Fix spring force in forceLink.

[rogerdehe]

Here is the thing, I think forceLink is mean to implement a spring force, if so, now code of the force has a issue.

1. Prove the implementation is spring force

   I just give some reason to prove this is a implementation of spring force, you can skip this part if you alredy believe this.

   According to Hooke's law:

   F = k * dl // here F is the spring force,k is a positive real number, characteristic of the spring, dl is the delta length of spring.

   And according to Newton's laws:

   F = m * a // here F is force, m is the mass of object, a is acceleration of object

   So we can get a = k * dl / m, we can set strength = k / m, then get this:

   a = strength * dl

   Then we get delta x and delta y like this:

   // if we alread computed delta x as x, delta y as y
   l = Math.sqrt(x * x + y * y);

   dl = (l - distance); acceleration = strength dl; // => strength (l - distance) dv = acceleration dt; // => strength (l - distance) dt // next (x / l) means get delta in x axis dvx = dv dt x / l; // => x (l - distance) strength dt dt / l // next (y / l) means get delta in y axis dvy = dv dt y / l; // => y (l - distance) strength dt * dt / l

   Here we do some change to the variable.

   l = Math.sqrt(x * x + y * y);
   l = (l - distances[i]) / l * strengths[i] * (dt * dt);
   x *= l, y *= l;

   You can see the only difference with here forceLink code is dt * dt and alpha.

2. My problem with compute delta x and delta y

   My problem is here:

   x = target.x - source.x; // instead of target.x + target.vx - source.x - source.vx
   y = target.y - source.y; // insrtead of target.y + target.vy - source.y - source.vy

   If we add target.vx - source.vx (call this dvx) or target.vy - source.vy (call this dvy), image that,

• spring distance is geting larger and larger, so dlx = target.x - source.x is getting lagger

• the velocity is geting smaller and smaller, so dvx = target.vx - source.vx is getting smaller

• al last, dlx + dvx will become smaller, it will make the force become smaller, then the dx and dy will change less.

[Fil]

This is addressed in https://github.com/d3/d3-force#forces:

forces may also “peek ahead” to the anticipated next position of the node,

[rogerdehe]

@Fil Sorry, I ignored this.