penetration.
We can use SAT to compute a contact manifold
in one shot.We can use GJK to build up a contact manifold point-by-point.
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Презентация на тему Contact Manifolds
Содержание
- 2. Executive SummaryConstraint solvers need contact points to
- 3. ContactContact occurs when two shapes touch.We model
- 4. Contact ManifoldsFor convex polyhedra, a contact manifold
- 5. Overlap HappensWhat we want.What we get.
- 6. Approximate ManifoldsWe use a collection of contact
- 7. Contact PointsPositionNormalPenetrationContact ID
- 8. Example ManifoldTwo points and a common normal
- 9. Contact Manifold QualityWhen objects penetrate significantly the
- 10. Fuzzinessmanifold 1manifold 2manifold 3
- 11. Extreme Fuzzinessmanifold 1manifold 2
- 12. Using the SATMainly useful for convex polyhedra
- 13. Example: 2D Box-Box SATFirst find the separating
- 14. Box-Box Clipping SetupIdentify reference faceIdentify incident faceincidentreference
- 15. Box-Box ClippingClip incident face against reference face
- 16. Feature Flip-FlopWhich normal is the min separating axis?Apply weightings to prefer one axis over another.Improved coherence.
- 17. CoherenceApply old force/impulse solution at the beginning
- 18. Feature-Based Contact PointsEach contact point is the
- 19. Contact Point IDs12
- 20. GJK Contact PointsThree cases:- No contact- Shallow contact- Deep contact
- 21. GJK Shallow ContactThe support points are scaled
- 22. GJK Contact MarginsCore ShapeMarginCore Shape
- 23. GJK Contact Pointpointnormaldistance
- 24. GJK Deep ContactAn awkward encounter …
- 25. Deep ContactUse some other algorithm.It will be
- 26. GJK ManifoldsGJK only gives one contact point
- 27. Building the Manifoldt = 0t = 1t = 2
- 28. Manifold PersistenceTrack the points in each body.If
- 29. Adding New PointsKeep a minimal set of
- 30. Manifold ReductionThis applies to one-shot and incremental
- 31. Example ReductionA TableBeforeAfter
- 32. Скачать презентацию
- 33. Похожие презентации
Executive SummaryConstraint solvers need contact points to prevent penetration.We can use SAT to compute a contact manifold in one shot.We can use GJK to build up a contact manifold point-by-point.
Слайд 2
Executive Summary
Constraint solvers need contact points to prevent
penetration.
in one shot.We can use GJK to build up a contact manifold point-by-point.
Слайд 3
Contact
Contact occurs when two shapes touch.
We model contact
to prevent penetration and to simulate friction.
Modeling contact requires
some geometry and a lot of finesse.
Слайд 4
Contact Manifolds
For convex polyhedra, a contact manifold is
ideally a single point, a line segment, or a
convex polygon.For general convex 3D shapes, the contact manifold is a convex 2D shape.
Did I mention overlap?
Слайд 6
Approximate Manifolds
We use a collection of contact points
to approximate the contact manifold.
Our goal is fast, stable,
and plausible simulation.In this sense, computing good manifolds is an art.
Слайд 9
Contact Manifold Quality
When objects penetrate significantly the contact
manifold is fuzzy.
Contact solvers like coherence.
Be consistent from step-to-step.
Слайд 12
Using the SAT
Mainly useful for convex polyhedra (boxes,
triangles, etc).
Find the axis of minimum penetration.
For edge-edge contact,
find the midpoint.For face contact, use Sutherland-Hodgeman clipping.
Слайд 13
Example: 2D Box-Box SAT
First find the separating axis
with the minimum penetration.
In 2D the separating axis is
a face normal.
Слайд 15
Box-Box Clipping
Clip incident face against reference face side
planes (but not the reference face).
Consider clip points with
positive penetration.clipping planes
Слайд 16
Feature Flip-Flop
Which normal is the min separating axis?
Apply
weightings to prefer one axis over another.
Improved coherence.
Слайд 17
Coherence
Apply old force/impulse solution at the beginning of
the step.
Fewer iterations and greater stability.
We need a way
to match old and new contacts.
Слайд 18
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 21
GJK Shallow Contact
The support points are scaled up
by a small margin to detect contact.
Compute the closest
points (no margin).This gives the position and normal.
The penetration is the margin minus the true distance.
Слайд 25
Deep Contact
Use some other algorithm.
It will be slower
than GJK, but it won’t last long.
SAT, EPA, brute
force.Read Gino’s book to learn EPA.
Слайд 26
GJK Manifolds
GJK only gives one contact point at
a time.
We hold on to and treasure each contact
point.Build a manifold over several time steps.
This automatically provides coherence.
Слайд 28
Manifold Persistence
Track the points in each body.
If the
points move too far apart, dismiss them.
This is bad
for sliding.Use Contact IDs?
Слайд 29
Adding New Points
Keep a minimal set of points
per manifold (e.g. 4 points).
Reject new points that are
too close to old points.
Слайд 30
Manifold Reduction
This applies to one-shot and incremental manifolds.
We
want to keep the minimum number of contact points
for a stable simulation.This improves performance drastically.
