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# 2D Collision detection and response - Support for fast moving objects

Started by Jul 10 2008 09:17 AM

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6 replies to this topic

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#1
Members - Reputation: **122**

Posted 10 July 2008 - 09:17 AM

Hello guys,
I'm learning about 2D collisions. And I have some issues that I can't solve.
I'm trying to implement the support for fast moving objects don't just "bypass" the collision check because of it's elevated linear velocity.
I'm using the algorithm of separating axis.
And for detecting if it will collide forward in time because of it's velocity I'm just projecting the relative linear velocity of the two objects on the axis being tested, and if the projected velocity is > than the distance between the two intervals (projected polygons on tested axis) it will collide on next frame.
So I don't know what to do in the next frame with this information.
I'll post the code of my function that tests if the polygons are separated in the given axis or not.
http://w17.easy-share.com/1700875375.html
the function is SeparatedByAxisPolygonPolygon()
Please, I really need help with this...
Thanks all

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#4
Members - Reputation: **122**

Posted 10 July 2008 - 04:11 PM

Ok, sorry if I don't explained clearly.

* I'll see the code in .rar file, thanks for reply

My problem is: When there are fast moving objects, I know if the object will collide or not in the forward time, so what I'll do with this information? If I know it'll collide forward in time, what do I need to do?

Thanks

*EDIT I really can't understand this function separatedByAxis_swept(). I know what's the d0, d1, axis etc are, but I can't understand what's t0 and t1, why swap the values, etc, can someone explain me?

* I'll see the code in .rar file, thanks for reply

My problem is: When there are fast moving objects, I know if the object will collide or not in the forward time, so what I'll do with this information? If I know it'll collide forward in time, what do I need to do?

Thanks

*EDIT I really can't understand this function separatedByAxis_swept(). I know what's the d0, d1, axis etc are, but I can't understand what's t0 and t1, why swap the values, etc, can someone explain me?

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#5
Members - Reputation: **235**

Posted 11 July 2008 - 03:00 AM

If you're worried about really fast moving objects missing a collision over a time step, why not test the collision of extruded objects?

When testing for collision between objects A, and B

let A

let A

let A' be the volume that A passes through from A

(assume you've constructed something similar for B')

Test for collision between A' and B'.

When testing for collision between objects A, and B

let A

_{s}be A at the start of the framelet A

_{d}be A at the intended destination (given that moving from A_{s}to A_{d}doesn't collide with anything)let A' be the volume that A passes through from A

_{s}to A_{d}(assume you've constructed something similar for B')

Test for collision between A' and B'.

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#6
Crossbones+ - Reputation: **2194**

Posted 11 July 2008 - 04:42 AM

Quote:

Original post by Taturana

Ok, sorry if I don't explained clearly.

* I'll see the code in .rar file, thanks for reply

My problem is: When there are fast moving objects, I know if the object will collide or not in the forward time, so what I'll do with this information? If I know it'll collide forward in time, what do I need to do?

Once you know the objects will collide at time t, you can move the objects to the time of collision, apply a collision response (make the objects bounce), then check for another collision.

Quote:

Thanks

*EDIT I really can't understand this function separatedByAxis_swept(). I know what's the d0, d1, axis etc are, but I can't understand what's t0 and t1, why swap the values, etc, can someone explain me?

The explanation isn't straight forward, and requires a mental leap.

the principle of the swept SAT I use is based on ray-casting points against polygons. The swept SAT is an extention of that algorythm.

When you trace a point against a polygon (say a axis aligned box), you will have two points of intersection, t_enter, and t_exit. for the swept SAT, t_enter and t_exit will give you the time where the two polygons enter the collision state, and when the two polygons then leave the collison state. Basically the times when the two polygons just touch each other (and there are only two).

The second time t_exit is not really useful in itself. What you usually want is the time they first collide.

BTW, The values dont really get swapped, they get 'ordered'. t_enter should always be < t_exit.

By sorting the values, we can detect when the point trace intersects or misses the polygon by comparing intervals. you can also deduce things, for example,

1) t_exit < 0.0, the collision is missed.

2) t_enter < 0.0 && t_exit > 0.0, there is an intersection.

The algorythm uses interval reduction, and that's just that particular algo works. The time of collisions for each SAT axis are manipulated in such a way that the t_enter for the polygon is the maxima of all the t_enter calculated for each SAT axis, t_exit is the minima of all the t_exit calculated for each SAT axis.

You can look at this thread which explains the algo in more details.

[Edited by - oliii on July 11, 2008 10:42:29 AM]

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#7
Members - Reputation: **122**

Posted 11 July 2008 - 07:16 PM

I tried something in code but it don't worked...

Look:

The function above is a collision test for line-polygon. If it return true means it's not colliding else it's colliding.

This function is not working... what I did wrong?

Thanks

Look:

bool CollisionBody::SeparatedByAxisLinePolygon(const Vector2D &axis, const CollisionBody *bodyToCheck, CollisionInfo &colInf)

{

double LineProjMin, LineProjMax, minB, maxB;

LineProjMin = LineProjMax = Vector2D(GetVerticePosition(1)).GetProjectedVectorOnto(axis);

{

Vector2D v0J = GetVerticePosition(2);

double length = v0J.GetProjectedVectorOnto(axis);

if(length > LineProjMax)

LineProjMax = length;

else if(length < LineProjMin)

LineProjMin = length;

}

minB = maxB = Vector2D(bodyToCheck->GetVerticePosition(1)).GetProjectedVectorOnto(axis);

for(int j = 2; j <= bodyToCheck->GetVerticesCount(); j++)

{

Vector2D v0J = bodyToCheck->GetVerticePosition(j);

double length = v0J.GetProjectedVectorOnto(axis);

if(length > maxB)

maxB = length;

else if(length < minB)

minB = length;

}

//Testing the distance of the intervals

float D0 = (maxB - LineProjMin);

float D1 = (minB - LineProjMax);

double overlapDepth;

std::stringstream ss;

float ProjectedVelocity = fabs(Vector2D(bodyToCheck->GetLinearVelocity() - GetLinearVelocity()).GetProjectedVectorOnto(axis));

if (ProjectedVelocity > 0.0000001f)

{

float t0 = D0 / ProjectedVelocity; // time of impact to d0 reaches 0

float t1 = D1 / ProjectedVelocity; // time of impact to d0 reaches 1

if (t0 > t1) { float temp = t0; t0 = t1; t1 = temp; }

overlapDepth = (t0 > 0.0f)? t0 : t1;

}

if(D0 > 0.0f && D1 < 0.0f)

{

overlapDepth += (D0 < -D1)? D0 : D1;

}

else

{

if (overlapDepth < 0.0f)

return true;

}

Vector2D currentMtd = axis.GetNormalized() * overlapDepth;

double mtdLength = currentMtd.GetLength();

if(mtdLength < colInf.length || colInf.length < 0.0f)

{

colInf.MTD = currentMtd;

colInf.length = mtdLength;

}

return false;

}

The function above is a collision test for line-polygon. If it return true means it's not colliding else it's colliding.

This function is not working... what I did wrong?

Thanks