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2d Physics of Rope

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Hello all.

 

  I want to model a rope physics in 2d. What I would like to is an infinitely thin line that represents the rope physics shape. I have the idea to have some vertices connected together to form the rope but I don't know how should I apply forces to this . 

 Do you know how the ropes in The Cut The Rope is done ?

 

Thanks.

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One way to do it at least is to treat each vertex as a small mass.

 

You then do collisions to those vertices individually.

 

Then you have some constraints which attempt to keep the rope in a rope like form (keep adjacent points at a set distance apart basically). Youll likely need a proper integrator to avoid the rope exploding all the time too...

 

 

I guess you could also test collisions against the edges for more accuracy, but testing only the points is probably sufficient in most cases if they are not too sparsely spaced.

Edited by Waterlimon

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Thanks.

So you mean for each vertex I apply the forces , and set the velocity based on a hacking mass . Then tweak the velocity based on the constraint . For collision I want to check against the lines connecting these vertices. Let's say an object with the mass of M and velocity of V hits one of the lines connecting two vertices. How should I apply the reaction here ?

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I dont know, ive never implemented anything like it.

 

I guess you could throw away the concept of edges entirely and only have vertices, but the vertices dont need to be points, they could also be lines.

 

So all you would need to change is to make collisions be against a line instead of a point, and modify them constraints such that they try to match up the endpoints of the lines instead of the centers.

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I don't know what Cut The Rope did, but it looks pretty simple to me. You can implement a rope in either 2D or 3D like this with some very simple position based dynamics. Say your rope is, like you said, an array of points that are all connected from one to another. I'm assuming we can use one end of the rope as the "anchor" that will be attached to something, like the level or a character.

 

Lets define a distance constraint that will make sure that for any point a on the rope, the next point b will stay within a specified distance:

void SolveSegment( point a, point b )
{
  dist = distance( a, b );

  if ( dist != 0 )
  {
    Vector correction = (MaxDistance / dist - 1.0) * (b - a);

    if ( a is not anchor )
    {
      a.position -= 0.5 * correction;
      b.position += 0.5 * correction;
    }
    else
      b.position += 0.8 * correction;
  }
}

You can continually run this on all the pairs of segments. Care should be taken to make sure the "anchor" point, or the first point on the rope is always passed in as the a parameter.

 

Each point on your rope should look something like this:

struct RopePoint
{
  Vector velocity;
  Vector position;
  Vector oldPosition;
};

Now all that's left is to integrate the positions of the rope based on their velocity. You can calculate velocity based on a point's previous and current position. You can probably get away with symplectic Euler and don't need to do any fancy integration.

 

So when you solve the entire rope you'll do something like this:

void Rope::SolveRope( dt )
{
  // Use velocity to integrate all points. They can have different masses if you like.
  // Apply gravity in here too.
  Integrate( dt );

  for each point a and b in rope
  {
    SolveSegment( a, b );
  }

  // Use previous and current position to set velocity
  CalculateVelocity( 1.0f / dt );
}

This is about all you'd need for a pretty nice rope! It can be attached to the world or onto a moving character, and will wave around appropriately and not stretch a whole lot. You can adjust behavior by changing the SolveSegment function to do whatever you like. You can also add in some kind of collision detection on the segments, if you were interested in doing this. It might be simpler to have pretty short segments and just approximate the collision detection with a circle on each point.

 

You can thank Erin Catto for providing resources I learned from, which let me write this post smile.png

Edited by Randy Gaul

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Oh Thanks . It was a huge help. And also thank Erin Catto.

 

Well this is not a force/accleration model so where the mass comes in ?

This is what I think it would be , correct ?

void SolveSegment( point a, point b )
{
  dist = distance( a, b );

  if ( dist != 0 )
  {
    Vector correction = (MaxDistance / dist - 1.0) * (b - a);

    if ( a is not anchor )
    {
      float TotalMass = a.mass + b.mass;
      a.position -= (b.mass)/(TotalMass)* correction;
      b.position += (a.mass)/(TotalMass) * correction;
    }
    else
      b.position += 1.0 * correction; // get rid of streches 
  }
}

I also modified it to have no streches(that way u need to account for F=kdx )

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Yeah you can do something like this. Biasing the solve will only matter if the particles have different masses. Usually you'll want to assign a single mass value for the entire cloth so that you can use it when you apply forces, since acceleration is related to mass and force. Also if you want your cloth to hit other things you'll probably want some sort of mass value for the particles.

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