S95 Arial, Bld, YW8, 37 points, 105% line spacing

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Collision Detection
MAJ Keith M. Perkins, USA kmperkin_at_nps.navy.mil
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Outline

• Overview of Collision Detection
• Classification of the Problem
• Collision Detection Algorithms/Solutions
• Public Domain Packages
• Optimizing Collision Detection
• Collision Detection in Games
• Questions

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Overview of Collision Detection

• The goal of collision detection (also known as
  interference detection or contact determination)
  is to automatically report a geometric contact
  when it is about to occur or has actually
  occurred..
• -Ming C. Lin Stefan Gottschalk
• University of North Carolina

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Where is there a need?

• Computer-Aided Design and Machining (CAD/CAM)
• Robotics and Automation
• Manufacturing
• Computer Graphics
• Animation
• Computer Simulated Environments.

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A Taxonomy of 3D Model Representations

• 3D Models
• Nonpolygonal Models
  Polygonal Models
• Constructive Implicit Parametric
  Structured Polygon Soups
• Solid Surfaces Surfaces
  
• 
  Geometry
• Convex Nonconvex

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Polygonal Models

• Most Commonly Used (Graphics/Modeling)
• Simple Representation
• Versatile
• Hardware Accelerated Rendering Widely Available
• Polygon Soup (Most General Class)
• Proper Solid
• Convex

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Constructive Solid Geometry(CSG)

• Forms Objects From Primatives
• Enables an Intuitive Design Process of Building
  Shapes
• Finding a Collision Witness Easier
• Certain Ops Difficult to Describe
• Hard to Compute an Accurate Boundary or Surface
  Representation

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Implicit Surfaces

• Defined with Mappings from Space to the Real
  Numbers F R3 ? R
• f(x y z) 0 Model
• f(x y z) lt 0 Inside Model
• f(x y z) gt 0 Outside Model
• Generically Closed Manifolds (a desirable
  property)
• Algebraic
• Quadrics

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Parametric surfaces

• Defined with Mappings from Some Subset of the
  Plane to Space F R2 ? R3
• Not Generally Closed Manifolds
• Easier to Polygonalize and Render
• (NURBS)
• Bezier patches

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What do We Need to Know?

• Whether two models touch?
• Which parts (if any) touch (find their
• intersection)?
• Their separation?
• The minimum Euclidean distance between
• disjoint objects?
• Minimum translational distance required to
• separate penetrating objects?
• When will be their next collision be? (ETA Comp)

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When do We Need to Know?

• Different Applications need different Queries
• Distance Information
• Robot Motion Control
• Dynamic Simulation
• Intersection Computation
• Physically Based Modeling
• Animation Systems
• ETA Solution
• Time Step Simulation (Quidditch)

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Simulation Environments

• Pair processing vs. nbody processing
• Motions static vs. dynamic
• Temporal Coherence.
• Rigid bodies vs. deformable models
• Collision detection between geometric
• models a survey
• Ming C. Lin Stefan Gottschalk

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Algorithms

• Lin-Canny Closest Feature Algorithm
• V-Clip
• I-COLLIDE
• RAPID
• V-COLLIDE
• Q-COLLIDE
• SOLID
• OBB-Tree
• QuickCD
• KDS
• Distance computation between convex polytopes

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Lin-Canny Closest Features

• Maintain Closest Features Pair
• Find Distance
• D lt epsilon ? Collision

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V-Clip

• Tracks Closest Features Pair
• Less Complex (Lin-Canny)
• More Robust (Lin-Canny)
• Handles Penetrating Polyhedra

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I-COLLIDE

• Large Environments of Convex Polyhedra
• Exploits Coherance and convexity
• Achieving fast and exact Collision Detection
• Tested
• Time required for Collision Detection Small

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RAPID

• Robust and accurate
• For pairs
• Polygon Soups
• Close proximity configurations

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V-COLLIDE

• Unites the nbody processing algorithm of
• I-COLLIDE and the pair processing algorithm
  of
• RAPID
• Allows dynamic addition or deletion of objects

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Q-COLLIDE

• Simple and Exact
• Separating Plane
• Witness
• Coherence

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SOLID

• Multiple three-dimensional polygonal objects
• polygon soups
• Rigid motion
• Performance V-COLLIDE

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OBB-Tree

• Oriented Bounding Boxes
• Tightly enclosing object
• OOBs allows fewer boxes than AABBs

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QuickCD

• Bounding Volumes (BV-trees)
• K-dops

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KDS

• Proof
• Certificates
• Allows for time-cost analysis and practical
  solutions

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Distance Computation

• Distance computation between convex polytopes
• Distance tracking
• Requires a list of all edges for best performance
• Performance Lin_Canny

