Push particles away from mouseposition in glsl and three js

I have the following setup for my THREE.Points Object:

        this.particleGeometry = new THREE.BufferGeometry()
        this.particleMaterial = new THREE.ShaderMaterial(
            {
                vertexShader: vshader,
                fragmentShader: fshader,
                blending: THREE.AdditiveBlending,
                depthWrite: false,
                uniforms: {
                    uTime: new THREE.Uniform(0),
                    uMousePosition: this.mousePosition
                }
            }
        )

and then some code to place points in the BufferGeometry on a sphere. That is working fine.

I also set up a Raycaster to track the mouse position intersecting a hidden plane and then update the uniform uMousePosition accordingly. That also works fine, I get the mouse position sent to my vertex shader.

Now I am trying to make the particles that are in a certain distance d to the mouse push away from it where the closest ones are pushed most of course, and also apply a gravity back to their original position to restore everything after time.

So here is what I have in my vertex shader:

void main() {
float lerp(float a, float b, float amount) {
    return a + (b - a) * amount;
}

void main() {
    vec3 p = position;

    float dist = min(distance(p, mousePosition), 1.);

    float lerpFactor = .2;

    p.x = lerp(p.x, position.x * dist, lerpFactor);
    p.y = lerp(p.y, position.y * dist, lerpFactor);
    p.z = lerp(p.z, position.z * dist, lerpFactor);//Mouse is always in z=0

    vec4 mvPosition = modelViewMatrix * vec4(p, 1.);
    gl_PointSize = 30. * (1. / -mvPosition.z );
    gl_Position = projectionMatrix * mvPosition;
}
}

And here is what it looks like when the mouse is outside the sphere (added a small sphere that moves with the mouseposition to indicate the mouseposition)

And here when the mouse is inside:

Outside already looks kind of correct, but mouse inside only moves the particles closer back to their original position, where it should push them further outside instead. I guess I somehow have to determine the direction of the distance.

Also, the lerp method does not lerp, the particles directly jump to their position.

So I wonder how I get the correct distance to the mouse to always move the particles in a certain area and also how to animate the lerp / gravity effect.

That's how you could do it as a first approximation:

body{
  overflow: hidden;
  margin: 0;
}

<script type="module">
import * as THREE from "https://cdn.skypack.dev/three@0.136.0";
import {OrbitControls} from "https://cdn.skypack.dev/three@0.136.0/examples/jsm/controls/OrbitControls.js";
import * as BufferGeometryUtils from "https://cdn.skypack.dev/three@0.136.0/examples/jsm/utils/BufferGeometryUtils.js";

let scene = new THREE.Scene();
let camera = new THREE.PerspectiveCamera(60, innerWidth / innerHeight, 1, 100);
camera.position.set(0, 0, 10);
let renderer = new THREE.WebGLRenderer();
renderer.setSize(innerWidth, innerHeight);
document.body.appendChild(renderer.domElement);

let controls = new OrbitControls(camera, renderer.domElement);

let marker = new THREE.Mesh(new THREE.SphereGeometry(0.5, 16, 8), new THREE.MeshBasicMaterial({color: "red", wireframe: true}));
scene.add(marker);

let g = new THREE.IcosahedronGeometry(4, 20);
g = BufferGeometryUtils.mergeVertices(g);
let uniforms = {
  mousePos: {value: new THREE.Vector3()}
}
let m = new THREE.PointsMaterial({
  size: 0.1,
  onBeforeCompile: shader => {
    shader.uniforms.mousePos = uniforms.mousePos;
    shader.vertexShader = `
      uniform vec3 mousePos;
      ${shader.vertexShader}
    `.replace(
      `#include <begin_vertex>`,
      `#include <begin_vertex>
        
        vec3 seg = position - mousePos;
        vec3 dir = normalize(seg);
        float dist = length(seg);
        if (dist < 2.){
          float force = clamp(1. / (dist * dist), 0., 1.);
          transformed += dir * force;
        }
      
      `
    );
    console.log(shader.vertexShader);
  }
});
let p = new THREE.Points(g, m);
scene.add(p);

let clock = new THREE.Clock();

renderer.setAnimationLoop( _ => {
  let t = clock.getElapsedTime();
  marker.position.x = Math.sin(t * 0.5) * 5;
  marker.position.y = Math.cos(t * 0.3) * 5;
  uniforms.mousePos.value.copy(marker.position);
  renderer.render(scene, camera);
})
</script>