网页CAD的mxdraw库实现Autocad中的圆

前言

Web端显示CAD图纸的应用场景很广泛，单纯的浏览DWG逐渐满足不了用户的实际需求，浏览的同时再加上简单的绘制和批注更符合大家的应用场景，

在线CAD功能测试：https://demo.mxdraw3d.com:3000/mxcad/

接下来我们讲一下如何利用Mxdraw库实现AutoCAD中的画圆命令。

首先我们知道DWG图纸要在网页上显示需要安装转换程序，在测试开始之前，我们要熟悉转换方法和原理，请查看快速入门中的《如何在自己系统中浏览dwg文件》章节，如下图所示：

如果还有疑问可以查看：https://help.mxdraw.com/?pid=107中《mxdraw前端库预览图纸》章节，如下图：

关于[MxDbCircleShape]

mxdraw库是一款用于绘制CAD图形的JavaScript库，它提供了一系列的图形形状类，可以实现类似于Autocad的绘图功能，在此之前先看一下圆弧形状类的描述：

[MxDbCircleShape圆(弧)形状类]，基于这个形状类, 我们可以实现类似autocad绘制圆的功能，首先我们先通过继承类的方式，为圆提供可以改变这个圆的夹点，代码如下：

import { MxDbCircleShape } from "mxdraw";
 
class MxDbCircle extends MxDbCircleShape {
 
   /**是否闭合到中心位置 */
 
  isClosedToCenter = false
 
  /**
 
   * 返回自定义对象的夹点.
 
   * @param
 
   * @returns Array<THREE.Vector3>
 
   */
 
  getGripPoints() {
 
    const { x, y, z } = this.center;
 
    // 计算圆的上下左右夹点
 
    let upPoint = new THREE.Vector3(x, y + this.radius, z),
 
      downPoint = new THREE.Vector3(x, y - this.radius, z),
 
      leftPoint = new THREE.Vector3(x - this.radius, y, z),
 
      rightPoint = new THREE.Vector3(x + this.radius, y, z);
 
    return [this.center, upPoint, downPoint, leftPoint, rightPoint];
 
  }
 
  /**
 
   * 移动自定义对象的夹点.
 
   * @param
 
   * @returns boolean
 
   */
 
  moveGripPointsAt(index: number, offset: THREE.Vector3) {
 
    const [center, upPoint, downPoint, leftPoint, rightPoint] =
 
      this.getGripPoints();
 
    // 改变上下左右的夹点则改变radius半径
 
    if (index === 0) this.center = center.add(offset);
 
    if (index === 1) this.radius = upPoint.add(offset).distanceTo(this.center);
 
    if (index === 2)
 
      this.radius = downPoint.add(offset).distanceTo(this.center);
 
    if (index === 3)
 
      this.radius = leftPoint.add(offset).distanceTo(this.center);
 
    if (index === 4)
 
      this.radius = rightPoint.add(offset).distanceTo(this.center);
 
    return true;
 
  }
 
}

属性列表如下：

属性名	类型	描述
center	Vector3	圆心坐标
radius	number	圆半径
startAngle	number	弧开始角度
endAngle	number	弧结束角度
clockwise	boolean	是否以顺时针方向创建（扫过）弧线
isClosedToCenter	boolean	是否闭合到中心位置

需要注意的是，MxDbCircleShape继承自 [MxDbEllipseShape]，因此MxDbCircleShape也拥有MxDbEllipseShape的所有属性。我们只需要知道圆心和半径就可与直接绘制一个圆了。

绘制圆的方法

方法1：两点绘制圆

参考代码如下：

import { MrxDbgUiPrPoint, MxFun, MxDbCircleShape, McEdGetPointWorldDrawObject, } from "mxdraw";
 
const drawCircleAtTwoPoints = async () => {
 
    const getPoint = new MrxDbgUiPrPoint();
 
    const circle = new MxDbCircle();
 
    // 直接确定圆心
 
    circle.center = await getPoint.go()
 
    getPoint.setUserDraw(
 
        (
 
            currentPoint: THREE.Vector3,
 
            pWorldDraw: McEdGetPointWorldDrawObject
 
        )=> {
 
            // 根据圆心和圆弧上任意一点确定半径
 
            circle.radius = circle.center.distanceTo(currentPoint)
 
            pWorldDraw.drawCustomEntity(circle);
 
            // 再绘制一根圆弧和圆心的连接线表示现在正在确定半径
 
            pWorldDraw.drawLine(circle.center, currentPoint);
 
        }
 
    );
 
    // 确定最后绘制的圆的半径
 
    circle.radius = circle.center.distanceTo(await getPoint.go())
 
    MxFun.getCurrentDraw().addMxEntity(circle);
 
}
 
drawCircleAtTwoPoints()

方法2：三点绘制圆

通过三元一次方程组求解圆心的坐标的具体步骤如下：

1）假设圆心的坐标为(cx, cy, cz)，将三个点的坐标代入圆的一般方程，得到三个方程：

a1 * cx + b1 * cy + c1 * cz + d1 = 0

a2 * cx + b2 * cy + c2 * cz + d2 = 0

a3 * cx + b3 * cy + c3 * cz + d3 = 0

2）将三个方程进行整理，得到以下形式的方程：

(a1 * b2 * c3 - a1 * b3 * c2 - a2 * b1 * c3 + a2 * b3 * c1 + a3 * b1 * c2 - a3 * b2 * c1) * cx +

