I am not sure if I have understood your requirements correctly.
But maybe the examples
Addon to create special / extended geometries
Construction of frames with contour/profile
https://hofk.de/main/threejs/sandboxthreep/
can help.
The area needed to close the figure must always be recalculated. But if the effort for this is not too big, it can be done quickly.
For each new point and when the slider is changed, this is done e.g. at https://hofk.de/main/threejs/ConstructFrame/ConstructFrame.html.
In the sandbox you would only have to make the appropriate adjustment in the control using sliders. This is surely only useful, if otherwise only a few parameters for the geometry are left variable and the others are made constant.
This post could also be helpful.
Create a curved plane surface which dynamically changes its size
The drawing of only a part of the total defined values:
" .setDrawRange ( start : Integer, count : Integer ) : null
Set the .drawRange property. For non-indexed BufferGeometry, count is the number of vertices to render. For indexed BufferGeometry, count is the number of indices to render.
https://threejs.org/docs/index.html#api/en/core/BufferGeometry
This allows you to define a BufferGeometry with maximum size, but only draws the existing part."
In this example this is used in the animation. ( slider left side )
https://hofk.de/main/threejs/sandboxthreei/triangulationImplicitSurface.html
function animate( ) {
g.setDrawRange( 0, range.value * 3 * progressFactor );
requestAnimationFrame( animate );
renderer.render( scene, camera );
controls.update( );
}