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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.

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Computer game design and development

Computer Game Design and Development

Mathematics, Collision, and Physics

Havok Destruction





Collision approximations minkowski sum sweep origin of x across y
Collision ApproximationsMinkowski Sum – sweep origin of X across Y



Performance
Performance

Possible collisionbetween R and B

since overlap in

all axis (2 in this case)

Subdivide such that on averageone object in each cell.


Terrain collision
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
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
Particle Physics Basics

  • Use consistent units (SI)

  • Particles

    • 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






Rigid body collision center of mass consideration
Rigid Body CollisionCenter of Mass Consideration


Physics engines
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


Computer game design and development
Demo

http://www.havok.com/content/view/584/96/

http://www.tokamakphysics.com/index.htm