potree-sdk/src/custom/utils/math.js

import * as THREE from "../../../libs/three.js/build/three.module.js";
import searchRings from "./searchRings.js";
import {ExtendView} from '../../viewer/ExtendView.js'
 

var math = {
    getBaseLog(x, y) {//返回以 x 为底 y 的对数（即 logx y） .  Math.log 返回一个数的自然对数
        return Math.log(y) / Math.log(x);
    }
    ,
    convertVector : {
        ZupToYup: function(e){//navvis -> 4dkk
            return new THREE.Vector3(e.x,e.z,-e.y)
        },
        YupToZup: function(e){//4dkk -> navvis
            return new THREE.Vector3(e.x,-e.z,e.y)
        },
        
        
    },
    convertQuaternion: {
        ZupToYup: function(e){//navvis -> 4dkk  //不同于convertVisionQuaternion
            let rotation = new THREE.Euler(-Math.PI/2,0,0)   
            let quaternion = new THREE.Quaternion().setFromEuler(rotation)
            return e.clone().premultiply(quaternion)
            //return new THREE.Quaternion(e.x,e.z,-e.y,e.w).multiply((new THREE.Quaternion).setFromAxisAngle(new THREE.Vector3(1,0,0), THREE.Math.degToRad(90)))
        },
        YupToZup: function(e){//4dkk -> navvis
            let rotation = new THREE.Euler(Math.PI/2,0,0)
            let quaternion = new THREE.Quaternion().setFromEuler(rotation)
            return e.clone().premultiply(quaternion)
        },
        
        
    },
	 
    convertVisionQuaternion: function(e) {
        return new THREE.Quaternion(e.x,e.z,-e.y,e.w).multiply((new THREE.Quaternion).setFromAxisAngle(new THREE.Vector3(0,1,0), THREE.Math.degToRad(90)))
    },
    invertVisionQuaternion : function(e) {//反转给算法部
        var a = e.clone().multiply((new THREE.Quaternion).setFromAxisAngle(new THREE.Vector3(0,1,0), THREE.Math.degToRad(-90)))
        return new THREE.Quaternion(a.x,-a.z,a.y,a.w)
    },
    //------------
    
    getVec2Angle : function(dir1,dir2){ 
        return Math.acos( THREE.Math.clamp(this.getVec2Cos(dir1,dir2), -1,1) )  
    },
    getVec2Cos :  function(dir1,dir2){ 
        return dir1.dot(dir2) / dir1.length() / dir2.length()    
    },
    getAngle:function(vec1, vec2, axis='z'){//带方向的角度 vector3
        if(!vec1.isVector3){
            vec1 = new THREE.Vector3(vec1.x, vec1.y, 0)
            vec2 = new THREE.Vector3(vec2.x, vec2.y, 0)
        }
        var angle = vec1.angleTo(vec2)
        var axis_ = vec1.clone().cross(vec2);
        if(typeof axis == 'string'){
            if(axis_[axis] < 0){
                angle *= -1
            }
        }else{//vector3
            if(axis_.dot(axis)< 0){
                angle *= -1
            }
        }
        
        return angle
    }, 
    
    closeTo : function(a,b, precision=1e-6){ 
        let f = (a,b)=>{
            return Math.abs(a-b) < precision;
        } 
          
        if(typeof (a) == 'number'){
            return f(a, b);
        }else{
            let judge = (name)=>{
                if(a[name] == void 0)return true //有值就判断，没值就不判断
                else return f(a[name],b[name])
            }
            return judge('x') && judge('y') && judge('z') && judge('w')  
        } 
        
    }, 
     

    
	toPrecision: function (e, t) {//xzw change 保留小数
		var f = function (e, t) {
			var i = Math.pow(10, t);
			return Math.round(e * i) / i
		}
		if (e instanceof Array) {
			for (var s = 0; s < e.length; s++) {
				e[s] = f(e[s], t);
			}
			return e;
		} else if (e instanceof Object) {
			for (var s in e) {
				e[s] = f(e[s], t);
			}
			return e;
		} else if(typeof e == 'number'){
            return f(e, t)
        }else{
            return e
        }
            
