Computer Game Design and
Development
Mathematics, Collision, and Physics
Havok Destruction
Overlap Bisection
Limitations of Overlap Testing
Intersection Testing
Collision Approximations
Minkowski Sum – sweep origin of X across Y
Bounding Volumes
AABB
OBB
Performance
Possible collision
between R and B
since overlap in
all axis (2 in this case)
Subdivide such that on average
one object in each cell.
Terrain Collision
• Heightmap information
• Look up terrain height
• 3 LERPs – Linear Interpretation between
points
–X
–Z
– Between x and z
http://creators.xna.com/en-US/sample/collision3dheightmap
Resolving Collision
• Gross collision & subdivide if needed
• Three phases
– Prologue – ignore or trigger other events
– Collision – point of impact, new velocities
– Epilogue – destroy object, effects, damage
Particle Physics Basics
• Use consistent units (SI)
• Particles
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–
–
–
Position (p) in 3-space, vector3 (x,y,z) = p(t)
Velocity (v) = change in position over time, V(t)
Acceleration (a) = change in velocity over time, a(t)
Force (f) = results in change in acceleration over time,
F(t) = ma(t)
• Calculus
– Derivatives and integrals go from one to another
Collision Response (frictionless)
Springs & Damping
Friction
Center of Mass
Rigid Body Collision
Center of Mass Consideration
Physics Engines
• Commercial
– Game Dynamics SDK (Havok)
– Renderware Physcis
– NovodeX SDK
• Free/Shareware
– Open Dynamics Engine (ODE)
– Tokamak Game Physics SDK
– Newton Game Dynamics SDK
Demo
http://www.havok.com/content/view/584/96/
http://www.tokamakphysics.com/index.htm