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Optimizing Collision Detection

• O(n2) ?(n2n)/2
• Objects Collision Tests
• 2 1
• 3 3
• 4 6
• 5 10
• 6 16
• 7 21
• 8 28
• 9 36
• 10 45
• 15 105
• 20 190

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Optimizing Collision Detection

• Eliminating Collision Tests
• 1 Player Spaceship
• 5 Player Missiles
• 20 Aliens
• 10 Alien Missiles
• -----
• 36 Objects 1296 tests (n2)
• 630 tests (n2n)/2
• Can Reduce to 180 tests (71 reduction)

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Optimizing Collision Detection

• Spatial-Test Elimination
• Good for large numbers of objects
• Requires additional bookeeping
• Sorts objects by position
• Objects only tested with object near by

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Optimizing Collision Detection

• Axis Sorting
• Sprite X-Coord Sprite Width
• 1 10 10
• 2 15 5
• 3 18 8
• 4 40 10
• 5 45 10

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Axis (Cont)
typedef struct _SPRITE_DATA
struct _SPRITE_DATA Next
int Top / sprite location /
int Left
int Width / sprite dimensions /
int Height
SPRITE_DATA
 
/
Function CollisionTestSorted
Description
Tests a linked list of sorted sprites to
see if they
potentially overlap. If so, they are
collision tested.
/
void CollisionTestSorted(SPRITE_DATA SpriteList)

SPRITE_DATA s1, s2
int s1Right
 
s1 SpriteList
while (s1 ! NULL)
s1Right s1-gtLeft s1-gtWidth - 1
/ Compare s1 with all following sprites
until left edge /
/ of a following sprite is located
beyond the right /
/ edge of s2. /
s2 s1-gtNext
while (s2 ! NULL (s1Right gt
s2-gtLeft))
CollisionTest(s1, s2)
s2 s2-gtNext

s1 s1-gtNext


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Optimizing Collision Detection

• Sector Method

 
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Optimizing Collision Detection

• Hybrid Techniques
• Game Rules and Spatial
• Sector and Game Rules
• etc

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Optimizing Collision Detection

• Quick Tests
• Bounding based (use geometric objects)
• Fast, imperfect
• Pixel based
• More precise, much slower

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Bounding based (cont)
 
typedef struct
int Left
int Top
int Right
int Bottom
RECT
 
/
Function CollisionTestRect
Description
Tests two bounding rectangles to see if
they overlap.
Returns TRUE if so, FALSE otherwise.
/
BOOL CollisionTestRect(RECT r1, RECT r2)

if (r1-gtLeft gt r2-gtRight r2-gtLeft gt
r1-gtRight
r1-gtTop gt r2-gtBottom r2-gtTop gt
r1-gtBottom)
return FALSE

else
return TRUE


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Optimizing Collision Detection

• Combine Bounding and Pixel based
• Bounding first (usually negative)
• When positive, do the More Accurate Pixel
• Getting the most out of your collision tests
• Dave Roberts

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Collision Detection in Games

• We want realism (no phantom bullets)
• Many Avatars are Biped (Whats the problem)
• Most Shooter Games Navigate the user as a simple
  shape

MDK2
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Collision Detection in Games

• Resolving Collisions
• Sliding Vt Ni (-dot(Ni,Vt)-Nd)
• Vt Desired Target or Destination of Player
• Ni Normal to the plane of impact
• Nd The "D" of the hit poly's "plane equation"

MDK2
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Collision Detection in Games

• Resolving Collisions
• Stepping
• When was the last time you were crossing the
  street and tripped on the curb?
• Users dont want to worry about small steps and
  stairs
• Lift path

MDK2
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Collision Detection in Games

• Resolving Collisions
• Climbing
• A basic extension of step up ability
• Implementing if height transition is large enough
• Climbing animation also invoked
• Ease for user, no key press required, no special
  skill to learn
• BSP Collision Detection As Used in MDK2 and
  NeverWinter Nights

MDK2
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Questions?
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Questions

• Name two Collision Detection Algorithms
• I-COLLIDE, RAPID, SOLID, V-CLIP, OBB
• Name two methods to Optimize CD
• Spatial, Sector method, Axis Sorting
• Compare Bounding and Pixel Base Optimization
• Bounding Base is fast/imperfect
• Pixel Base is slow/accurate

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Contact Information

• Keith M. Perkins
• 2 University Circle, 2425
• Monterey, CA 93943
• [phone]
• kmperkin_at_nps.navy.mil