Collision Detection and Collision Detection and ResponseResponse

MotivationMotivation

OpenGL is a rendering systemOpenGL is a rendering system OpenGL has no underlying knowledge of OpenGL has no underlying knowledge of

the objects it drawsthe objects it draws Collision Detection == Intersection Collision Detection == Intersection

DetectionDetection

MotivationMotivation

Collision DetectionCollision Detection Identifying the intersection of 3D modelsIdentifying the intersection of 3D models

Collision ResponseCollision Response Calculating the appropriate post collision Calculating the appropriate post collision

response of the 3D modelsresponse of the 3D models AssumptionsAssumptions

Closed 3D polygonal objectsClosed 3D polygonal objects

Overall ApproachOverall Approach

Where is collision detection and Where is collision detection and response in code?response in code?

In animation functionIn animation functionUsually in Idle or DisplayUsually in Idle or DisplayUpdate object positionsUpdate object positionsIf (CollisionDetection())If (CollisionDetection())

Collision Response()Collision Response()Draw ObjectsDraw Objects

Collision DetectionCollision Detection

Basic Collision Detection functionBasic Collision Detection function for (i=0;i<num_of_objects-1;i++)for (i=0;i<num_of_objects-1;i++)

for (j=i+1;j<num_of_objects;j++)for (j=i+1;j<num_of_objects;j++)X=TestIntersection(Object I, Object j)X=TestIntersection(Object I, Object j)If (x==1) return 1;If (x==1) return 1;

Collision Detection PackagesCollision Detection Packages

SWIFT++SWIFT++http://www.cs.unc.edu/~geom/SWIFT++http://www.cs.unc.edu/~geom/SWIFT++

//Works on ‘polygon soup’Works on ‘polygon soup’

Why is collision detection Why is collision detection difficult?difficult?

Too many calculationsToo many calculationsReduce # of calculationsReduce # of calculations

AccuracyAccuracyAccept approximationsAccept approximations

Lots of poor casesLots of poor casesGuarantee detection?Guarantee detection?Accuracy requirements?Accuracy requirements?

http://www.cs.unc.edu/~geom/http://www.cs.unc.edu/~geom/collide/index.shtmlcollide/index.shtml

Reduce CalculationsReduce Calculations

Reduce object Reduce object complexitycomplexity

Test with only Test with only other objects other objects that might be that might be within collision within collision spacesspacesSpatial divisionsSpatial divisions

Pre-process vs. Pre-process vs. runtimeruntime

Approximate Object ShapeApproximate Object Shape

For many For many applications, it is not applications, it is not necessary to get necessary to get absolute collision absolute collision detection accuracydetection accuracy

How can we How can we approximate the approximate the shape?shape?

Bounding BoxesBounding Boxes

Calculate a 3D box that Calculate a 3D box that bounds the objectbounds the object

In the collision detection In the collision detection test, use the 3D box to test, use the 3D box to test for collision in place test for collision in place of the full modelof the full model

Two typesTwo types Axis AlignedAxis Aligned

Bounding boxes are aligned Bounding boxes are aligned w/ the world coordinate w/ the world coordinate axesaxes

Object AlignedObject Aligned Bounding boxes are aligned Bounding boxes are aligned

w/ the object coordinate w/ the object coordinate axesaxes

Axis Aligned Bounding BoxesAxis Aligned Bounding Boxes

How do we calculate a How do we calculate a AABB?AABB? Take max and min for each Take max and min for each

dimensiondimension ProsPros

Very fastVery fast Works for many situationsWorks for many situations

ConsCons Collision detection accuracy Collision detection accuracy

reduced for many casesreduced for many cases

Axis Aligned Bounding BoxesAxis Aligned Bounding Boxes

How do we calculate How do we calculate intersections?intersections? Calculate overlap for the min-Calculate overlap for the min-

max range for each dimensionmax range for each dimension ProsPros

Very fastVery fast Works for many situationsWorks for many situations

ConsCons Collision detection accuracy Collision detection accuracy

reduced for many casesreduced for many cases

Object-Aligned Bounding Object-Aligned Bounding BoxesBoxes

Calculate BB based on object’s primary dimensionsCalculate BB based on object’s primary dimensions Object’s dimensions could be encoded in model or Object’s dimensions could be encoded in model or

calculated real-timecalculated real-time Apply M matrix to bounding box coordinatesApply M matrix to bounding box coordinates

Other bounding shapesOther bounding shapes

BoxesBoxesCubesCubesCylindersCylindersPolygonsPolygonsUser-defined User-defined

shapesshapesShould be easy to Should be easy to

calculate and testcalculate and test

Bounding Box ApproachBounding Box Approach

Test collisions Test collisions with BBwith BB

Can either report Can either report collisioncollision

Or then calculate Or then calculate more accurate more accurate collisioncollision Benefits of this Benefits of this

include more include more accurate responseaccurate response

Poor casesPoor cases

Thin objectsThin objects

Poor casesPoor cases

Numerical PrecisionNumerical Precision

Collision ResponseCollision Response

Assuming rigid bodiesAssuming rigid bodies Idea is to “rewind time” and to point Idea is to “rewind time” and to point

of collision and calculate resulting of collision and calculate resulting locationlocation

Why is collision response Why is collision response difficult?difficult?

Resolving interpenetration is difficultResolving interpenetration is difficultMultiple objectsMultiple objects

http://www.peroxide.dk/download/tutorials/tut10/pics/pic04.jpg

Numerical ImprecisionNumerical Imprecision

VibrationsVibrationsSolutions? Minimum deltaSolutions? Minimum delta