation
• Can also detect self-collision
• By labeling entry leaving points explicitly
• Accuracy is related to the resolution of LDI
• Restricted to water-tight models
• Otherwise the scan-conversion will fail
• Need buffer read-backs
• Use graphics hardware for complex scenes!

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CULLIDE GRLM03

• A solution to N-body problem
• Does not use 3D discretized representation of the
  models
• Only use visibility queries
• Cull those objects that cannot be colliding
• Keep a potentially colliding set (PCS)
• For large environment

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CULLIDE GRLM03

• Given an environment composed of n objects, O1,
  O2, , On
• If Oi is fully-visible with respect to all other
  objects, then Oi cannot collide with any other
  object, thus is not in PCS
• Choose three axis to perform orthogonal
  projection
• The second pass tests visibility of sub-objects
  in a similar manner
• Only test those still in the PCS after first pass

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CULLIDE GRLM03

• Final step
• The primitives remaining in the PCS are tested
  with exact collision detection methods
• Results

100 deforming cylinders
100 cylinders 200 polygons
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CULLIDE GRLM03

• Visibility query done by graphics hardware
• Does not need to read back buffers
• Accuracy governed by image resolution
• Errors can be overcome by fattened
  representation
• GLM04
• Does not need pre-computation
• Suitable for any polygonal mesh, large scene
• Cannot be used for self-collision
• Adjacent faces cannot be culled
• Need decomposition of the mesh?

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Chromatic Decomposition Govindaraju et al. 05

• Modify CULLIDE to handle self-collision
• transforms self-collision detection into
  pair-wise N-body CD between non-adjacent
  primitives
• Decompose the mesh into k independent sets
  S1,,Sk
• For every pair of independent set, (Si, Sj),
  ensure each primitive in Si has only one adjacent
  primitive that is in Sj
• To simplify the adjacency
• Building a corresponding graph G, and decompose
  it with graph coloring

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Graph Coloring Govindaraju et al. 05

• Construct a 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
• Primitives pl and pm are vertex-adjacent
• There exists primitive p in the mesh that is
  adjacent to both pl and pm
• Ensures each primitive in Si has only one
  adjacent primitive that is in Sj

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Graph Coloring Govindaraju et al. 05

• Each node is given a color that is different from
  its neighbors in graph G
• Nodes with the same color forms an independent
  set
• Each independent set has a PCS

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Reordering Govindaraju et al. 05

• Consider each pair Si and Sj, compute pairs of
  adjacent primitives between them
• Give the adjacent primitives the same index

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Collision Culling Govindaraju et al. 05

• Collision culling using AABB tree
• Test the tree against itself
• Ignore overlaps with adjacent primitives here
• 2.5D test build PCS for each set
• 1st pass traverse the primitives in Si from last
  to first
• Test if pim is fully-visible against previously
  rendered primitives in Si and Sj, namely pigtm
  pjgtm
• 2nd pass traverse the primitives from first to
  last, namely test pim against piltm pjltm

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GPU Culling Govindaraju et al. 05
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AABB Culling vs. GPU culling Govindaraju et al.
05

• Results of culling

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Exact Tests Govindaraju et al. 05

• For the primitives left in the PCS, perform exact
  intersection tests on non-adjacent primitives
• Merge the PCS of all independent sets
• Use AABB tree to test these primitives
• For adjacent primitives, perform elementary EE
  and VF tests, but do not test the shared edge or
  vertex

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Benchmarks Govindaraju et al. 05
More than 23K triangles 400-550ms during each step
13K triangles 400-500ms during each step
32,500 triangles each curtain 100ms for each
curtain
Path planning for a deformable object 60-90ms
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Comparison Govindaraju et al. 05
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Chromatic Decomposition Govindaraju et al. 05

• Transform self-collision detection into N-body
  collision detection by decomposing the mesh
• Use BVHs and image-space technique to do
  collision culling
• Utilize graphics hardware

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Conclusion

• BVHs are still an important tool for collision
  detection for deformable objects
• Need to optimize update procedure
• Self-collision can be culled in object space
• Curvature criterion (object space)
• Decompose into independent set
• Image-space techniques can be accelerated by
  graphics hardware
• But accuracy is limited by discretization
• Can still be powerful for culling, followed by
  object-space exact collision detection

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Reference

• Lin, M. C., and Manocha, D. 2004. Collision and
  proximity queries. In Handbook of Discrete and
  Computational Geometry, 2nd Ed., J. E. Goodman
  and J. O'Rourke, Eds. CRC Press LLC, Boca Raton,
  FL, ch. 35, 787.807.
• Teschner, M., Kimmerle, S., Heidelberger, B.,
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• Larsson T., Akenine-Möller T. 2001. Collision
  detection for continuously deforming bodies. In
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• Larsson T., Akenine-Möller T. 2003. Efficient
  collision detection for models deformed by
  morphing. The Visual Computer 19, 2 (May2003),
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Reference

• Mezger J., Kimmerle S., Etzmuss O. 2003.
  Hierarchical Techniques in Collision Detection
  for Cloth Animation. Journal of WSCG 11, 2,
  322329.
• Volino P., Magnenat-Thalmann N. 1994. Efficient
  Self-Collision Detection on Smoothly Discretized
  Surface Animations using Geometrical Shape
  Regularity. Computer Graphics Forum 13, 3,
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• Provot, X. 1997. Collision and Self-Collision
  Handling in Cloth Model Dedicated to Design
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  Canadian Information Processing Society, Canadian
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  177189.

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Reference

• Heidelberger, B., Teschner, M., and Gross, M.
  2003. Real-time volumetic intersections of
  deforming objects. Proc. of Vision, Modeling and
  Visualization.
• 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
• Govindaraju, N., Knott, D., Jain, N., Kabul, I.,
  Tamstorf, R., Gayle, R., Lin, M. C., and Manocha,
  D. 2005. Interactive Collision Detection between
  Deformable Models using Chromatic Decomposition.
  Proc. of ACM SIGGRAPH.