How can I add a curve to a geometry using threejs?

Questions
1

I am creating a 3D plane using the pseudo code below.

  var point_records = [
    new THREE.Vector3(0,  0, 0),
    new THREE.Vector3(100,0, 0),
    new THREE.Vector3(100,50, 0),
    new THREE.Vector3(0,50, 0),
  ]

  let shape = new three.Shape(point_records); 

  let geometry = new three.ExtrudeBufferGeometry(shape, {
      depth: 1,
      bevelEnabled: false,
      steps: 1,
      bevelThickness: 0,
      bevelSize: 10,
      bevelSegments: 0,
      material: 0,
      extrudeMaterial: 1
    } );
    
  var mesh = new three.Mesh(geometry, materials);

I am limited to use a list of coordinates as a starting point for the shape. (there can be 5 or move points)
This creates a 3d flat plane. I want to add a curve to this plane.

My initial idea is that I need to subdivide the plane into a lot of smaller triangles so I can manipulate their coordinates. But I am not sure how to proceed.
I am trying to add a curve to the geometry like this.

Screenshot 2023-04-21 at 16.53.01
Screenshot 2023-04-21 at 16.53.011388×724 65.8 KB

2

you can start by making a picture of what the end result should look like (for example me - I have no idea)

3

Thanks, I added a photo I found from the internet, I hope this makes it make sense a bit more.

4

Why not bend PlaneGeometry?
Or use CylinderGeometry?

5

The coordinates are dynamic and it can be 3 points, or 5 points,

6

the simplest way to do this would be like this

My initial idea is that I need to subdivide the plane into a lot of smaller triangles

yes, do that