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Edward PowellVectric Ltd

@VeraShackle

XNA-UK Blog

vera@XNA-UK.net

3D Collisions

Assumptions

• You have reasonable understand basic 3D rendering with BasicEffect, Components, Services and the Content Pipeline.

• You have had a crack at some 2D games• You have some ideas about the principles

2D collision detection.• You’re probably better at C# than me!

Content

• 15 mins - A bit of theory• 15 mins - Building a simple, but flexible

system • 5 mins - The Full Isaac Newton!

Elements of a collision system

• Collision detection– Have any objects collided?– Which object pairs have collided?– In what way have the objects collided?

• Collision Resolution– Simple event?– Complex interaction?– Correcting for detection lag?

Collision Detection

Discrete time step between checks

• The actual moment of collision is never going to coincide with the checking algorithm.

• So Two Options:– Look forward to find collisions about to occur

• Complex interactions, complex algorithm• Never quite sure when the next check will be

– Look back at collisions that have already occurred• Simple algorithm (relatively!)• Know time since the last check• But, have to correct things that have already occurred

Looking back (hopefully not in anger)

• Things to watch out for:– Some overlap already at the point of

detection- ‘Drill through’...– Complete containment – boundaries no

longer intersect• Swept volumes?

– Multiple apparently ‘simultaneous’ collisions

Have objects collided – the lessons from 2D?

• Pixel perfect collision was too expensive– We checked for overlapping bounding

rectangle or circle – Multiple collision shapes per object– Use hierarchy of collision areas to reduce

the pixel perfect search to a manageable area

Same principles apply in 3D - Especially under WP7!

• triangle-triangle is the new pixel perfect!• Same solutions, but replace 2D areas

with 3D entities...

Collision Entities

• XNA Intrinsics– BoundingBox (AABB)– BoundingFrustum– BoundingSphere– Plane– Ray– Model (via spheres)

• Other common ones– Capsule – swept volumes– Oriented Bounding Box (OBB)– Height map– ‘Slabs’– Discrete Oriented Polytopes (DOP)!!– Triangle Mesh

Reduced Poly Collision Skin

Collision Primitives Summary...

• We don’t need a one-to-one mapping of collision primitive to drawable object

• Several simple volumes is generally cheaper than a single more complicated one.

• We can still do high-accuracy collision tests, but limit the volume with cheaper tests first.

(Image Source: http://sharky.bluecog.co.nz )

Pruning the Collision Search Space

• Brute force• Refining Bounding Volumes• Sweep & Prune (SAP)

– Insertion sort, relies on the fact that objects tend to be in a similar state between time steps.

• Grid Registration• BSP, kd-tree, quad-tree , oct-tree...

Collision Resolution

Wotcha gonna do about it...

Approaches to Resolvers

• Distinct Resolver Class– Single location for all your resolution code– Needs to be modified as new entities are added– What collision information is needed?

• Entities Resolve their own collisions– Collision entities are self-contained– Entities need to ‘know’ about at least some

others– Easily extensible

How much information do you need about the collision?

• When did the collision occur?• Which point (or points) contacted?• Other significant properties of the

object?– Velocity– Mass– Angular Momentum, coefficient of

restitution... etc. etc.!

Implementation

• Simple Collision Manager Component– Brute force check each update for...

• ICollidable Interface– Collision check– Collision resolution

• 2 Basic Classes:– CollidableSphere– CollidablePlane

Implementation

Simple start, but...

• Bounding Spheres are calculated by the pipeline for meshes

• Discrete Oriented Polytope (DOP) – defining convex volumes using only planes.

(Image Source: epicgames.com)

Defining a volume with Planes

Has a sphere collided with a plane?

Distance = Plane.DotCoordinate(sphere.Centre)

1. If the distance is positive, the sphere is in front of the plane

2. If the distance is negative, the sphere is behind the plane

3. If the distance from the plane is less than the radius of the sphere - COLLISION

Collision with Volume

In front of 1 plane, but intersecting 0. No collision

In front = 2Intersecting = 0No Collision

In front = 2Intersecting = 1No Collision

Rule: Must be intersecting all the planes we’re in front of...?

Collision with Volume

In front = 1Intersecting = 1COLLISION

In front = 2Intersecting = 2COLLISION

Rule: Must be intersecting all the planes we’re in front of...?

In front = 0COLLISION

Volume Edges & Corners

In front = 2Intersecting = 2But no collision

Simple Collision System Demo

http://www.youtube.com/watch?v=5Xe2twpDe_8

XNACollisions_1

Duration: 1:14s

Using a Full Physics Engine

• Examples– Jitter (jitter-physics.com)

• Full & free use of dll• Source code access US$400

– BEPUPhysics (www.bepu-games.com) • Free for non-commercial use• Open Source as of last week!!

– JigLibX (jiglibx.codeplex.com)• Free• Open-source

JigLibX Phyics Demo

http://www.youtube.com/watch?v=Sc7XOJgCVdc

XNACollisions_2

Duration: 1:00s

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