Collision Using Spring Force

When two objects rebound after colliding with each other, it is due to a spring force, even though it may not look like it. When two billiard balls collide, the compression of the ball is limited to a miniscule fraction of its width but it still happens.

Using a spring force requires higher model rates to realistically collide faster, harder objects. The fps display in the demo shows the actual frame rate. The movie itself is set to 999 fps. On a 1.3 GHz P3 it averages about 980 actual fps.

Collision using spring force - source movie

repeat with s = 1 to 4
  if s <> me.spritenum then
    spOther = sprite(s)

    --distance components
    distX = (spOther.x) - x
    distY = (spOther.y) - y

    --pythagorean theorem to get distance
    dist = sqrt(power(distX,2) + power(distY,2))

    --spring force
    xSpring = 0
    ySpring = 0
    minDist = (sp.width + spOther.width) / 2.0 - 10
    if dist < minDist then
      springF = (minDist - dist) * .02
      xSpring = springF * -(distX/dist)
      ySpring = springF * -(distY/dist)
    end if

    xTotalForce = xTotalForce + xSpring
    yTotalForce = yTotalForce + ySpring
  end if
end repeat

The algorithm is almost identical to general gravity, so only the repeat loop is shown. Instead of calculating gravity, it calculates spring force. Spring force only acts when the objects are within a certain distance of each other, expressed as dist < minDist.

The magnitude of the spring force is given by minDist - dist. This is the restPosition - position equation from the Spring Forces section. Scaling by .02 puts the force into proportion with other values in the animation. It can be considered the stiffness of the object, the higher it is the stiffer the object.

This demo gives each object a mass, and uses the mass in the
accel = force / mass equation. The behavior of the large object shows how mass affects acceleration. When two objects collide, each experiences the same amount of force, acting in opposite directions. This force translates into a smaller acceleration for more massive objects.

Mass can be set however you'd like. In this demo it is set to the cube of the sprite width, which would roughly correspond to its mass if it was a
3-dimensional sphere.

The type of collision modelled in this demo is for round objects with no friction between them. Friction or non-round shape would cause part of the energy in the collision to go into rotational velocity, making the objects spin.

For comments on the rest of the script, see General Gravity.