Reshape vertices from a square to a circle in the vertex shader - three.js

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);
}