Reshape vertices from a square to a circle in the vertex shader

Question

How can you change the position of instanced vertexes from a square to a circle?

I'm attempting to control the positioning of the vertices, specifically to constrain them into the shape of a circle rather than a square. I can't use the fragment shader (which I'm more comfortable with moulding shapes in) because I'm instancing the vertexes.

//UV for texture
  vUv = uv;

    vec3 pos;
    vec3 globalPos;
    vec3 tile;

    globalPos.x = offset.x-posX*delta;
    globalPos.z = offset.z-posZ*delta;

    tile.x = floor((globalPos.x + 0.5 * width) / width);
    tile.z = floor((globalPos.z + 0.5 * width) / width);

    pos.x = globalPos.x - tile.x * width;
    pos.z = globalPos.z - tile.z * width;

    pos.y = max(0.0, placeOnSphere(pos)) - radius;
    pos.y += getYPosition(vec2(pos.x+delta*posX, pos.z+delta*posZ));

    //Position of the blade in the visible patch [0->1]
  vec2 fractionalPos = 0.5 + offset.xz / width;

Can anyone point me in the right direction for how I would do this?

Picture for illustration purposes:

The entire vertex shader:

precision mediump float;
attribute vec3 position;
attribute vec3 normal;
attribute vec3 offset;
attribute vec2 uv;
attribute vec2 halfRootAngle;
attribute float scale;
attribute float index;
uniform float time;

uniform float delta;
uniform float posX;
uniform float posZ;
uniform float radius;
uniform float width;
uniform float bladeHeight;

uniform mat4 modelViewMatrix;
uniform mat4 projectionMatrix;

varying vec2 vUv;
varying vec3 vNormal;
varying vec3 vPosition;
varying float frc;
varying float idx;

const float PI = 3.1415;
const float TWO_PI = 2.0 * PI;


//https://www.geeks3d.com/20141201/how-to-rotate-a-vertex-by-a-quaternion-in-glsl/
vec3 rotateVectorByQuaternion(vec3 v, vec4 q){
  return 2.0 * cross(q.xyz, v * q.w + cross(q.xyz, v)) + v;
}

float placeOnSphere(vec3 v){
  float theta = acos(v.z/radius);
  float phi = acos(v.x/(radius * sin(theta)));
  float sV = radius * sin(theta) * sin(phi);
  //If undefined, set to default value
  if(sV != sV){
    sV = v.y;
  }
  return sV;
}

void main() {

    //Vertex height in blade geometry
    frc = position.y / float(bladeHeight);

    //Scale vertices
  vec3 vPosition = position;
    vPosition.y *= scale;

    //Invert scaling for normals
    vNormal = normal;
    vNormal.y /= scale;

    //Rotate blade around Y axis
  vec4 direction = vec4(0.0, halfRootAngle.x, 0.0, halfRootAngle.y);
    vPosition = rotateVectorByQuaternion(vPosition, direction);
    vNormal = rotateVectorByQuaternion(vNormal, direction);

  //UV for texture
  vUv = uv;

    vec3 pos;
    vec3 globalPos;
    vec3 tile;

    globalPos.x = offset.x-posX*delta;
    globalPos.z = offset.z-posZ*delta;

    tile.x = floor((globalPos.x + 0.5 * width) / width);
    tile.z = floor((globalPos.z + 0.5 * width) / width);

    pos.x = globalPos.x - tile.x * width;
    pos.z = globalPos.z - tile.z * width;

    pos.y = max(0.0, placeOnSphere(pos)) - radius;
    pos.y += getYPosition(vec2(pos.x+delta*posX, pos.z+delta*posZ));
    
    //Position of the blade in the visible patch [0->1]
  vec2 fractionalPos = 0.5 + offset.xz / width;
  //To make it seamless, make it a multiple of 2*PI
  fractionalPos *= TWO_PI;

  //Wind is sine waves in time. 
  float noise = sin(fractionalPos.x + time);
  float halfAngle = noise * 0.1;
  noise = 0.5 + 0.5 * cos(fractionalPos.y + 0.25 * time);
  halfAngle -= noise * 0.2;

    direction = normalize(vec4(sin(halfAngle), 0.0, -sin(halfAngle), cos(halfAngle)));

    //Rotate blade and normals according to the wind
  vPosition = rotateVectorByQuaternion(vPosition, direction);
    vNormal = rotateVectorByQuaternion(vNormal, direction);

    //Move vertex to global location
    vPosition += pos;

    //Index of instance for varying colour in fragment shader
    idx = index;

  gl_Position = projectionMatrix * modelViewMatrix * vec4(vPosition, 1.0);

}