How can I implement gravity? I have made this: http://jsfiddle.net/X2XvC/5/ but all dots simply follow your cursor (that's not gravitation). I heard about Eulers method, but I don't know how to implement it into my code.
what I found:
void update(float dt) { position += velocity * dt + acceleration * 0.5 * dt * dt; velocity += acceleration * dt; } As Pointy already suggested, you have to affect the points' velocity vector.
Gravity is a force that is calculated by:
F_G = gamma * mass1 * mass2 / distance^2 Where gamma is the Gravitational constant and mass1 and mass2 are the objects' masses. You get the resulting acceleration with:
F_G = a * mass1 a = F_G / mass1 = gamma * mass2 / distance^2 And you'll see that the acceleration is independent of the moving object's mass. What remains is gamma * mass2 which you can set to an arbitrary constant. Whichever meets your needs best.
Now we have the length of the acceleration vector. The direction is of course normalize(cursorPosition - pointPosition). So the overall acceleration is:
d = cursorPosition - pointPosition a = constant * d / length(d)^3 Knowing this, you can update the point's velocity and speed in every frame by:
velocity += a * dt position += velocity * dt where dt is the duration of the last frame.
Here is your changed example code. The line if(distance < 6)... is used to cap the acceleration (if a point moves through the gravity center, it is infinitely accelerated).