(b1 * c2 * d3 - b1 * c3 * d2 - b2 * c1 * d3 + b2 * c3 * d1 + b3 * c1 * d2 - b3 * c2 * d1) * cy +

(a1 * b2 * d3 - a1 * b3 * d2 - a2 * b1 * d3 + a2 * b3 * d1 + a3 * b1 * d2 - a3 * b2 * d1) * cz +

(a1 * b2 * c3 - a1 * b3 * c2 - a2 * b1 * c3 + a2 * b3 * c1 + a3 * b1 * c2 - a3 * b2 * c1) = 0

3）根据方程的系数，将cx、cy和cz的系数分别除以(a1 * b2 * c3 - a1 * b3 * c2 - a2 * b1 * c3 + a2 * b3 * c1 + a3 * b1 * c2 - a3 * b2 * c1)，得到cx、cy和cz的值。将得到的cx、cy和cz的值作为圆心的坐标，返回一个新的THREE.Vector3对象。

4）这样就可以通过三元一次方程组的求解方法，求得三个点确定的圆心的坐标，代码如下:

export const threePointsToDetermineTheCenterOfTheCircle = (

  points: [THREE.Vector3, THREE.Vector3, THREE.Vector3]

) => {

  const [point1, point2, point3] = points;

  const { x: x1, y: y1, z: z1 } = point1;

  const { x: x2, y: y2, z: z2 } = point2;

  const { x: x3, y: y3, z: z3 } = point3;

  const a1 = y1 * z2 - y2 * z1 - y1 * z3 + y3 * z1 + y2 * z3 - y3 * z2,

    b1 = -(x1 * z2 - x2 * z1 - x1 * z3 + x3 * z1 + x2 * z3 - x3 * z2),

    c1 = x1 * y2 - x2 * y1 - x1 * y3 + x3 * y1 + x2 * y3 - x3 * y2,

    d1 = -(

      x1 * y2 * z3 -

      x1 * y3 * z2 -

      x2 * y1 * z3 +

      x2 * y3 * z1 +

      x3 * y1 * z2 -

      x3 * y2 * z1

    ),

    a2 = 2 * (x2 - x1),

    b2 = 2 * (y2 - y1),

    c2 = 2 * (z2 - z1),

    d2 = x1 * x1 + y1 * y1 + z1 * z1 - x2 * x2 - y2 * y2 - z2 * z2,

    a3 = 2 * (x3 - x1),

    b3 = 2 * (y3 - y1),

    c3 = 2 * (z3 - z1),

    d3 = x1 * x1 + y1 * y1 + z1 * z1 - x3 * x3 - y3 * y3 - z3 * z3,

    // 计算圆心的坐标

    cx =

      -(

        b1 * c2 * d3 -

        b1 * c3 * d2 -

        b2 * c1 * d3 +

        b2 * c3 * d1 +

        b3 * c1 * d2 -

        b3 * c2 * d1

      ) /

      (a1 * b2 * c3 -

        a1 * b3 * c2 -

        a2 * b1 * c3 +

        a2 * b3 * c1 +

        a3 * b1 * c2 -

        a3 * b2 * c1),

    cy =

      (a1 * c2 * d3 -

        a1 * c3 * d2 -

        a2 * c1 * d3 +

        a2 * c3 * d1 +

        a3 * c1 * d2 -

        a3 * c2 * d1) /

      (a1 * b2 * c3 -

        a1 * b3 * c2 -

        a2 * b1 * c3 +

        a2 * b3 * c1 +

        a3 * b1 * c2 -

        a3 * b2 * c1),

    cz =

      -(

        a1 * b2 * d3 -

        a1 * b3 * d2 -

        a2 * b1 * d3 +

        a2 * b3 * d1 +

        a3 * b1 * d2 -

        a3 * b2 * d1

      ) /

      (a1 * b2 * c3 -

        a1 * b3 * c2 -

        a2 * b1 * c3 +

        a2 * b3 * c1 +

        a3 * b1 * c2 -

        a3 * b2 * c1);

 

  return new THREE.Vector3(cx, cy, cz);

};

5）已经知道通过三个圆上的点计算出圆心的算法，那么我们就可以通过三个点绘制一个圆，代码如下:

import { MrxDbgUiPrPoint, MxFun, McEdGetPointWorldDrawObject, } from "mxdraw"

const drawCircleAtThreePoints = async () => {

    const getPoint = new MrxDbgUiPrPoint();

    const circle = new MxDbCircle();

    let points = [] as unknown as [THREE.Vector3, THREE.Vector3, THREE.Vector3]

    points.push(await getPoint.go())

    getPoint.setUserDraw((currentPoint, pWorldDraw) => {

        pWorldDraw.drawLine(points[0], currentPoint)

    })

    points.push(await getPoint.go())

    getPoint.setUserDraw(

        (

            currentPoint: THREE.Vector3,

            pWorldDraw: McEdGetPointWorldDrawObject

        )=> {

            circle.center = threePointsToDetermineTheCenterOfTheCircle([points[0], points[1], currentPoint])

            circle.radius = circle.center.distanceTo(currentPoint)

            pWorldDraw.drawCustomEntity(circle);

        }

    );

    points.push(await getPoint.go())

    circle.center = threePointsToDetermineTheCenterOfTheCircle(points);

    circle.radius = circle.center.distanceTo(points[0]);

    MxFun.getCurrentDraw().addMxEntity(circle);

}

drawCircleAtThreePoints()