objective c - Applying a vortex / whirlpool effect in Box2d / Cocos2d for iPhone

Question

I've used Nick Vellios' tutorial to create radial gravity with a Box2D object. I am aware of Make a Vortex here on SO, but I couldn't figure out how to implement it in my project.

I have made a vortex object, which is a Box2D circleShape sensor that rotates with a consistent angular velocity. When other Box2D objects contact this vortex object I want them to rotate around at the same angular velocity as the vortex, gradually getting closer to the vortex's centre. At the moment the object is attracted to the vortex's centre but it will head straight for the centre of the vortex, rather than spinning around it slowly like I want it to. It will also travel in the opposite direction than the vortex as well as with the vortex's rotation.

Given a vortex and a box2D body, how can I set the box2d body to rotate with the vortex as it gets 'sucked in'.

I set the rotation of the vortex when I create it like this:

b2BodyDef bodyDef;
bodyDef.type = b2_dynamicBody;
bodyDef.angle = 2.0f;
bodyDef.angularVelocity = 2.0f;

Here is how I'm applying the radial gravity, as per Nick Vellios' sample code.

-(void)applyVortexForcesOnSprite:(CCSpriteSubclass*)sprite spriteBody:(b2Body*)spriteBody withVortex:(Vortex*)vortex VortexBody:(b2Body*)vortexBody vortexCircleShape:(b2CircleShape*)vortexCircleShape{

    //From RadialGravity.xcodeproj
    b2Body* ground = vortexBody;
    b2CircleShape* circle = vortexCircleShape;
    // Get position of our "Planet" - Nick
    b2Vec2 center = ground->GetWorldPoint(circle->m_p);
    // Get position of our current body in the iteration - Nick
    b2Vec2 position = spriteBody->GetPosition();
    // Get the distance between the two objects. - Nick
    b2Vec2 d = center - position;
    // The further away the objects are, the weaker the gravitational force is - Nick
    float force = 1 / d.LengthSquared(); // 150 can be changed to adjust the amount of force - Nick
    d.Normalize();
    b2Vec2 F = force * d;
    // Finally apply a force on the body in the direction of the "Planet" - Nick
    spriteBody->ApplyForce(F, position);
    //end radialGravity.xcodeproj


}

Update I think iForce2d has given me enough info to get on my way, now it's just tweaking. This is what I'm doing at the moment, in addition to the above code. What is happening is the body gains enough velocity to exit the vortex's gravity well - somewhere I'll need to check that the velocity stays below this figure. I'm a little concerned I'm not taking into account the object's mass at the moment.

b2Vec2 vortexVelocity = vortexBody->GetLinearVelocityFromWorldPoint(spriteBody->GetPosition() );

b2Vec2 vortexVelNormal = vortexVelocity;
vortexVelNormal.Normalize();
b2Vec2 bodyVelocity = b2Dot( vortexVelNormal, spriteBody->GetLinearVelocity() ) * vortexVelNormal;

//Using a force
b2Vec2 vel = bodyVelocity;
float forceCircleX =    .6 * bodyVelocity.x;
float forceCircleY =    .6 * bodyVelocity.y;

spriteBody->ApplyForce( b2Vec2(forceCircleX,forceCircleY), spriteBody->GetWorldCenter() );

Answer 1

It sounds like you just need to apply another force according to the direction of the vortex at the current point of the body. You can use b2Body::GetLinearVelocityFromWorldPoint to find the velocity of the vortex at any point in the world. From Box2D source:

/// Get the world linear velocity of a world point attached to this body.
/// @param a point in world coordinates.
/// @return the world velocity of a point.
b2Vec2 GetLinearVelocityFromWorldPoint(const b2Vec2& worldPoint) const;

So that would be:

b2Vec2 vortexVelocity = vortexBody->GetLinearVelocityFromWorldPoint( suckedInBody->GetPosition() );

Once you know the velocity you're aiming for, you can calculate how much force is needed to go from the current velocity, to the desired velocity. This might be helpful: http://www.iforce2d.net/b2dtut/constant-speed

The topic in that link only discusses a 1-dimensional situation. For your case it is also essentially 1-dimensional, if you project the current velocity of the sucked-in body onto the vortexVelocity vector:

b2Vec2 vortexVelNormal = vortexVelocity;
vortexVelNormal.Normalize();
b2Vec2 bodyVelocity = b2Dot( vortexVelNormal, suckedInBody->GetLinearVelocity() ) * vortexVelNormal;

Now bodyVelocity and vortexVelocity will be in the same direction and you can calculate how much force to apply. However, if you simply apply enough force to match the vortex velocity exactly, the sucked in body will probably go into orbit around the vortex and never actually get sucked in. I think you would want to make the force quite a bit less than that, and I would scale it down according to the gravity strength as well, otherwise the sucked-in body will be flung away sideways as soon as it contacts the outer edge of the vortex. It could take a lot of tweaking to get the effect you want.

EDIT:

The force you apply should be based on the difference between the current velocity (bodyVelocity) and the desired velocity (vortexVelocity), ie. if the body is already moving with the vortex then you don't need to apply any force. Take a look at the last code block in the sub-section titled 'Using forces' in the link I gave above. The last three lines there do pretty much what you need if you replace 'vel' and 'desiredVel' with the sizes of your bodyVelocity and vortexVelocity vectors:

float desiredVel = vortexVelocity.Length();
float currentVel = bodyVelocity.Length();
float velChange = desiredVel - currentVel;
float force = body->GetMass() * velChange / (1/60.0); //for a 1/60 sec timestep
body->ApplyForce( b2Vec2(force,0), body->GetWorldCenter() );

But remember this would probably put the body into orbit, so somewhere along the way you would want to reduce the size of the force you apply, eg. reduce 'desiredVel' by some percentage, reduce 'force' by some percentage etc. It would probably look better if you could also scale the force down so that it was zero at the outer edge of the vortex.