        
	},
    isEmptyQuaternion: function(e) {
        return 0 === Math.abs(e.x) && 0 === Math.abs(e.y) && 0 === Math.abs(e.z) && 0 === Math.abs(e.w)
    },
    projectPositionToCanvas: function(e, t, i) {
        i = i || new THREE.Vector3,
        i.copy(e);
		var r = .5 * $('#player').width()
			, o = .5 * $('#player').height();
        return i.project(t),
        i.x = i.x * r + r,
        i.y = -(i.y * o) + o,
        i
    },
     
	
	handelPadResize:false,
	/* handelPadding : function () { //去除player左边和上面的宽高,因为pc的player左上有其他element  许钟文
		
		var pads = [];//记录下来避免反复计算
		var index = [];
		var resetPad = function(){
			pads = []; 
			index = [];
			math.handelPadResize = false; //switchview时resized为true
		}
		
		if(config.isEdit && !config.isMobile){
			window.addEventListener('resize',resetPad);
		}
		return function(x, y, domE){
			if(!config.isEdit || config.isMobile) {
				return {
					x: x,
					y: y
				}  
			}
			
			if(this.handelPadResize)resetPad(); 
			domE = domE || $('#player')[0];
			var pad;
			var i = index.indexOf(domE);
			if (i == -1){ 
				index.push(domE);
				pad = {
					x: this.getOffset("left", domE),
					y: this.getOffset("top", domE)
				}
				pads.push(pad)  
			}					
			else pad = pads[i];
			return {
				x: x - pad.x,
				y: y - pad.y
			}
		}
		
	}(),  */
	
	getOffset: function (type, element, parent) {//获取元素的边距 许钟文
		var offset = (type == "left") ? element.offsetLeft : element.offsetTop;
		if (!parent) parent = $("body")[0];
		while (element = element.offsetParent) {
			if (element == parent) break;
			offset += (type == "left") ? element.offsetLeft : element.offsetTop;
		}
		return offset;
	}

	,
    constrainedTurn: function(e) {
        var t = e % (2 * Math.PI);
        return t = t > Math.PI ? t -= 2 * Math.PI : t < -Math.PI ? t += 2 * Math.PI : t
    },
    getFOVDotThreshold: function(e) {
        return Math.cos(THREE.Math.degToRad(e / 2))
    },
    transform2DForwardVectorByCubeFace: function(e, t, i, n) {
        switch (e) {
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_POSITIVE_X:
            i.set(1, t.y, t.x);
            break;
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_NEGATIVE_X:
            i.set(-1, t.y, -t.x);
            break;
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_POSITIVE_Y:
            i.set(-t.x, 1, -t.y);
            break;
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_NEGATIVE_Y:
            i.set(-t.x, -1, t.y);
            break;
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_POSITIVE_Z:
            i.set(-t.x, t.y, 1);
            break;
        case GLCubeFaces.GL_TEXTURE_CUBE_MAP_NEGATIVE_Z:
            i.set(t.x, t.y, -1)
        }
        n && i.normalize()
    },
	
	
	
	getFootPoint : function(oldPos, p1, p2, restricInline){ //找oldPos在线段p1, p2上的垂足
		/* if(isWorld){//输出全局坐标 需要考虑meshGroup.position
			p1 = p1.clone();
			p2 = p2.clone();
			p1.y += mainDesign.meshGroup.position.y;
			p2.y += mainDesign.meshGroup.position.y;
		} */
        if(p1.equals(p2))return p1.clone()
		var op1 = oldPos.clone().sub(p1); 
		var p1p2 = p1.clone().sub(p2)
		var p1p2Len = p1p2.length()
		var leftLen = op1.dot(p1p2) / p1p2Len;
		var pos = p1.clone().add(p1p2.multiplyScalar( leftLen/p1p2Len )); 
         
        if(restricInline && pos.clone().sub(p1).dot( pos.clone().sub(p2)   ) > 0){//foot不在线段上
            if(pos.distanceTo(p1) < pos.distanceTo(p2)) pos = p1.clone();
            else pos = p2.clone();
        }
        
		return pos;
	},

	
	
	
	
