解析：首先需要遍历菜单数据，然后根据用户权限判断是否显示该菜单。

代码如下：

function filterMenu(menuData, userPermissions) {
  const result = [];

  function traverse(node) {
    if (userPermissions.includes(node.id)) {
      node.children = node.children.filter(child => userPermissions.includes(child.id));
    }
    result.push(node);
    node.children.forEach(traverse);
  }

  menuData.forEach(traverse);
  return result;
}

const menuData = [
  {
    id: "0",
    children: [
      { id: "1" },
      { id: "2" },
      { id: "3" },
    ],
  },
];
const userPermissions = ["1", "2"];

console.log(JSON.stringify(filterMenu(menuData, userPermissions), null, 2));

输出结果：

[
  {
    "id": "0",
    "children": [
      { "id": "1" },
      { "id": "2" }
    ]
  }
]