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What is wrong with my SAT implementation?


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#1 Finalspace   Members   -  Reputation: 300

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Posted 10 March 2013 - 12:39 PM

Hi everybody,

 

i have implemented discrete SAT (Separating Axis Theorem) in the past successfully.

Therefore i have now remade this to fix the "fast moving issue" - calculate the time when the collision first happens - to get a value for scaling the velocity to remove the penetration in the first place.

 

What i basically do is to test two OBB with two fixed axis of (1, 0) and (0, 1) with the following algorythm:

 

- Get the relative position (distance) between the 2 OBBs (pA - pA)

- Get the relative velocity between the 2 OBBs (vA - Vb) - Just to remove the second velocity to make the second one static.

- For loop over the two axes

- Project the relative position onto the axis to get an offset based on current axis

- Project A onto current axes and get min/max projection

- Add the offset to projection of A

- Project B onto current axes and get min/max projection

- Calculate distances between min/max projections of A and B (d0, d1)

- Calculate time enter and time leave factor by divide both distances by projected velocity on axis

- Swap time enter with time leave if required (Time enter must always be smaller than time leave)

- Get the highest overlap to skip out collisions which not happens or are too late

- Time Enter is the factor used to fix the velocity.

 

These steps are implemented a simple JSFiddle demo i have written to visualize the entire process, see here:

http://jsfiddle.net/dku72/

 
Now what the problem is: There are something missing on it, because the visualized velocity/corrected projection is wrong in some cases (Inverted for Y Axis) and i havent found a solution yet to find the correct single time enter/leave factor. What i want in the end is a "Time of impact" value which can be used to fix the velocity, to project the box on the other box without penetration.

 

 

It would be really great if you can help me to fix these problems.

 

Thanks,

Final


Edited by Finalspace, 10 March 2013 - 12:41 PM.


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#2 DT....   Members   -  Reputation: 487

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Posted 10 March 2013 - 04:04 PM

Everything looks correct, except maybe this:

 

- Swap time enter with time leave if required (Time enter must always be smaller than time leave)

 

 

1)  Keep track of your latest "time enter" and earliest "time leave"

2)  If  (time enter > time leave), there is no collision.

3)  When all axes are checked and there is a collision, Time of Impact = latest "time enter"

 

HTH.



#3 Finalspace   Members   -  Reputation: 300

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Posted 12 March 2013 - 01:34 PM

Everything looks correct, except maybe this:

 

 

- Swap time enter with time leave if required (Time enter must always be smaller than time leave)

 

 

1)  Keep track of your latest "time enter" and earliest "time leave"

2)  If  (time enter > time leave), there is no collision.

3)  When all axes are checked and there is a collision, Time of Impact = latest "time enter"

 

HTH.

 

Thanks for your answer - i fixed most of the issues but i am not sure if i made it correct... one thing remains is to cancel the projection drawing when there is no real swept overlap. Ghost projections appears :(

 

I made new js fiddle: http://jsfiddle.net/sbYnp/

 

It would be glad if you can help me to make it right. It seems that its nearly fine.



#4 Finalspace   Members   -  Reputation: 300

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Posted 12 March 2013 - 03:49 PM

k i made it a little simpler and got it working now. Ghost projections still happens but these are fine, because this will be filtered out in the next collision step before i can get to the next stage to calculate the exact contact points  / pairs - wahh what a pain.

 

Here is the update: http://jsfiddle.net/sbYnp/4/



#5 Finalspace   Members   -  Reputation: 300

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Posted 18 March 2013 - 09:22 AM

Hmm, i have a problem with my implementation. If seems if i move the second object - (Displacement of B) everything goes off.

 

The resulting projection / time of factor is incorrect - because of the relative velocity. Adding the velB to the relative velocity is no solution after all.

What i am looking for is a solution to find always the correct projection (Multiply vel A to a amount that its just touching Obj B, even when obj B moves then it shoud touches the movement of Obj B). Is there a solution for that? Currently i could not come up with anything working at all sad.png

 

What i am trying to achive is to create a speculative contacts system using separating axis theorem. The essence of that technique requires that obj A vel must be decrease to a level to just touch obj A even if obj B is moving. Basically the Time-Of-Impact factor (Earliest time enter) takes care of that by multiplies the relative velocity (vA - Vb) to fix that.

 

To see that in real, check out my latest update: http://jsfiddle.net/sbYnp/6/

See the green box is wrong projected, cause it uses relative velocity.

 

It would be really great is someone can push me in the right direction.

 

Thanks,

Final


Edited by Finalspace, 18 March 2013 - 09:22 AM.





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