	
	/**
   * 计算多边形的重心
   * @param {*} points
   */
	getCenterOfGravityPoint : function(mPoints){
		var area = 0.0;//多边形面积
		var Gx = 0.0, Gy = 0.0;// 重心的x、y

		for (var i = 1; i <= mPoints.length; i++) {
			var ix = mPoints[i % mPoints.length].x;
			var iy = mPoints[i % mPoints.length].y;
			var nx = mPoints[i - 1].x;
			var ny = mPoints[i - 1].y;
			var temp = (ix * ny - iy * nx) / 2.0;
			area += temp;
			Gx += temp * (ix + nx) / 3.0;
			Gy += temp * (iy + ny) / 3.0;
		}
		Gx = Gx / area;
		Gy = Gy / area;
		return { x: Gx, y: Gy };
	},
	 
	getBound : function(ring){
		var bound = new THREE.Box2();
		for(var j=0,len = ring.length; j<len; j++){
			bound.expandByPoint(ring[j])
		}
		return bound;
	},

	isPointInArea : function(ring, holes, point, ifAtLine){//判断点是否在某个环内, 若传递了holes代表还要不能在内环内
		var bound = this.getBound(ring);
		if(point.x < bound.min.x || point.x > bound.max.x || point.y < bound.min.y || point.y > bound.max.y)return false;
		
		 
		var inside = false;
		var x = point.x,
		  y = point.y;

		for (var i = 0, j = ring.length - 1; i < ring.length; j = i++) {
		  var xi = ring[i].x,
			yi = ring[i].y;
		  var xj = ring[j].x,
			yj = ring[j].y;
 
		  if((xi - x)*(yj - y) == (xi - x)*(yi - y) && x>=Math.min(xi,xj) && x<=Math.max(xi,xj)//xzw add
			  && y>=Math.min(yi,yj) && y<=Math.max(yi,yj)
		  ){
			  //return !!ifAtLine;//在线段上，则判断为…… （默认在外）
              return {atLine:true}
		  }
		  
		   if (((yi > y) != (yj > y)) &&
			(x < (xj - xi) * (y - yi) / (yj - yi) + xi) 
			) {
			inside = !inside;
		  } 
		  
		}
        
        if(inside && holes){
            return !holes.some(ring=>this.isPointInArea(ring, null, point, ifAtLine) )   //不能存在于任何一个二级内环内
        }else{
            return inside;
        }
        

		
	},
	
	getArea : function (ring) { //求面积  顺时针为正  来自three shape
		for (var t = ring.length, i = 0, n = t - 1, r = 0; r < t; n = r++)
			i += ring[n].x * ring[r].y - ring[r].x * ring[n].y;
		return -.5 * i
	},
    
    
    getVolume:function(faceArr){//求三角多面体的体积。和求面积同理都用鞋带计算法 https://blog.csdn.net/weixin_43414513/article/details/123758897
        //问题：怎么确定方向
        //每个三角形的顺序必须是右手螺旋法则指向物体外(外向里看为逆时针)，分别为ABC，则每个三角形和原点O构成的三棱锥体积为 (OA cross OB) dot(OC) / 6 .  结果一般朝向原点的为负，反之为正
   
    },
    
    
	isInBetween : function(a, b, c, precision) {
        // 如果b几乎等于a或c，返回false.为了避免浮点运行时两值几乎相等，但存在相差0.00000...0001的这种情况出现使用下面方式进行避免

        /* if (Math.abs(a - b) < 0.000001 || Math.abs(b - c) < 0.000001) {
            return false;
        } 
 
        return (a <= b && b <= c) || (c <= b && b <= a);*/
        
        
        //更改：如果b和a或c中一个接近 就算在a和c之间
        return (a <= b && b <= c) || (c <= b && b <= a) || this.closeTo(a,b,precision) || this.closeTo(b,c,precision); 
        
    },
	 
    
    ifPointAtLineBound:function(point, linePoints, precision){
        //待验证  横线和竖线比较特殊
        return  math.isInBetween(linePoints[0].x, point.x, linePoints[1].x, precision) && math.isInBetween(linePoints[0].y, point.y, linePoints[1].y, precision) 
    }
    
    , 
	
	isLineIntersect: function (line1, line2, notSegment, precision) {//线段和线段是否有交点.  notSegment代表是直线而不是线段
		var a1 = line1[1].y - line1[0].y;
		var b1 = line1[0].x - line1[1].x;
		var c1 = a1 * line1[0].x + b1 * line1[0].y;
		//转换成一般式: Ax+By = C
		var a2 = line2[1].y - line2[0].y;
		var b2 = line2[0].x - line2[1].x;
		var c2 = a2 * line2[0].x + b2 * line2[0].y;
		// 计算交点		
		var d = a1 * b2 - a2 * b1;

		// 当d==0时，两线平行
		if (d == 0) {
		  return false;
		} else {
		  var x = (b2 * c1 - b1 * c2) / d;
		  var y = (a1 * c2 - a2 * c1) / d;

