🗊 Презентация Fast and Simple Physics using Sequential Impulses

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Слайды и текст этой презентации

Слайд 1


Fast and Simple Physics using Sequential Impulses Erin Catto Crystal Dynamics
Описание слайда:
Fast and Simple Physics using Sequential Impulses Erin Catto Crystal Dynamics

Слайд 2


Physics Engine Checklist Collision and contact Friction: static and dynamic Stacking Joints Fast, simple, and robust
Описание слайда:
Physics Engine Checklist Collision and contact Friction: static and dynamic Stacking Joints Fast, simple, and robust

Слайд 3


Box2D Demo It’s got collision It’s got friction It’s got stacking It’s got joints Check the code, it’s simple!
Описание слайда:
Box2D Demo It’s got collision It’s got friction It’s got stacking It’s got joints Check the code, it’s simple!

Слайд 4


Fast and Simple Physics Penalty method? Nope Linear complementarity (LCP)? Nope Joint coordinates (Featherstone)? Nope Particles (Jakobsen)? Nope...
Описание слайда:
Fast and Simple Physics Penalty method? Nope Linear complementarity (LCP)? Nope Joint coordinates (Featherstone)? Nope Particles (Jakobsen)? Nope Impulses? Bingo!

Слайд 5


Why Impulses? Most people don’t hate impulses The math is almost understandable Intuition often works Impulses can be robust
Описание слайда:
Why Impulses? Most people don’t hate impulses The math is almost understandable Intuition often works Impulses can be robust

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Making Impulses not Suck Impulses are good at making things bounce. Many attempts to use impulses leads to bouncy simulations (aka jitter). Forget...
Описание слайда:
Making Impulses not Suck Impulses are good at making things bounce. Many attempts to use impulses leads to bouncy simulations (aka jitter). Forget static friction. Forget stacking.

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Impulses without the Bounce Forget bounces for a moment. Let’s concentrate on keeping things still. It’s always easy to add back in the bounce.
Описание слайда:
Impulses without the Bounce Forget bounces for a moment. Let’s concentrate on keeping things still. It’s always easy to add back in the bounce.

Слайд 8


The 5 Step Program Accept penetration Remember the past Apply impulses early and often Pursue the true impulse Update position last
Описание слайда:
The 5 Step Program Accept penetration Remember the past Apply impulses early and often Pursue the true impulse Update position last

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Penetration Performance Simplicity Coherence Game logic Fewer cracks
Описание слайда:
Penetration Performance Simplicity Coherence Game logic Fewer cracks

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Algorithm Overview Compute contact points Apply forces (gravity) Apply impulses Update position Loop
Описание слайда:
Algorithm Overview Compute contact points Apply forces (gravity) Apply impulses Update position Loop

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Contact Points Position, normal, and penetration Box-box using the SAT Find the axis of minimum penetration Find the incident face on the other box...
Описание слайда:
Contact Points Position, normal, and penetration Box-box using the SAT Find the axis of minimum penetration Find the incident face on the other box Clip

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Box-Box SAT First find the separating axis with the minimum penetration. In 2D the separating axis is a face normal.
Описание слайда:
Box-Box SAT First find the separating axis with the minimum penetration. In 2D the separating axis is a face normal.

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Box-Box Clipping Setup Identify reference face Identify incident face
Описание слайда:
Box-Box Clipping Setup Identify reference face Identify incident face

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Box-Box Clipping Clip incident face against reference face side planes (but not the reference face). Consider clip points with positive penetration.
Описание слайда:
Box-Box Clipping Clip incident face against reference face side planes (but not the reference face). Consider clip points with positive penetration.

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Feature Flip-Flop Which normal is the separating axis? Apply weightings to prefer one axis over another. Improved coherence.
Описание слайда:
Feature Flip-Flop Which normal is the separating axis? Apply weightings to prefer one axis over another. Improved coherence.

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Apply Forces
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Apply Forces

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Impulses Impulses are applied at each contact point. Normal impulses to prevent penetration. Tangent impulses to impose friction.
Описание слайда:
Impulses Impulses are applied at each contact point. Normal impulses to prevent penetration. Tangent impulses to impose friction.

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Computing the Impulse
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Computing the Impulse

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Linear Momentum
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Linear Momentum

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Relative Velocity
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Relative Velocity

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The Normal Impulse
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The Normal Impulse

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Bias Impulse Give the normal impulse some extra oomph. Proportional to the penetration. Allow some slop. Be gentle.
Описание слайда:
Bias Impulse Give the normal impulse some extra oomph. Proportional to the penetration. Allow some slop. Be gentle.

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Bias Velocity
Описание слайда:
Bias Velocity

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Bias Impulse
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Bias Impulse

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Friction Impulse
Описание слайда:
Friction Impulse

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Sequential Impulses Apply an impulse at each contact point. Continue applying impulses for several iterations. Terminate after: - fixed number of...
Описание слайда:
Sequential Impulses Apply an impulse at each contact point. Continue applying impulses for several iterations. Terminate after: - fixed number of iterations - impulses become small

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Naïve Impulses
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Naïve Impulses

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Where Did We Go Wrong? Each contact point forgets its impulse history. Each contact point requires that every impulse be positive. There is no way to...
Описание слайда:
Where Did We Go Wrong? Each contact point forgets its impulse history. Each contact point requires that every impulse be positive. There is no way to recover from a bad impulse.

