Collision Detection

1
Collision Detection

• Jason Stine
• CS 4473
• 25 FEB 2000

2
What is Collision Detection?

• Report geometric contact between objects
• Convey enough information to determine logical
  consequences
• A major computational bottleneck - O(N2)

3
Categories of CD Problems

• Polygon soup - no geometric connections, no
  topology information
• Structured polygons - solid objects
• Constructive Solid Geometry (CSG)

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Categories of CD Problems

• Implicit surfaces - defined by functions
  (quadrics)
• Parametric surfaces - defined by parametric
  functions (NURBS)

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Convex vs. Concave Objects

• Easy case -----------------------gt
• Harder case ---------------------gt
• Really difficult -----------------gt

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What does the model need to know?

• Simplest case - do two objects touch?
• What parts touch?
• What is the minimum distance between disjoint
  objects?
• If objects penetrate, by how much?
• When will the next contact happen?

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Brute Force Approach

• Algebraically solve for the intersection of each
  pair of polygons
• Simple and good for very small models

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Brute Force Approach

• O(N2) quickly becomes unworkable for larger
  models
• Improved with use of a collidable field

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Bounding Volumes

• Complex objects are enclosed by bounding regions
• Easier to test mathematically
• If volumes intersect, more exact tests may be done

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Bounding Volume Problems

• Still O(N2) for objects in scene
• Very effective for rejection tests - much less
  so for close proximity
• Revert to O(N2) for polygons if the scene becomes
  crowded
• Too much wasted space with cubes and spheres

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Collisions in Vega

• Isectors define collision behavior
• Volume associated is converted to a set of line
  segments
• Line segments tested for intersection against the
  scene graph
• 32 bit bitmask determines if the collision is of
  interest

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Collisions in Vega

• Polygons indicated are tested for exact
  intersection
• This method determines height above terrain, HPR
  orientation, terrain following, and line of sight

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Collisions in Java3D

• Bounding volumes can be defined as spheres,
  boxes, or polytopes
• Each frame, all objects that have the COLLIDABLE
  field set to true are tested for intersection
  with each other
• Intersections return a collision event

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Collisions in Java3D

• Event listener structure must be used to control
  the applications response
• Most effective when used in conjunction with
  picking
• Picking is highly optimized in version 1.2

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Collisions in Java3D

• Problems
• Discrete nature of samplings - can miss
  collisions
• Highly inefficient for large, complex
  environments
• Return collisions only on bounding volumes, not
  on objects

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Advanced Approaches

• Better bounding regions
• Clever ordering of the virtual world
• Know when to revert to brute force method

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Voronoi Regions

• A set of points closer to a feature than to any
  other feature
• One region (plane) per face and edge
• Constraint planes separate them

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Voronoi Regions - 2D Example

• Set distance from sides - region side length
  polygon side length
• connect side region boundaries to form corner
  region boundaries

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Voronoi Regions in Practice

• CP eliminates Cell 1, points to Cell 2
• VB and Pa are returned as the closest pair

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Voronoi Regions in Practice

• Both internal and external regions used
• Internal not computed as carefully

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Internal vs. External Voronoi Region
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RAPID - Oriented Bounding Boxes

• Developed at UNC in 1996
• Uses a data structure for progressively more
  detailed Voronoi regions
• RAPID includes both the OBB algorithm and a fast
  way to implement it

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OBB Tree Development

• Recursive partitioning along major axis
• Stops when each box contains one polygon
• Two-dimensional example at right

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Sweep and Prune

• Volumes are projected onto each axis
• Sorted list of objects - relies on temporal,
  geometric coherence
• 1-D example at right

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I-COLLIDE Advanced Collision Detection

• Requires data structure separate from rendering
  structures
• Takes advantage of temporal and geometric
  coherence

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Step 1Axis-Aligned Bounding Boxes
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Step2Oriented Bounding Boxes/Voronoi Regions

• When the sweep and prune indicates collision, OBB
  tree takes over
• Voronoi regions allow identification of closest
  pairs

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I-COLLIDE /RAPID Performance
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I-COLLIDE /RAPID Performance
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IMMPACT - Industrial Strength CD

• For very large (107) numbers of polygons, even
  these are too slow
• IMMPACT combines I-COLLIDE with overlap graphs of
  regions of interest

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IMMPACT Flowchart
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IMMPACT collisions