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copied!<p>You need to think in proper physics terms. You have a velocity, and you want to add an acceleration. That's all there is to it - the acceleration is a gradual change in velocity that will draw the enemy towards to player, allow it to overshoot, slow down (or turn) and then head back towards the player.</p> <p>Acceleration is measured as d(velocity)/time. You want to accelerate towards the player at any point in time, so every interval (second, hundredth of a second or whatever you choose) you need to add the vector between enemy and player, multiplied by some constant, to your velocity.</p> <pre><code>Velocity = Velocity + c * (Player-Enemy vector) </code></pre> <p>Constant c will depend on how fast you want to accelerate towards the player, and how often you are updating your velocity.</p> <p>If you want to 'cap' the maximum speed of the enemy so that it doesn't continue to increase the magnitude of its velocity indefinitely, you can also do so.</p> <pre><code>Velocity = Velocity * (Maximum magniture / |Velocity|) </code></pre> <p>EDIT: to clarify further, adding a Velocity simply means adding the component vectors. So </p> <pre><code>Vx = Vx + c * Ax Vy = Vy + c * Ay </code></pre> <p>where V is velocity and A is acceleration. Magnitude is measured as <code>sqrt(Vx^2 + Vy^2)</code>, ie the hypotenuse of a right triangle. So if you want maximum speed of the enemy to be m,</p> <pre><code>Vx = Vx * ( m / sqrt(Vx^2 + Vy^2) Vy = Vy * ( m / sqrt(Vx^2 + Vy^2) </code></pre>

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