想要在地图上绘制自由图形，只需要在new Draw的时候多加一个配置项就行。

 function addInteraction() {
      const value = typeSelect.value;
      if (value !== "None") {
        draw = new Draw({
          source: source,
          type: typeSelect.value,
          freehand: true, //是否自由绘制
        });
        map.addInteraction(draw);
      }
    }

 完整代码：

<template>
  <div class="box">
    <h1>Freehand Drawing</h1>
    <div id="map"></div>
    <form>
      <label for="type">Geometry type &nbsp;</label>
      <select id="type">
        <option value="LineString">LineString</option>
        <option value="Polygon">Polygon</option>
        <option value="Circle">Circle</option>
        <option value="None">None</option>
      </select>
    </form>
  </div>
</template>

<script>
import Draw from "ol/interaction/Draw.js";
import Map from "ol/Map.js";
import View from "ol/View.js";
import StadiaMaps from "ol/source/StadiaMaps.js";
import { OSM, Vector as VectorSource } from "ol/source.js";
import { Tile as TileLayer, Vector as VectorLayer } from "ol/layer.js";
var arc = require("arc");
export default {
  name: "",
  components: {},
  data() {
    return {
      map: null,
      extentData: "",
    };
  },
  computed: {},
  created() {},
  mounted() {
    const raster = new TileLayer({
      source: new StadiaMaps({
        layer: "outdoors",
      }),
    });

    const source = new VectorSource({ wrapX: false });

    const vector = new VectorLayer({
      source: source,
    });

    const map = new Map({
      layers: [raster, vector],
      target: "map",
      view: new View({
        center: [-11000000, 4600000],
        zoom: 4,
      }),
    });

    const typeSelect = document.getElementById("type");

    let draw; 
    function addInteraction() {
      const value = typeSelect.value;
      if (value !== "None") {
        draw = new Draw({
          source: source,
          type: typeSelect.value,
          freehand: true,
        });
        map.addInteraction(draw);
      }
    }

    typeSelect.onchange = function () {
      map.removeInteraction(draw);
      addInteraction();
    };

    addInteraction();
  },
  methods: {},
};
</script>

<style lang="scss" scoped>
#map {
  width: 100%;
  height: 500px;
}
.box {
  height: 100%;
}
</style>