Physics simulation in a 3D environment

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Physics simulation in a 3D environment

• Sylvain EUDIER
• MSCS Candidate

Union College May 28th, Spring 2004
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Agenda

• Why Physics Simulation?
• Where am I, where am I going?
• Start Coding
• Entry point The Spring Model
• Extension to the Flag / Cloth simulation
• Introduction to Collision Detection
• Collision improvement an example
• Conclusion

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Why Physics Simulation?

• Getting more and more interest from the game
  industry
• How does it work behind the scenes?
• Combines physics and CS

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Where am I?

• Physics are used in many programs (CAD, games,
  simulators)
• Commercial physics libraries exist
• As well as open source
• Evolution of the simulation models up to now

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Evolution Quake 2 Doom 3
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Where am I going?

• How precisely do we want to simulate the world
• How do we want to represent it
• For what expected quality / expense

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Start Coding Define the rules

• Use of C
• Representation using the OpenGL API
• Game-like precision
• Find a model for this problem (classes)
• Starting point Write a stable and easy-to-use
  CVector3D class

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The CVector3D class

• 3 constructors Default, copy, by components
• Overloading of operators
• , -, , /, , -, , /
• Methods length, normalize, unit, crossProduct
  and dotProduct

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What can I start with?

• The spring model
• Simulate the behavior of a deformable object
• under certain constraints.
• Easy to implement (as a beginning)
• Gives convincing results rapidly
• Allows me to test the architecture of my program

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The Spring Model

• To the basic formula, we add the inner friction
  (to stabilize it)

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The Spring Model

• These properties are the basics we can give to a
  mass.
• Considered as a dot

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The Spring Model

• For the computation
• L steady length
• x actual length of the spring
• u unit vector between mass1 and mass2

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Application to a rope

• The rope is made of several masses that interact
  with each other
• By changing the variables, the rope may be
  stiffer, more / less extendable
• We can create different kinds of extensible
  material

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Demonstration

• Rope simulation 1
• Rope simulation 2

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Spring Model First impressions

• () The result looks good enough for such a
  simple simulation.
• (-) The rope behaved differently on different
  machines (different speeds)
• (-) The rope cannot be very stiff

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Spring Model Speed problem

• Need for a time regulation algorithm
• Why?
• How?
• After the first try, I had a slow and fast
  behavior
• Due to the GetTickCount() function
• Use of the QueryPerformanceCounter()

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Spring Model Stiffness issue

• The stiffness problem
• Due to the Eulers approximation method

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Spring Model Stiffness issue Why?
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Euler function stability comparison
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Spring Model Extensions

• The rope does not include any bending
  information
• Can be solved using interleaved springs
  (explained later, cf. Flag)
• Stiffness problem
• Regarding the sources I found, the Runge-Kutta
  algorithm should solve the problem

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The Runge-Kutta Algorithm
Runge-Kutta 4 (55, 200000)
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Spring Model Flag simulation

• A flag is just a patch of springs
• Create nm masses
• Create (n-1)(m-1) springs
• Connect the springs to the masses
• Possibility to add a wind effect

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Spring Model Flag simulation

• Flag simulation

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Flag simulation Results

• () The mesh reacts well to the wind and gravity
• (-) The flag is harder to simulate because of the
  stiffness problem and the lack of bending factor

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Flag simulation Extensions

• Can simulate a flag flexibility with interleaved
  springs
• and add a universal repulsive force to every node

• More complex and realistic simulation

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High quality flag simulation

• Demonstration

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Collision Detection

• Why?
• How?
• Dependencies
• A strong math library vectors, matrices,
  plane-point collision, face-face collision
• Possibility to work on predefined meshes

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On the way to the collision

• Math library
• Matrices
• Overloading of arithmetic operators (, -, ,
  )
• Overloading of input / output operators (, ltlt)
• Matrices functions determinant,
  multiplications, inversions, transposition,
  identity
• Matrix-related functions rotate, scale,
  translate
• Vectors
• Collision functions PointToPlaneDistance,
  IsPointInPolygon

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Importing 3DS files

• 3DS is a standard in the industry
• I already had an importing class for 3DS files
• .3DS files have several advantages
• Face defined clockwise,
• Texture information,
• Normals information,
• And a lot more

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Into the collision

• Brute force algorithm
• CheckForCollisions()
• MakePreselection(Scene, Collisions)
• For all objects in the Collision List
• if(this object collides with another one)
• Find the collision point
• Apply the physics on the objects, at that point
• But this will never work!!!

