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An efficient and realistic collision handling mechanism is fundamental to any physically plausible a

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Title: An efficient and realistic collision handling mechanism is fundamental to any physically plausible a


1
Collision Handling
  • An efficient and realistic collision handling
    mechanism is fundamental to any physically
    plausible animation system.

2
(No Transcript)
3
Collision Handling
Collision Detection
Contact Modelling
Collision Response
4
Applications
  • Offline Analysis
  • CAD, robotics, movies
  • Realtime and Interactive systems
  • Virtual Environments, autonomous robots, Games
  • Much cross-over research between robotics and
    graphics

5
More Applications
  • Molecular modeling
  • Training and education systems
  • E.g. virtual surgery, what-if analysis.
  • Human character animation
  • clothes and hair, self-collisions
  • Haptic interfaces
  • touching virtual objects.

6
Virtual Environments
  • Allow users to enter a computer-generated virtual
    world and interact with graphical objects.
  • May be immersive or desktop based.
  • Requirement for extremely high and constant
    frame-rates.

7
Virtual Environments
  • Physical interactions triggered by collision.
  • Non-deterministic ? can't pre-process most of the
    work.
  • More objects, more complexity ? greater burden on
    the engine that powers the simulation
  • Need very fast collision handling

8
Problem
Mirtich 2000
  • Timewarp simulation
  • Avalanche took 97 seconds per frame on an SGI
    Onyx

9
Problem
  • Bottleneck is not the simulation
  • but the number and complexity of contact groups
    formed.
  • Mirtich favours robustness over efficiency
  • For VEs this is not an option ?
  • Speed-accuracy trade-off is often needed

10
Topics - Collision Detection
  • Multi-phase approaches
  • Hierarchical techniques and progressive
    refinement
  • Interruptible collision detection
  • Scheduling

11
Rigid body collision detection
  • All-pairs problem
  • O(N2) problem of detecting collisions between all
    N objects.
  • Solution
  • Eliminate objects that couldn't be colliding

12
Multi-phase approach
  • Broad Phase
  • (Eliminate objects that couldn't be colliding)
  • Narrow Phase
  • Progressive refinement levels
  • Exact level (optional)

13
Narrow Phase Exact Level
  • Depends on model representation
  • In V.Es, polygonal models prevalent
  • Often many polygons to approximate surfaces ? CD
    can be expensive
  • Problems special cases, tunnelling…

14
Exact Level - Assumptions
  • Exact level algorithms usually assume convexity.
  • Non-convex polytopes must be represented by
    hierarchies of convex components

15
Exact Level Algorithms
  • Feature-based methods
  • examine vertices, edges and faces of two
    polytopes, i.e. their features.
  • Simplex-based methods
  • simplex the generalisation of a triangle to
    arbitrary dimensions.
  • treat a polytope as the convex hull of a point
    set.

16
Feature-based Algorithms
  • Main goal is to detect whether two polytopes are
    touching or not
  • All are broadly derived from Lin-Canny Closest
    Features algorithm.
  • determines whether two objects are disjoint or
    not, by computing the distance between their
    closest features.

17
Closest Features - 1
  • Voronoi Region constructed for each feature
  • the set of points closer to that feature than any
    other.
  • Key theorem If f1 is the closest feature on
    object 1, and f2 is the closest feature on object
    2, then f1 lies in f2 s Voronoi region and vice
    versa

face
edge
vertex
18
Closest Features - 2
  • Tracks these features, and caches them between
    subsequent calls to the algorithm.
  • Exploits coherency
  • uses feature-stepping
  • if closest features have changed, they are going
    to be adjacent to those cached, and hence finding
    them is quite efficient.

19
Performance
  • runs in expected constant time if the collision
    detection time-step is small relative to the
    objects' speed.
  • I-Collide, V-Collide, Rapid, SWIFT available on
    the web

20
Problems
  • Pair-processing weakness
  • cycling behaviour for penetrating polytopes
  • Difficult to implement due to special cases
  • Needs tolerances to be adjusted
  • No measure of penetration

21
Simplex-based algorithms
  • Treat a polytope as the convex hull of a point
    set.
  • Operations performed on simplices defined by
    subsets of these points.
  • Gilbert-Johnson-Keerthi (GJK), Enhanced GJK

22
Exact level - conclusions
  • GJK/simplex-based algorithms return the best
    measure of interpenetration.
  • V-Clip/feature-based algorithms requires fewer
    floating-point operations
  • Both work well for slightly non-convex objects,
    but become very inefficient as the level of
    non-convexity increases.

