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Collision Detection and Resolution

Zhi Yuan

Course: Introduction to Game Development

zyuan@cs.kent.edu

11/28/2011

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Overview

Collision Detection Identify the intersection of objects.

Collision ResponseCalculate the appropriate response after collision.

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Collision Detection

High complexity for two reasons:Geometry is typically very complex, potentially requiring

expensive testing.

Naïve solution is O(n2) time complexity, since every object can potentially collide with every other object.

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Dealing with Complexity

Two directionsComplex geometry must be simplified.

Reduce number of object pair tests.

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Simplified Geometry

Approximate complex objects with simpler geometry, like this ellipsoid.

Simpler Shape is cheaper to test.

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BV: Bounding Volume

Key idea:Surround the object with a (simpler) bounding

object (the Bounding Volume).If something does not collide with the bounding

volume, it does not collide with the object inside.Often, to intersect two objects, first intersect their

bounding volumes.

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Choosing a Bounding Volume

Lots of choices, each with tradeoffs.Tighter fitting is better. More likely to eliminate “false” intersections.

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Choosing a Bounding Volume

Lots of choices, each with tradeoffs.Tighter fitting is better.Simpler shape is better.

Make it faster to compute with.

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Choosing a Bounding Volume

Lots of choices, each with tradeoffs.Tighter fitting is better.Simpler shape is better.Rotation Invariant is better.

Easier to update as object moves.

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Choosing a Bounding Volume

Lots of choices, each with tradeoffs.Tighter fitting is better.Simpler shape is better.Rotation Invariant is better.Convex is usually better.

Gives simpler shape, easier computation.

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Common Bounding Volumes: Sphere

Rotationally invariant. Usually fast to compute with.Store: center point and radius.

Center point: object’s center of mass.

Radius: distance of farthest point on object from center of mass.

Often not very tight fit.

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Common Bounding Volumes:Axis Aligned Bounding Box (AABB)

Very fast to compute with.Store: max and min along x, y

axes. Look at all points and record max, min.Moderately tight fit.Must update after rotation.

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Common Bounding Volumes:Oriented Bounding Box (OBB)

Store rectangle oriented to best fit the object.

Store: Center.Orthonormal set of axes.Extent along each axis.

Tight fit, but takes work to get good initial fit.

Computation is slower than for AABBs.

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Testing for Collision

Will depend on type of objects and bounding volumes.

Specialized algorithms for each:Sphere/sphereAABB/AABBOBB/OBB

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Collision Test Sphere vs. Sphere

Find distance between centers of spheres.Compare to sum of sphere radii.

If distance is less, they collide.For efficiency, check squared distance vs. square of

sum of radii.

dr2

r1

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Collision Test AABB vs. AABB

Project AABBs onto given axes.If overlapping on all axes, the boxes overlap.

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Collision Test OBB vs. OBB

Separating Axis Theorem:Two convex shapes do not overlap if and only if there exists an axis such that the projections of the two shapes do not overlap.

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Enumerating Separating Axes

Two convex shapes do not overlap if and only if there exists an axis such that the projections of the two shapes do not overlap.

How do we find axes to test for overlap?

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Enumerating Separating Axes

Two convex shapes do not overlap if and only if there exists an axis such that the projections of the two shapes do not overlap.

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Enumerating Separating Axes

2D: check axis aligned with normal of each face.3D: check axis aligned with normal of each face and

cross product of each pair of edges.

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Enumerating Separating Axes

2D: check axis aligned with normal of each face.3D: check axis aligned with normal of each face and

cross product of each pair of edges.

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Enumerating Separating Axes

Two convex shapes do not overlap if and only if there exists an axis such that the projections of the two shapes do not overlap.

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Reduce number of object pair tests

One solution is to partition space uniformly.

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Reduce number of object pair tests

Another solution is the plane sweep algorithm.

C

B

R

A

x

y

A 0 A 1 R 0 B0 R 1 C 0 C 1B1

B0

B1A 1

A 0

R 1

R 0

C 1

C 0

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References Textbook: Introduction to Game Development by Steve

Rabin, 2010, Second Edition, ISBN: 1584506792

http://coitweb.uncc.edu/~tbarnes2/GameDesignFall05/.../Ch4.2-CollDet.ppt

http://www.sfu.ca/~shaw/iat410/Lectures/08CollDet.ppt

http://www.cs.duke.edu/courses/cps004/spring04/notes/collision.ppt