Collision Detection and Response

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Collision Detection and Response
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Motivation

• OpenGL is a rendering system
• OpenGL has no underlying knowledge of the objects
  it draws
• Collision Detection Intersection Detection

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Motivation

• Collision Detection
• Identifying the intersection of 3D models
• Collision Response
• Calculating the appropriate post collision
  response of the 3D models
• Assumptions
• Closed 3D polygonal objects

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Overall Approach

• Where is collision detection and response in
  code?
• In animation function
• Usually in Idle or Display
• Update object positions
• If (CollisionDetection())
• Collision Response()
• Draw Objects

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Collision Detection

• Basic Collision Detection function
• for (i0iltnum_of_objects-1i)
• for (ji1jltnum_of_objectsj)
• XTestIntersection(Object I, Object j)
• If (x1) return 1

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Collision Detection Packages

• SWIFT
• http//www.cs.unc.edu/geom/SWIFT/
• Works on polygon soup

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Why is collision detection difficult?

• Too many calculations
• Reduce of calculations
• Accuracy
• Accept approximations
• Lots of poor cases
• Guarantee detection?
• Accuracy requirements?
• http//www.cs.unc.edu/geom/collide/index.shtml

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Reduce Calculations

• Reduce object complexity
• Test with only other objects that might be within
  collision spaces
• Spatial divisions
• Pre-process vs. runtime

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Approximate Object Shape

• For many applications, it is not necessary to get
  absolute collision detection accuracy
• How can we approximate the shape?

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Bounding Boxes

• Calculate a 3D box that bounds the object
• In the collision detection test, use the 3D box
  to test for collision in place of the full model
• Two types
• Axis Aligned
• Bounding boxes are aligned w/ the world
  coordinate axes
• Object Aligned
• Bounding boxes are aligned w/ the object
  coordinate axes

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Axis Aligned Bounding Boxes

• How do we calculate a AABB?
• Take max and min for each dimension
• Pros
• Very fast
• Works for many situations
• Cons
• Collision detection accuracy reduced for many
  cases

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Axis Aligned Bounding Boxes

• How do we calculate intersections?
• Calculate overlap for the min-max range for each
  dimension
• Pros
• Very fast
• Works for many situations
• Cons
• Collision detection accuracy reduced for many
  cases

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Object-Aligned Bounding Boxes

• Calculate BB based on objects primary dimensions
• Objects dimensions could be encoded in model or
  calculated real-time
• Apply M matrix to bounding box coordinates

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Other bounding shapes

• Boxes
• Cubes
• Cylinders
• Polygons
• User-defined shapes
• Should be easy to calculate and test

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Bounding Box Approach

• Test collisions with BB
• Can either report collision
• Or then calculate more accurate collision
• Benefits of this include more accurate response

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Poor cases

• Thin objects

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Poor cases

• Numerical Precision

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Collision Response

• Assuming rigid bodies
• Idea is to rewind time and to point of
  collision and calculate resulting location

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Why is collision response difficult?

• Resolving interpenetration is difficult
• Multiple objects

http//www.peroxide.dk/download/tutorials/tut10/pi
cs/pic04.jpg
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Numerical Imprecision

• Vibrations
• Solutions? Minimum delta