Слайд 29


Accumulated Impulses
Описание слайда:
Accumulated Impulses

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The True Impulse Each impulse adds to an accumulated impulse for each contact point. The accumulated impulse approaches the true impulse (hopefully)....
Описание слайда:
The True Impulse Each impulse adds to an accumulated impulse for each contact point. The accumulated impulse approaches the true impulse (hopefully). True impulse: an exact global solution.

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Accumulated Impulse Clamp the accumulated impulse, not the incremental impulses.
Описание слайда:
Accumulated Impulse Clamp the accumulated impulse, not the incremental impulses.

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Correct Clamping
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Correct Clamping

Слайд 33


Position Update Use the new velocities to integrate the positions. The time step is complete.
Описание слайда:
Position Update Use the new velocities to integrate the positions. The time step is complete.

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Extras Coherence Feature-based contact points Joints Engine layout Loose ends 3D Issues
Описание слайда:
Extras Coherence Feature-based contact points Joints Engine layout Loose ends 3D Issues

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Coherence Apply old accumulated impulses at the beginning of the step. Less iterations and greater stability. We need a way to match old and new...
Описание слайда:
Coherence Apply old accumulated impulses at the beginning of the step. Less iterations and greater stability. We need a way to match old and new contacts.

Слайд 36


Feature-Based Contact Points Each contact point is the result of clipping. It is the junction of two different edges. An edge may come from either...
Описание слайда:
Feature-Based Contact Points Each contact point is the result of clipping. It is the junction of two different edges. An edge may come from either box. Store the two edge numbers with each contact point – this is the Contact ID.

Слайд 37


Contact Point IDs
Описание слайда:
Contact Point IDs

Слайд 38


Joints Specify (constrain) part of the motion. Compute the impulse necessary to achieve the constraint. Use an accumulator to pursue the true...
Описание слайда:
Joints Specify (constrain) part of the motion. Compute the impulse necessary to achieve the constraint. Use an accumulator to pursue the true impulse. Bias impulse to prevent separation.

Слайд 39


Revolute Joint Two bodies share a common point. They rotate freely about the point.
Описание слайда:
Revolute Joint Two bodies share a common point. They rotate freely about the point.

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Revolute Joint The joint knows the local anchor point for both bodies.
Описание слайда:
Revolute Joint The joint knows the local anchor point for both bodies.

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Relative Velocity The relative velocity of the anchor points is zero.
Описание слайда:
Relative Velocity The relative velocity of the anchor points is zero.

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Linear Momentum Apply linear momentum to the relative velocity to get:
Описание слайда:
Linear Momentum Apply linear momentum to the relative velocity to get:

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K Matrix 2-by-2 matrix in 2D, 3-by-3 in 3D. Symmetric positive definite. Think of K as the inverse mass matrix of the constraint.
Описание слайда:
K Matrix 2-by-2 matrix in 2D, 3-by-3 in 3D. Symmetric positive definite. Think of K as the inverse mass matrix of the constraint.

Слайд 44


Bias Impulse The error is the separation between the anchor points
Описание слайда:
Bias Impulse The error is the separation between the anchor points

Слайд 45


Engine Layout The World class contains all bodies, contacts, and joints. Contacts are maintained by the Arbiter class.
Описание слайда:
Engine Layout The World class contains all bodies, contacts, and joints. Contacts are maintained by the Arbiter class.

Слайд 46


Arbiter An arbiter exists for every touching pair of boxes. Provides coherence. Matches new and old contact points using the Contact ID. Persistence...
Описание слайда:
Arbiter An arbiter exists for every touching pair of boxes. Provides coherence. Matches new and old contact points using the Contact ID. Persistence of accumulated impulses.

Слайд 47


Arbiters
Описание слайда:
Arbiters

Слайд 48


Collision Coherence Use the arbiter to store the separating axis. Improve performance at the cost of memory. Use with broad-phase.
Описание слайда:
Collision Coherence Use the arbiter to store the separating axis. Improve performance at the cost of memory. Use with broad-phase.

Слайд 49


More on Arbiters Arbiters are stored in a set according to the ordered body pointers. Use time-stamping to remove stale arbiters. Joints are...
Описание слайда:
More on Arbiters Arbiters are stored in a set according to the ordered body pointers. Use time-stamping to remove stale arbiters. Joints are permanent arbiters. Arbiters can be used for game logic.

Слайд 50


Loose Ends Ground is represented with bodies whose inverse mass is zero. Contact mass can be computed as a pre-step. Bias impulses shouldn’t affect...
Описание слайда:
Loose Ends Ground is represented with bodies whose inverse mass is zero. Contact mass can be computed as a pre-step. Bias impulses shouldn’t affect the velocity state (TODO).

Слайд 51


3D Issues Friction requires two axes. Align the axes with velocity if it is non-zero. Identify a contact patch (manifold) and apply friction at the...
Описание слайда:
3D Issues Friction requires two axes. Align the axes with velocity if it is non-zero. Identify a contact patch (manifold) and apply friction at the center. This requires a twist friction. Big CPU savings.

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Questions? erincatto at that domain Download the code there. Buy Tomb Raider Legend!
Описание слайда:
Questions? erincatto at that domain Download the code there. Buy Tomb Raider Legend!

Слайд 53


References Physics-Based Animation by Kenny Erleben et al. Real-Time Collision Detection by Christer Ericson. Collision Detection in Interactive 3D...
Описание слайда:
References Physics-Based Animation by Kenny Erleben et al. Real-Time Collision Detection by Christer Ericson. Collision Detection in Interactive 3D Environments by Gino van den Bergen. Fast Contact Reduction for Dynamics Simulation by Adam Moravanszky and Pierre Terdiman in Game Programming Gems 4.

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