网页CAD的mxdraw库实现Autocad中的圆

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，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（https://help.mxdraw.com/?pid=32）中的《如何在自己系统中浏览dwg文件》章节，如下图所示：

如果还有不清楚的，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]https://mxcadx.gitee.io/mxdraw_api_docs/classes/MxDbCircleShape.html。

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：

需要注意的是MxDbCircleShape继承自[MxDbEllipseShape](https://mxcadx.gitee.io/mxdraw_api_docs/classes/MxDbEllipseShape.html)，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，在Autocad中绘制圆的方式有很多种, 下面介绍两种方式来绘制圆：

方法一：两点绘制圆

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()

方法二：三点绘制圆

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 threePointsToDeterm.NETheCenterOfTheCircle = (

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()

效果图如下:

Demo源码：

https://gitee.com/mxcadx/mxdraw-article/tree/master/mxdraw%E5%BA%93%E5%AE%9E%E7%8E%B0autocad%E4%B8%AD%E7%9A%84%E5%9C%86