		  // 检测交点是否在两条线段上
		  /* if (notSegment || (isInBetween(line1[0].x, x, line1[1].x) || isInBetween(line1[0].y, y, line1[1].y)) &&
			(isInBetween(line2[0].x, x, line2[1].x) || isInBetween(line2[0].y, y, line2[1].y))) {
			return {x,y};
		  } */
          if (notSegment ||  math.ifPointAtLineBound({x,y}, line1, precision) && math.ifPointAtLineBound({x,y}, line2, precision)){ 
                return {x,y};
		  }
		}  
    },
     
	getNormal2d : function(o={} ){//获取二维法向量 方向向内
		var x,y, x1,y1; 
		//line2d的向量
        if(o.vec){
            x1 = o.vec.x;  y1 = o.vec.y
        }else{
            x1 = o.p1.x - o.p2.x;
            y1 = o.p1.y - o.p2.y;
        }
		
		//假设法向量的x或y固定为1或-1
		if(y1 != 0){
			x = 1;
			y = - (x1 * x) / y1;
		}else if(x1 != 0){//y如果为0，正常情况x不会是0
			y = 1;
			x = - (y1 * y) / x1;
		}else{
			console.log("两个点一样");
			return null;
		}
		
		//判断方向里或者外：
		var vNormal = new THREE.Vector3(x, 0, y);
		var vLine = new THREE.Vector3(x1, 0, y1);
		var vDir = vNormal.cross(vLine);
		if(vDir.y>0){
			x *= -1;
			y *= -1;
		} 
		return new THREE.Vector2(x, y).normalize();
 	},
     
    getQuaBetween2Vector:function(oriVec, newVec, upVec){ //获取从oriVec旋转到newVec可以应用的quaternion
        var angle = oriVec.angleTo(newVec);
        var axis = oriVec.clone().cross( newVec).normalize();//两个up之间
        if(axis.length() == 0){//当夹角为180 或 0 度时，得到的axis为（0,0,0），故使用备用的指定upVec
            return new THREE.Quaternion().setFromAxisAngle( upVec, angle );
        }
        return new THREE.Quaternion().setFromAxisAngle( axis, angle );
    } ,
    /*
    getQuaBetween2Vector2 : function(oriVec, newVec   ){//not camera
        var _ = (new THREE.Matrix4).lookAt( oriVec, new THREE.Vector3, new THREE.Vector3(0,1,0))
        var aimQua = (new THREE.Quaternion).setFromRotationMatrix(_)
        var _2 = (new THREE.Matrix4).lookAt( newVec, new THREE.Vector3, new THREE.Vector3(0,1,0))
        var aimQua2 = (new THREE.Quaternion).setFromRotationMatrix(_2)
        
        return aimQua2.multiply(aimQua.clone().inverse()) 
        
    } */
    
    getQuaByAim: function (aim, center=new THREE.Vector3) { 
        let forward = new THREE.Vector3(0, 1, 0)
        let qua1 = new THREE.Quaternion().setFromUnitVectors(forward, aim.clone().sub(center).normalize())
        /*  var _ = (new THREE.Matrix4).lookAt(center,aim,   new THREE.Vector3(0,1,0));  
        let qua2 = (new THREE.Quaternion).setFromRotationMatrix(_);
        let rot1 = new THREE.Euler().setFromQuaternion(qua1)
        let rot2 = new THREE.Euler().setFromQuaternion(qua2)  //奇怪，qua2怎么都不对
        console.log(rot1,rot2) */
        return qua1
    },
    getAimByQua: function (quaternion, center=new THREE.Vector3) {
        return new THREE.Vector3(0, 0, -1).applyQuaternion(quaternion).add(center)
    },    
     
