Simulating Mouse Movement

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If you've ever had to display an interactive animation during a live talk or a class, then you may know that it's not always easy to interact with your slides and while talking.

This happened to me when I needed to show this particles demo to my students. I didn't want to have to stay next to my computer to move my mouse in order to show off the demo.

See the Pen
Particles (on move) by Louis Hoebregts (@Mamboleoo)
on CodePen.

If you do not interact with the iframe, you will see nothing but a blank space. As soon as you start moving your mouse or your finger, you can see the animation.

For that reason, I created the same demo but I used some extra code to simulate someone interacting with the demo.

See the Pen
Particles (fake) by Louis Hoebregts (@Mamboleoo)
on CodePen.

Simplex noise

The trick here is to use an algorithm that will generate "smooth" random positions. If we use a classic random function, the fake mouse will be at a purely random position on every frame. What we want is to have a position on every frame that is directly linked to the previous one. Thankfully, there is a technique that does exactly what we need: Simplex noise (or more commonly known as Perlin noise).

Let's take a look at this image where the height of each column is defined with random values on top, and values from Simplex noise algorithm below.

You can quickly notice that the bottom graph seems much smoother because every column height is connected to the previous one. Those graphs are only showing one dimension (the x-axis, from left to right) but with Simplex noise you can get values in multiples dimensions. In our case, we will need two dimensions for the X and Y coordinates of the fake mouse we're simulating.

If you are more interested to know how Simplex noise works, check out the video "I.5: Perlin Noise - The Nature of Code" by Daniel Shiffman

Get noise coordinates

The first thing we need to make our demo work is to implement a script that generates noise. In my case, I'm using this script by Seph.

Once the noise script is loaded, we can start using it on every frame to make our mouse move.

I will be using an image of a mouse for the demos that I put on position: fixed; with a class .mouse, but you could animate anything else for your own projects.

So, let's take a look at the code:

// We retrieve the image from the DOM
const el = document.querySelector('.mouse');

// The render function is called on every frame
function render (a) {
  // The a variable is the amount of milliseconds since we started our script
  
  // Get a noise value based on the elapsed time to get a new value on every frame
  // This noise algorithm is returning values between [-1, 1] so we need to map them to [0, 1] by adding one to the value and dividing it by 2
  const noiseX = (noise.simplex2(0, a*0.0005) + 1) / 2;
  // We get another noise value for the y axis but because we don't want the same value than x, we need to use another value for the first parameter
  const noiseY = (noise.simplex2(1, a*0.0005) + 1) / 2;
  
  // Convert the noise values from [0, 1] to the size of the window
  const x = noiseX * window.innerWidth;
  const y = noiseY * window.innerHeight;
  
  // Apply the x & y coordinates on our element
  el.style.transform = `translate(${x}px, ${y}px)`;
  
  // Call the render function once the browser is ready to make it an infinite loop
  requestAnimationFrame(render);
}

// Ask the browser to call render to start our animation
requestAnimationFrame(render);

Here is the result we get with the above script:

See the Pen
Virtual user 1 by Louis Hoebregts (@Mamboleoo)
on CodePen.

Allow interactivity

With the current code, we are not allowed to interact with our demo anymore. Let's add a bit more code to use our real mouse position when we interact with the demo and switch back to a fake mouse as soon as we stop.

const el = document.querySelector('.mouse');
let lastMove = 0;

// When the mouse is being moved
function onMouseMove (e) {
  // Get the x and y coordinates
  x = e.clientX;
  y = e.clientY;
  
  // Save the last move time
  lastMove = Date.now();
}

// Update the mouse position based on x & y
function updateMouse (x, y) {
  el.style.transform = `translate(${x}px, ${y}px)`;
}

function render (a) {
  // Check if last move was more than 500ms ago
  if (Date.now() - lastMove > 500) {
    // Generate a fake mouse position
    ...
    updateMouse(x, y);
  }
}

// Listen to mouse events
window.addEventListener('mousemove', onMouseMove);

Now, if you move your mouse, the fake mouse will follow yours. If you stop moving for 500ms, the fake mouse will start moving again.

See the Pen
Virtual user 3 by Louis Hoebregts (@Mamboleoo)
on CodePen.

Customized movement

The speed of the mouse can be updated by changing the value of the third parameter. So far, we are setting this value by taking the elapsed time multiplied by 0.0005, which is equal to a/2000.

// Define a speed ratio
const speed = a * 0.0005;
// Use the speed
const noiseX = (noise.simplex3(1, 0, speed) + 1) / 2;

We can also add a bit more randomness in the changes of direction by adding more noise from its position.

let random = 0;
function render (a) {
  ...
  // Update the random value
  random += 0.1;
  // Compute a x random offset based on the window width
  const randX = noise.simplex3(1, 0, random) * window.innerWidth * 0.1;
  // Compute a y random offset based on the window height
  const randY = noise.simplex3(3, 0, random) * window.innerHeight * 0.1;
  
  // Define the x & y values based on (noise * screen) + randomness
  const x = noiseX * innerWidth + randX;
  const y = noiseY * innerHeight + randY;
  ...
}

Play with the inputs to see how speed and randomly calculated values can influence the fake mouse movement.

See the Pen
Virtual user 4 by Louis Hoebregts (@Mamboleoo)
on CodePen.

More mice

Now that we have created one fake mouse, why not create 500 of them?

See the Pen
Virtual user 5 by Louis Hoebregts (@Mamboleoo)
on CodePen.

I now use this trick for almost all my demos. I think it's really cool to be able to display a project without using a video or being forced to keep moving the mouse randomly while trying to talk about the demo.

If you have any questions or remarks, please leave a comment below or ping me on Twitter.

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