Collision Detection for Deformable Models Huai-Ping Lee [email protected].

Collision Detection for Deformable Models

Huai-Ping Lee

[email protected]

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 imp

ortant than the tightness of BVs• AABBs are preferred


• 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


• 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


• 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


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


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


• 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 bu

ild 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 tr

avel 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 betw

een adjacent sub-objects

• Test the BVH against itself?– Need to skip some tests between adjacent su

b-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.


• 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


• V can be propagated bottom-up in the tree– Divide a sphere into 14 unit vectors– In each node, keep those vectors that have p

ositive 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


• Tree building (top-down)– Add one BV per node in the tree for each refer

ence 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


• Experiment—three reference models


• Compared with hybrid method [LAM01]

Image-Space Techniques

• Work with 2D or 3D discretized representation of objects– Do not perform exact collision detection due t

o discretization error

• Make use of graphics hardware– Have to worry about bandwidth to and from gr

aphics card• Too many read-backs of buffers (depth, color, sten

cil) 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:


• 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


• 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 v

ersion runs slower than CPU version


• 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


• Results—using intersection volume (3a)– Depth complexity is the number of layers in

LDI


• Results—using vertex-in-volume– Times for LDI generation for entire objects


• 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 N-bod

y CD between non-adjacent primitives– Decompose the mesh into k independent sets S1,…,S

k

– 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(p

i) 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 pi

m 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 pi

m 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 first

• For adjacent primitives, perform elementary EE and VF tests, but do not test the shared edge or vertex

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

Comparison [Govindaraju et al. 05]

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

Conclusion

• BVHs are still an important tool for collision detection for deformable objects– Need to optimize update procedure

• Self-collision can be culled– 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-sp

ace exact collision detection

Reference• Lin, M. C., and Manocha, D. 2004. Collision and proximity queries. I

n 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., Magnenat-Thalmann, 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 Self-Collision 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.

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