How to deform vertices in a planeBufferGeometry in a circular/smooth shape

Questions
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1

Hello! I am trying to make it so that when I drag points to deform a geometry, the vertices move to create a smooth, circular shape rather than going up and down to make a straight point currently VS end goal.

Here is the code I’m working with at the moment to deform the plane (after creating a planeBufferGeometry and aligning points):

var raycaster = new THREE.Raycaster();
        raycaster.params.Points.threshold = 0.40;
        var mouse = new THREE.Vector2();
        var intersects = null;
        var plane = new THREE.Plane();
        var planeNormal = new THREE.Vector3();
        var currentIndex = null;
        var planePoint = new THREE.Vector3();
        var dragging = false;

        window.addEventListener("mousedown", mouseDown, false);
        window.addEventListener("mousemove", mouseMove, false);
        window.addEventListener("mouseup", mouseUp, false);

        function mouseDown(event) {
            setRaycaster(event);
            getIndex();
            dragging = true;
        }

        function mouseMove(event) {
            if (dragging && currentIndex !== null) {
                controls.enabled = false;
                setRaycaster(event);
                raycaster.ray.intersectPlane(plane, planePoint);
                geometry.attributes.position.setZ(currentIndex, planePoint.z);
                geometry.attributes.position.needsUpdate = true;
            }
        }

        function mouseUp(event) {
            controls.enabled = true;
            dragging = false;
            currentIndex = null;
            updateCoordinates();
        }

        function getIndex() {
            intersects = raycaster.intersectObject(points);
            if (intersects.length === 0) {
                currentIndex = null;
                return;
            }
            currentIndex = intersects[0].index;
            setPlane(intersects[0].point);
        }

        function setPlane(point) {
            planeNormal.subVectors(camera.position, point).normalize();
            plane.setFromNormalAndCoplanarPoint(planeNormal, point);
        }

        function setRaycaster(event) {
            getMouse(event);
            raycaster.setFromCamera(mouse, camera);
        }

        function getMouse(event) {
            mouse.x = (event.clientX / window.innerWidth) * 2 - 1;
            mouse.y = -(event.clientY / window.innerHeight) * 2 + 1;
        }

I’ve also posted this here.

Thanks in advance!