23
Narrow Phase Progressive Refinement Levels
  • Use bounding volumes and spatial decomposition
    techniques in a hierarchical manner.
  • Simple tests at a given node in the object
    hierarchy ? branches below can be identified as
    irrelevant and pruned from the search.

24
Hierarchies
  • Trees of bounding volumes are used, each level
    approximating the object. (Bounding Volume
    Hierarchy, BVH)
  • Level Of Detail (LOD) representation (different
    from rendering LODs)
  • Usually conservative approximations
  • choice of volume based on speed of intersection
    tests and fit.

25
Some Hierarchies
  • Octrees, Sphere Trees, C-trees, OBB-trees (used
    in UNC libraries) AABB-trees, K-DOPs, ShellTrees,
    Swept Sphere Volumes

26
BVH - Example
  • Quad-tree (2D equivalent of oct-tree)

Second Level 4 children per node
Third Level 4 children per node
Top Level 4 nodes
27
BHV - Desirable Properties
  • The hierarchy approximates the bounding volume of
    the object, each level representing a tighter fit
    than its parent
  • For any node in the hierarchy, its children
    should collectively cover the area of the object
    contained within the parent node
  • The nodes of the hierarchy should fit the
    original model as tightly as possible

28
BHV - Desirable Properties (2)
  • The hierarchy should be able to be constructed in
    an automatic predictable manner
  • The hierarchical representation should be able to
    approximate the original model to a high degree
    or accuracy
  • allow quick localisation of areas of contact
  • reduce the appearance of object repulsion

29
Cost of Narrow Phase
  • Object interactions determined by traversal of a
    pair of hierarchies
  • Update a node in the hierarchy (Cu, Nu)
  • Detection of overlap between nodes (Cv, Nv)
  • Nu Nv depends on the number of nodes
  • Cu Cv depends on the primitive used

Tc NuCu NvCv
30
Sphere-Tree
R1
  • Nodes of BVH are spheres.
  • Low update cost Cu
  • translate sphere center
  • Cheap overlap test Cv
  • D2 lt (R1 R2)2
  • Slow convergence (Linear) to object geometry
  • Relatively high Nu Nv

R2
D
31
Sphere-Tree Construction
32
Sphere-Tree Properties
  • Hierarchy of spheres
  • Children cover parents volume
  • Finer Approximation
  • Collision Culling

33
Example Traversal
  • Top Level Spheres Overlap
  • ? Step down a level

34
Example Traversal
  • One Sphere Passes Overlap Test
  • ?Need to test it against children on other tree

35
Example Traversal
  • One Sphere Passes Overlap Test
  • ?New pair of overlapping spheres

36
Putting it all together
Sphere-Tree
Medial Axis
Create initial medial axis approximation Create
top level of sphere-tree
37
Broad Phase
  • Fixed-timestep weakness.
  • Big timestep ? more efficient but could have
    tunnelling
  • Small time-step causes a lot of extra unnecessary
    intersection tests.
  • One solution Use an adaptive timestep

38
4-dimensional bounds
  • Space-time bounds provide a conservative estimate
    of where an object may be in the future
  • A fourth dimension represents time
  • Adapt time-step when objects more likely to
    collide
  • Overlaps of these bounds trigger the narrow phase

39
Sweep and Prune
  • Orthogonally project axis-aligned bounding boxes
    onto the x, y and z-axes.
  • Intervals which overlap in all three dimensions
    indicate potential collisions
  • Exploits coherence by using insertion sort
  • Runs in almost constant time for a given number
    of objects

40
Interruptible CD
  • Maintain consistently high frame-rates
  • Smooth simulation
  • prevents simulator sickness
  • Omits the final stage and interrupts the narrow
    phase when time slot has expired
  • Time critical computing
  • BVH approximation is used for collision response
  • Tightness of BHV is critical to simulation
    quality

41
Interactive Simulation Recap
  • Time-Step Simulation
  • Update bodys position and orientation based on
    linear and angular velocities
  • Update bodys linear and angular velocities based
    on acceleration and gravity
  • Determine interactions (Collision Detection) and
    apply relevant impulses (Collision Response)
  • Modelling objects for detection and response
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