Collision Detection for
Deformable Models
Huai-Ping Lee
lhp@cs.unc.edu
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
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
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 topdown approach)
– Recursion depth during collision tests is lower
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
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 nonupdated nodes top-down as needed
Hybrid Approach [LAM01]
• Results for hard cases
– All intersecting face pairs are reported
Hybrid Approach [LAM01]
• Results for simple cases
– Only the first intersecting face pair is reported
Hybrid Approach [LAM01]
• Improved bounding volume hierarchies for
deformable models
– More efficient update
• Self-collisions are not considered
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
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 εclose – 2b is to be
detected
• The BVs have been fattened by εclose / 2
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]
Curvature Criterion [VMT94]
• If: There exists a vector V for which N.V >
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.
Curvature Criterion [VMT94]
• For each sub-surface
– Search for V
– If V exists, test the projected region for selfintersection
– If both succeeded, there is no self-intersection
– Otherwise, check for self intersections in the
sub-surface
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
Normal Cones [Pro97]
• In each BV, keep a cone representing a
super set of normal directions
• Parent cones are easily computed from
child cones
– α =β/2 + max(α1, α2)
• If α≧π, check for self-intersection
Lazy Update [MKE03]
• Another way to improve hierarchy update
• Also detects self-intersection using normal
cones
• Results
– HU=Hierarchy Update, CT=Collision Test
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
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
Morphing of Tree [LAM03]
• Experiment—three reference models
Morphing of Tree [LAM03]
• Compared with hybrid method [LAM01]
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
Layered Depth Image (LDI)
Decomposition [HTG03]
• Use discretized 3D representation to
accelerate collision detection
– Look like this:
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
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
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 object’s volume
Layered Depth Image (LDI)
Decomposition [HTG03]
• Results—using intersection volume (3a)
– Depth complexity is the number of layers in
LDI
Layered Depth Image (LDI)
Decomposition [HTG03]
• Results—using vertex-in-volume
– Times for LDI generation for entire objects
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!
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
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
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
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?
Chromatic Decomposition
[Govindaraju et al. 05]
• Modify CULLIDE to handle self-collision
– transforms self-collision detection into pair-wise Nbody 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
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
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
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
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 pi>m& pj>m
– 2nd pass: traverse the primitives from first to
last, namely test pim against pi<m & pj<m
GPU Culling [Govindaraju et al. 05]
AABB Culling vs. GPU culling
[Govindaraju et al. 05]
• Results of culling
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
Benchmarks [Govindaraju et al. 05]
13K triangles
More than 23K triangles
400-500ms during each step
400-550ms during each step
32,500 triangles each curtain
Path planning for a deformable object
100ms for each curtain
60-90ms
Comparison [Govindaraju et al. 05]
Chromatic Decomposition
[Govindaraju et al. 05]
• Transform self-collision detection into Nbody collision detection by decomposing
the mesh
• Use BVHs and image-space technique to
do collision culling
– Utilize graphics hardware
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 objectspace exact collision detection
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., Zachmann, G.,
Raghupathi, L., Fuhrmann, A., Cani, M.-P., Faure, F., MagnenatThalmann, N., Strasser, W., and Volino, P. 2005. Collision detection
for deformable objects. Computer Graphics Forum
• Larsson T., Akenine-Möller T. 2001. Collision detection for
continuously deforming bodies. In Eurographics, pp. 325–333. short
presentation.
• Larsson T., Akenine-Möller T. 2003. Efficient collision detection for
models deformed by morphing. The Visual Computer 19, 2
(May2003), 164–174.
Reference
• Mezger J., Kimmerle S., Etzmuss O. 2003. Hierarchical
Techniques in Collision Detection for Cloth Animation.
Journal of WSCG 11, 2, 322–329.
• Volino P., Magnenat-Thalmann N. 1994. Efficient SelfCollision Detection on Smoothly Discretized Surface
Animations using Geometrical Shape Regularity.
Computer Graphics Forum 13, 3, 155–166.
• Provot, X. 1997. Collision and Self-Collision Handling in
Cloth Model Dedicated to Design Garments. In Graphics
Interface ’97 (May 1997), Canadian Information
Processing Society, Canadian Human-Computer
Communications Society, pp. 177–189.
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.