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Buggy Collision

• Demonstration

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Into the collision (2)

• New algorithm
• Do
• Do
• ComputePhysics(NextTimeChunk)
• CheckForCollisions(Scene, Collisions)
• if(MaxPenetrationInAnObject lt Limit)
• Problem is solved
• if(Problem NOT solved)
• NextTimeChunk PreviousTime / 2
• CancelTheComputations()
• else
• ValidateTheComputations()
• While(Problem is NOT solved)
• proceed to the next time chunk
• While(TimeChunknotSimulated)

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The rollback function
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Collision improvement

• We can extend the sphere collision test to a more
  general one.
• Add a real collision and motion behavior
  (friction, rotation)
• The MakePreselection function can improve a lot
  the computation time

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Improvements and trade-offs

• The vast majority of the program use an
  aggressive MakePreselection algorithm to be able
  to deal with a lot of objects
• Optimization without loss of information

AABB Axis Aligned Bounding Box OBB Oriented
Bounding Box 6-dop Discrete Orientation
Polytope Convex Hull
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Example of an approximation algorithm

• Approximation Based on some assumptions over
• insignificant constraints of objects (has to
  look
• good enough)
• The Opposing Face Geometry algorithm
• Algorithm in 8 steps,
• The pro
• And cons

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Opposing Face Geometry algorithm

• 1. Preselection check collision between object
  A's bounding sphere and object B's bounding
  sphere.
• 2. Find the closest k faces of object A relative
  to object B.

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O.F.G. algorithm

• 3. Calculate the geometric center of the new
  selection and the bounding sphere radius.
• 4. Find the closest k faces of object B relative
  to object A's new selection of k faces.
• 5. Calculate the geometric center of object B's
  new selection of faces and their maximal bounding
  sphere radius.

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The O.F.G. algorithm

• 6. PreSelection check collision between spheres
  to determine if there is even a chance for face
  collisions.
• 7. Sort the two sets of faces by increasing
  distance
• 8. Test the two sets of faces against each other,
  starting with the closest pairs of faces.

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Pro / Cons of such this algorithm

• () This is a lot faster. Runtime of O(k2)
• Where k is usually between 4 and 8
• (k is a variable representing the number of
  faces we want to work on)
• Brute force approach would be O(nm)
• n and m could be 1000 of faces
• (-) Cannot really work on concave polygons
• This is TRUE for most of todays engines

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The discrete Time problem

• Due to the intrinsic nature of the simulation
  Time-discrete based
• If the dt variation is too big, an object might
  be teleported through another one
• Solution Extrude the silhouette of the object.
  Test this polygon for collisions

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Summary

• Springs are the basis of a lot of models and can
  be used for powerful simulations (i.e. any kind
  of elastic models)
• Collision detection needs a robust design and
  math support. There is a lot to do about
  optimization and trade-offs
• Physics simulation is a vast field where a lot of
  techniques are to be discovered

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Selection of References

• Computer Graphics with OpenGL, third Edition by
  Hearn-Baker, Prentice Hall
• Huge source of information for game programming
• www.gamedev.net
• Chris Heckers famous columns about physics
• http//www.d6.com/users/checker/dynamics.htmarti
  cles
• Everything you need to know about geometry
• http//astronomy.swin.edu.au/pbourke/geometry/
• A lot about everything, from physics to light
  computations
• http//freespace.virgin.net/hugo.elias/

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Conclusion - Discussion

• Questions? Need Explanations?
• What kind of extensions could we add to a physics
  simulator?

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References

• Collision detection
• Advanced
• Gamasutra - Features - "Advanced Collision
  Detection Techniques" 03.30.00
• Advanced Collision Detection Techniques
• Advanced Collision Detection Techniques
• Chris Hecker's Rigid Body Dynamics Information
• DDJ
• GameDev.net - Opposing Face Geometry
• GameDev.net - Simple Bounding-Sphere Collision
  Detection
• GameDev.net - Practical Collision Detection
• GameDev.net - General Collision Detection for
  Games Using Ellipsoids
• Collision Response Bouncy, Trouncy, Fun
• Gamasutra - Features - "Crashing into the New
  Year" 02.10.00
• Snooker simulation (Formulaes)
• Rotation computation
• HyperPhysics
• MODEL-BASED ANIMATION
• SIGGRAPH - Collision Detection ('88)