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Collision Detection and Resolution

Zhi YuanCourse: Introduction to Game Development

zyuan@cs.kent.edu11/28/2011

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OverviewCollision Detection Identify the intersection of objects.

Collision ResponseCalculate the appropriate response after collision.

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Collision DetectionHigh 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 ComplexityTwo directions

Complex geometry must be simplified.

Reduce number of object pair tests.

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Simplified GeometryApproximate complex objects with simpler geometry,

like this ellipsoid.

Simpler Shape is cheaper to test.

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BV: Bounding VolumeKey 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 VolumeLots of choices, each with tradeoffs.Tighter fitting is better. More likely to eliminate “false” intersections.

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Choosing a Bounding VolumeLots 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 VolumeLots 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 VolumeLots 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: SphereRotationally 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 CollisionWill 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 AxesTwo 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 AxesTwo 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 Axes2D: 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 Axes2D: 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 AxesTwo 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 testsOne solution is to partition space uniformly.

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Reduce number of object pair testsAnother solution is the plane sweep algorithm.

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A0 A 1 R 0 B0 R 1 C 0 C 1B1

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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