    
    getScaleForConstantSize : function(){ //获得规定二维大小的mesh的scale值。可以避免因camera的projection造成的mesh视觉大小改变。  来源：tag.updateDisc
        var w;  
        var i = new THREE.Vector3, o = new THREE.Vector3, l = new THREE.Vector3, c = new THREE.Vector3, h = new THREE.Vector3
        return function(op={}){ 
            if(op.width2d) w = op.width2d //如果恒定二维宽度
            else{//否则考虑上距离，加一丢丢近大远小的效果
                var currentDis, nearBound, farBound
                if(op.camera.type == "OrthographicCamera"){
                    currentDis = 200 / op.camera.zoom  //(op.camera.right - op.camera.left) / op.camera.zoom
                }else{
                    currentDis = op.position.distanceTo(op.camera.position);
                } 
                w = op.maxSize - ( op.maxSize -  op.minSize) * THREE.Math.smoothstep(currentDis,  op.nearBound,  op.farBound);
                //maxSize ： mesh要表现的最大像素宽度；   nearBound： 最近距离，若比nearBound近，则使用maxSize
            }
            i.copy(op.position).project(op.camera);  //tag中心在屏幕上的二维坐标
            o.set(op.resolution.x / 2, op.resolution.y / 2, 1).multiply(i); //转化成px   -w/2 到 w/2的范围
            l.set(w / 2, 0, 0).add(o);  //加上tag宽度的一半
            c.set(2 / op.resolution.x, 2 / op.resolution.y, 1).multiply(l); //再转回  -1 到 1的范围
            h.copy(c).unproject(op.camera);//再转成三维坐标，求得tag边缘的位置
            var g = h.distanceTo(op.position)//就能得到tag的三维半径
            //这里使用的都是resolution2， 好处是手机端不会太小， 坏处是pc更改网页显示百分比时显示的大小会变（或许可以自己算出设备真实的deviceRatio, 因window.screen是不会改变的）,但考虑到用户可以自行调节字大小也许是好的
            return g  //可能NAN  当相机和position重叠时
        }
    }()
    ,
    
    //W , H, left, top分别是rect的宽、高、左、上
    getCrossPointAtRect : function(p1, aim, W , H, left, top){//求射线p1-aim在rect边界上的交点，其中aim在rect范围内，p1则不一定(交点在aim这边的延长线上)
        
        var x,y, borderX;
        var r = (aim.x - p1.x) / (aim.y - p1.y);//根据相似三角形原理先求出这个比值	
        var getX = function(y){
            return  r * (y-p1.y) + p1.x;
        }
        var getY = function(x){
            return  1/r * (x-p1.x) + p1.y;
        }
        if(aim.x >= p1.x){ 
            borderX = W+left;
        }else{
            borderX = left; 
        }
        x = borderX;
        y = getY(x);
        if(y < top || y > top+H){
            if(y < top){
                y = top; 
            }else{
                y = top+H; 
            }
            x = getX(y)			
        }
        return new THREE.Vector2(x, y);  
    },
    getDirFromUV : function(uv){ //获取dir   反向计算 - -  二维转三维比较麻烦 
        var dirB; //所求 单位向量
        
        
        
        var y = Math.cos(uv.y * Math.PI);              //uv中纵向可以直接确定y，  根据上面getUVfromDir的反向计算 
                            // 故 uv.y * Math.PI  就是到垂直线（向上）的夹角
        var angle = 2 * Math.PI * uv.x - Math.PI       //x/z代表的是角度

        var axisX, axisZ; //axis为1代表是正，-1是负数
        if (-Math.PI <= angle && angle < 0) {
            axisX = -1 //下半圆
        } else {
            axisX = 1 //上半圆
        }
        if (-Math.PI / 2 <= angle && angle < Math.PI / 2) {
            axisZ = 1 //右半圆
        } else {
            axisZ = -1 //左半圆
        }



        var XDivideZ = Math.tan(angle);
        var z = Math.sqrt((1 - y * y) / (1 + XDivideZ * XDivideZ));
        var x = XDivideZ * z


        if (z * axisZ < 0) { //异号
            z *= -1;
            x *= -1;
            if (x * axisX < 0) {
          //      console.log("wrong!!!!!??????????")
            }
        }

        x *= -1 //计算完成后这里不能漏掉 *= -1	
        dirB = this.convertVector.YupToZup(new THREE.Vector3(x, y, z))   

        //理想状态下x和z和anotherDir相同
        return dirB


    },
    
    getUVfromDir : function(dir) { //获取UV  同shader里的计算 
        var dir = this.convertVector.ZupToYup(dir)
        dir.x *= -1; //计算前这里不能漏掉 *= -1  见shader
        var tx = Math.atan2(dir.x, dir.z) / (Math.PI * 2.0) + 0.5; //atan2(y,x) 返回从 X 轴正向逆时针旋转到点 (x,y) 时经过的角度。区间是-PI 到 PI 之间的值
        var ty = Math.acos(dir.y) / Math.PI;
        return new THREE.Vector2(tx,  ty)  

