Threejs splited torus is showing black dotted

my goal is to split the shape e.g. like a torus but it could be a circle triangle etc. I want to split the shape by using a custom plane. Once the torus is split-into two parts both parts need to be draggable separately.

So far I am able to split the torus but

  1. both parts torusAbove and torusBelow are displayed in black dott. It is not taking colour or texture. What is the problem here?
  2. Another issue is if I would like to highlight the intersection of tours and planes with some colour e.g. green, how can I achieve it?
<!DOCTYPE html>
<html>

<head>
  <meta charset="UTF-8">
  <title>Three.js Plane and Torus Split Example</title>
  <style>
    body {
      margin: 0;
    }
    
    canvas {
      display: block;
    }
  </style>
</head>

<body>
  <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
  <script src="https://cdn.rawgit.com/mrdoob/three.js/r128/examples/js/controls/DragControls.js"></script>
  <script src="https://cdn.rawgit.com/mrdoob/three.js/r128/examples/js/controls/OrbitControls.js"></script>
  <script>
    // 1. Set up the scene, camera, and renderer
    const scene = new THREE.Scene();
    // Set the camera's perspective
    const camera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 0.1, 1000);
    // Set up the WebGL renderer
    const renderer = new THREE.WebGLRenderer();
    renderer.setSize(window.innerWidth, window.innerHeight);
    // Append the renderer's canvas element to the document body
    document.body.appendChild(renderer.domElement);
    // Set the clear color for the renderer (background color)
    renderer.setClearColor(0x00ffff); // Black background
    // 2. Create the plane geometry and material
    const planeGeometry = new THREE.PlaneGeometry(5, 5); // 5x5 units plane
    const planeMaterial = new THREE.MeshStandardMaterial({
      color: 0x00ff00
    });
    const plane = new THREE.Mesh(planeGeometry, planeMaterial);
    scene.add(plane);
    // Position the plane
    plane.rotation.x = -Math.PI / 2; // Rotate the plane to be horizontal
    // 3. Create the torus geometry and material
    const torusGeometry = new THREE.TorusGeometry(1, 0.4, 100, 100); // Increased radialSegments to 32
    const torusMaterial = new THREE.MeshStandardMaterial({
      color: 0xffff00,
      roughness: 0.5,
      metalness: 0.5
    }); // Red color, with some roughness and metalness
    let torus = new THREE.Mesh(torusGeometry, torusMaterial);
    scene.add(torus);
    // Position the torus
    torus.position.set(0, 1, 0); // Position the torus above the plane
    // 4. Add a light source
    const ambientLight = new THREE.AmbientLight(0x404040); // Soft white light
    scene.add(ambientLight);
    const pointLight = new THREE.PointLight(0xffffff, 1);
    pointLight.position.set(5, 5, 5);
    scene.add(pointLight);
    // Position the camera
    camera.position.set(0, 5, 5); // Place the camera at (0, 5, 5)
    camera.lookAt(0, 0, 0); // Make the camera look at the origin
    // 5. Enable OrbitControls for better navigation
    const orbitControls = new THREE.OrbitControls(camera, renderer.domElement);
    // 6. Function to split the torus
    function splitTorus() {
      const planeHeight = plane.position.y;
      const posAttr = torus.geometry.attributes.position;
      const verticesAbove = [];
      const verticesBelow = [];
      for (let i = 0; i < posAttr.count; i++) {
        const vertex = new THREE.Vector3().fromBufferAttribute(posAttr, i);
        vertex.applyMatrix4(torus.matrixWorld);
        if (vertex.y >= planeHeight) {
          verticesAbove.push(vertex);
        } else {
          verticesBelow.push(vertex);
        }
      }
      const geometryAbove = new THREE.BufferGeometry().setFromPoints(verticesAbove);
      const geometryBelow = new THREE.BufferGeometry().setFromPoints(verticesBelow);
      const materialAbove = new THREE.MeshStandardMaterial({
        color: 0x0000ff,
        roughness: 0.5,
        metalness: 0.5
      }); // Blue color, with some roughness and metalness
      const materialBelow = new THREE.MeshStandardMaterial({
        color: 0xffff00,
        roughness: 0.5,
        metalness: 0.5
      }); // Yellow color, with some roughness and metalness
      const torusAbove = new THREE.Mesh(geometryAbove, materialAbove);
      const torusBelow = new THREE.Mesh(geometryBelow, materialBelow);
      scene.remove(torus);
      scene.remove(plane);
      scene.add(torusAbove);
      scene.add(torusBelow);
      torusAbove.name = 'torusAbove';
      torusBelow.name = 'torusBelow';
      return [torusAbove, torusBelow];
    }
    let [torusAbove, torusBelow] = splitTorus();
    // 7. Enable DragControls for both parts
    const dragControlsAbove = new THREE.DragControls([torusAbove], camera, renderer.domElement);
    const dragControlsBelow = new THREE.DragControls([torusBelow], camera, renderer.domElement);
    // Highlight dragged objects
    dragControlsAbove.addEventListener('dragstart', function(event) {
      event.object.material.emissive.set(0xaaaaaa);
    });
    dragControlsAbove.addEventListener('dragend', function(event) {
      event.object.material.emissive.set(0xff00ff);
    });
    dragControlsBelow.addEventListener('dragstart', function(event) {
      event.object.material.emissive.set(0xaaaaff);
    });
    dragControlsBelow.addEventListener('dragend', function(event) {
      event.object.material.emissive.set(0x0000ff);
    });
    // 8. Render the scene
    function animate() {
      requestAnimationFrame(animate);
      renderer.render(scene, camera);
    }
    animate();
    // Handle window resize
    window.addEventListener('resize', () => {
      camera.aspect = window.innerWidth / window.innerHeight;
      camera.updateProjectionMatrix();
      renderer.setSize(window.innerWidth, window.innerHeight);
    });
  </script>
</body>

</html>

Here is my sample code