官网demo 地址：

Extent Interaction

在openlayers中可以使用ExtentInteraction添加交互事件，配合shiftKeyOnly实现按住shift键绘制边界区域。 

 const map = new Map({
      layers: [
        new TileLayer({
          source: new OSM(),
        }),
      ],
      target: "map",
      view: new View({
        center: [0, 0],
        zoom: 2,
      }),
    });

    const extent = new ExtentInteraction({ condition: shiftKeyOnly });
    map.addInteraction(extent);
    

按住shift绘制矩形，按住shift键点击图形删除。

监听extentchanged事件，记录绘制的矩形数据。

// 监听 extentchanged 事件，获取矩形选择范围
extent.on("extentchanged", (event) => {
    this.extentData = event.extent;
});
 
getData() {
   console.log("结果", this.extentData);
},

完整代码：

<template>
  <div class="box">
    <h1>Extent Interaction</h1>
    <div id="map"></div>
    <el-button type="primary" @click="getData">获取数据</el-button>
  </div>
</template>

<script>
import ExtentInteraction from "ol/interaction/Extent.js";
import Map from "ol/Map.js";
import OSM from "ol/source/OSM.js";
import TileLayer from "ol/layer/Tile.js";
import View from "ol/View.js";
import { shiftKeyOnly } from "ol/events/condition.js";
export default {
  name: "",
  components: {},
  data() {
    return {
      map: null,
      extentData: "",
    };
  },
  computed: {},
  created() {},
  mounted() {
    const map = new Map({
      layers: [
        new TileLayer({
          source: new OSM(),
        }),
      ],
      target: "map",
      view: new View({
        center: [0, 0],
        zoom: 2,
      }),
    });

    const extent = new ExtentInteraction({ condition: shiftKeyOnly });
    map.addInteraction(extent);
    // 监听 extentchanged 事件，获取矩形选择范围
    extent.on("extentchanged", (event) => {
      this.extentData = event.extent;
    });
  },
  methods: {
    getData() {
      console.log("结果", this.extentData);
    },
  },
};
</script>

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