        //理想状态下tx相同
    },
     
    getDirByLonLat : function(lon,lat){
        var dir = new THREE.Vector3
        var phi = THREE.Math.degToRad(90 - lat);
        var theta = THREE.Math.degToRad(lon);
        dir.x = Math.sin(phi) * Math.cos(theta);
        dir.y = Math.cos(phi);
        dir.z = Math.sin(phi) * Math.sin(theta);   
        return dir
    } //0,0 => (1,0,0)     270=>(0,0,-1)
    ,    
    projectPointAtPlane:function(o={}){//获取一个点在一个面上的投影 {facePoints:[a,b,c], point:}
        var plane = new THREE.Plane().setFromCoplanarPoints(...o.facePoints)
        return plane.projectPoint(o.point, new THREE.Vector3() )
    }
    ,
    
    getPolygonsMixedRings:function( polygons,  onlyGetOutRing){//{points:[vector2,...],holes:[[],[]]} 
         
         
        let points = [] 
        let lines = []
        let i = 0 
        
        polygons.forEach(e=> points.push(...e.map(a=>new THREE.Vector2().copy(a) )) )   
        polygons.forEach((ps,j)=>{
            let length = ps.length;
            let index = 0;
            while(index<length){
                lines.push({p1:index+i,p2:(index+1)%length+i});
                index ++;
            }
            i+=length
        })
    
             
        points.forEach((p,j)=>{p.id = j}) 
            
        let rings = searchRings({
            points,
            lines,
            onlyGetOutRing    
        })
        //console.log(rings)
        
        rings = rings.filter(e=>e.closetParent == void 0)// 子环不加，被外环包含了
        
        return rings 
        
    },

    getQuaFromPosAim( position, target ){ 
        /* let matrix = (new THREE.Matrix4).lookAt(position, target, new THREE.Vector3(0,0,1)) //这里垂直的话会默认给一个右向所以不这么写
        return (new THREE.Quaternion).setFromRotationMatrix(matrix) */
        let view = new ExtendView()
        view.direction = new THREE.Vector3().subVectors(target,position) 
        return view.quaternion
    },
    
    
    getBoundByPoints(points, minSize){ 
        var bound = new THREE.Box3
        points.forEach(point=>{
            bound.expandByPoint(point)
        }) 
        let center = bound.getCenter(new THREE.Vector3)
        if(minSize){
            let minBound = (new THREE.Box3()).setFromCenterAndSize(center, minSize)
            bound.union(minBound)
        }
        return {
            bounding:bound,
            size: bound.getSize(new THREE.Vector3),
            center,
        }
    },

        
    /* linearClamp(value,  x1,x2, y1, y2){//x为bound.min, bound.max
        value = THREE.Math.clamp(value, x1,x2)
        return y1 + ( y2 - y1) * (value - x1)  / (x2 - x1)  
    } */
    
    linearClamp(value, xArr , yArr){ //xArr需要按顺序从小到大，yArr对应xArr中的值
        
        let len = xArr.length 
        if(value <= xArr[0]) return yArr[0]
        if(value >= xArr[len - 1]) return yArr[len - 1]
        let i = 0 
        
        while(++i < len ){
            if(value < xArr[i]){
                let x1 = xArr[i-1], x2 = xArr[i], y1 = yArr[i-1], y2 = yArr[i] 
                value = y1 + ( y2 - y1) * (value - x1)  / (x2 - x1)  
                break
            }
        }
        return value
        
         
    } 
};

/* 

 如何将若干个点拟合出线段

 // 假设你有一个点数组，每个点表示为一个包含x和y坐标的对象
const points = [
  { x: 1, y: 2 },
  { x: 2, y: 3 },
  { x: 3, y: 4 },
  { x: 4, y: 5 },
  // ... 更多点
];

// 定义用于计算最小二乘法参数的函数
function leastSquares( ) {
  let sumX = 0;
  let sumY = 0;
  let sumXY = 0;
  let sumX2 = 0;
  let n = points.length;

  for (const point of points) {
    sumX += point.x;
    sumY += point.y;
    sumXY += point.x * point.y;
    sumX2 += point.x * point.x;
  }

  const k = (n * sumXY - sumX * sumY) / (n * sumX2 - sumX * sumX);  //不知道为何这样算，自己解不出来（使点到直线距离之和平方最小），但测了下似乎是准的
  const b = (sumY - k * sumX) / n;

  return { k, b };
}

// 使用上述函数计算拟合直线的参数
const { k, b } = leastSquares(points);

// 现在你可以使用这些参数来表示拟合出的线段 
console.log(`拟合线段的方程为: y = ${k}x + ${b}`);
 */
 
 
 

Potree.math = math


export default math