CODEWITHSUNDEEP
javascriptcollision-detectionpaperjs
Aron
Aron

Reputation: 9246

How to implement a repulsion between 2D circles (paperjs)

I am making a paperjs app where you have circles and each circle can move freely. Some circles are connected to each other by means of lines which would cause the circles to come nearer to one another - ie the line simulates an elastic band between circles. However the circles are not allowed to overlap, so I want to make some kind of collision repulsion. Currently I have implemented this as a repulsive force between circles. For each circle I check the location of all other circles, and each circle's velocity vector is increased in the opposite direction to the circle close to it, in proportion to how close it is to this one. So in effect something like velocityvector += -(vectorFromThereToHere / 10)

However this has the effect that between the attractive force between connected circles and the repulsive force between all circles, you end up with a continual back and forth jittering.

What then would be the best way to implement some kind of repulsion between circles that wouldn't cause any juddering but would simply allow the circles' edges to touch one another whilst not coming any closer together? In effect I want the circles to simply bump into each other, not be allowed to slide over one another, but they are allowed to slide along each other's outside edge frictionlessly to get to where their momentum carries them.

Upvotes: 2

Views: 346

Answers (1)

Tamas Hegedus
Tamas Hegedus

Reputation: 29926

You could implement an inelastic collision, followed by a position-fixing step. The idea is to apply an impulse on the objects in the direction of the normal of the impact.

// vx: velocity vector of object x
// ux: velocity vector of object x after impact
// mx: mass of the object x (1 if all objects are the same size)
// n: normal of impact (i.e.: p1-p2 in the case of circles)
// I: the coefficient of the impulse

// Equation of an inelastic collision
u1 * n = u2 * n
// Equations of the velocities after the impact
u1 = v1 + I * n / m1
u2 = v2 - I * n / m2

// solved for I:
I = (v1 - v2) * n / ((n*n)*(1/m1 + 1/m2))

When you have I you just have to apply the velocity changes. You might as well check if I > 0 before applying the impulses, to prevent the shapes stick together. Let's see how it works, and add position iterations if the balls start to overlap slowly after all these anyway.

PS: You might repeat the whole collision step in a single timeframe as well, to get better results when objects are involved in many collisions (because they are stuck together in a big ball)

Upvotes: 2

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