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Math.ts
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Math.ts
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///<amd-module name="world/Math"/>
import Kernel = require('./Kernel');
import Utils = require('./Utils');
import Vertice = require('./Vertice');
import Vector = require('./Vector');
import Line = require('./Line');
import Plan = require('./Plan');
const MathUtils = {
ONE_RADIAN_EQUAL_DEGREE:57.29577951308232,//180/Math.PI
ONE_DEGREE_EQUAL_RADIAN:0.017453292519943295,//Math.PI/180
LEFT_TOP:"LEFT_TOP",
RIGHT_TOP:"RIGHT_TOP",
LEFT_BOTTOM:"LEFT_BOTTOM",
RIGHT_BOTTOM:"RIGHT_BOTTOM",
LEFT:"LEFT",
RIGHT:"RIGHT",
TOP:"TOP",
BOTTOM:"BOTTOM",
izZero(value: any) : boolean {
if(!Utils.isNumber(value)){
throw "invalid value";
}
return Math.abs(value) < 0.000001;
},
/**
* 将其他进制的数字转换为10进制
* @param numSys 要准换的进制
* @param strNum 字符串形式的要转换的数据
* @returns {number} 整数的十进制数据
*/
numerationSystemTo10(numSys: number, strNum: string) : number{
var sum = 0;
for(var i=0;i<strNum.length;i++){
var level = strNum.length-1-i;
var key = parseInt(strNum[i]);
sum += key * Math.pow(numSys,level);
}
return sum;
},
/**
* 将10进制的数字转换为其他进制
* @param numSys 要转换成的进制
* @param num 要转换的十进制数字
* @returns {string} 字符串形式的其他进制的数据
*/
numerationSystemFrom10 : function(numSys: number, num: number){
var tempResultArray:any[] = [];
var quotient = Math.floor(num/numSys);
var remainder = num%numSys;
tempResultArray.push(remainder);
while(quotient != 0){
num = quotient;
quotient = Math.floor(num/numSys);
remainder = num%numSys;
tempResultArray.push(remainder);
}
tempResultArray.reverse();
var strResult = tempResultArray.join("");
return strResult;
},
/**
* 将数据从一个进制转换到另一个进制,输入和输出都是字符串
* @param numSysFrom
* @param numSysTo
* @param strNumFrom
* @returns {string}
*/
numerationSystemChange: function(numSysFrom: number,numSysTo:number,strNumFrom:string){
var temp10 = this.numerationSystemTo10(numSysFrom,strNumFrom);
var strResult = this.numerationSystemFrom10(numSysTo,temp10);
return strResult;
},
/**
* 计算三角形的面积
*/
getTriangleArea(v1: Vertice, v2: Vertice, v3: Vertice){
var v1Copy = v1.clone();
var v2Copy = v2.clone();
var v3Copy = v3.clone();
var direction = Vector.verticeMinusVertice(v3Copy, v2Copy);
var line = new Line(v2Copy,direction);
var h = this.getLengthFromVerticeToLine(v1Copy,line);
var w = this.getLengthFromVerticeToVertice(v2Copy,v3Copy);
var area = 0.5*w*h;
return area;
},
/**
* 计算三维空间中两点之间的直线距离
* @param vertice1
* @param vertice2
* @return {Number}
*/
getLengthFromVerticeToVertice(vertice1: Vertice, vertice2: Vertice){
var vertice1Copy = vertice1.clone();
var vertice2Copy = vertice2.clone();
var length2 = Math.pow(vertice1Copy.x-vertice2Copy.x,2) + Math.pow(vertice1Copy.y-vertice2Copy.y,2) + Math.pow(vertice1Copy.z-vertice2Copy.z,2);
var length = Math.sqrt(length2);
return length;
},
/**
* 已验证正确
* 获取点到直线的距离
* @param vertice 直线外一点
* @param line 直线
* @return {Number}
*/
getLengthFromVerticeToLine : function(vertice: Vertice, line: Line){
var verticeCopy = vertice.clone();
var lineCopy = line.clone();
var x0 = verticeCopy.x;
var y0 = verticeCopy.y;
var z0 = verticeCopy.z;
var verticeOnLine = lineCopy.vertice;
var x1 = verticeOnLine.x;
var y1 = verticeOnLine.y;
var z1 = verticeOnLine.z;
var lineVector = lineCopy.vector;
lineVector.normalize();
var a = lineVector.x;
var b = lineVector.y;
var c = lineVector.z;
var A = (y0-y1)*c-b*(z0-z1);
var B = (z0-z1)*a-c*(x0-x1);
var C = (x0-x1)*b-a*(y0-y1);
return Math.sqrt(A*A+B*B+C*C);
},
/**
* 已验证正确
* 计算点到平面的距离,平面方程由Ax+By+Cz+D=0决定
* @param vertice
* @param plan 平面,包含A、B、C、D四个参数信息
* @return {Number}
*/
getLengthFromVerticeToPlan(vertice: Vertice, plan: Plan){
var verticeCopy = vertice.clone();
var planCopy = plan.clone();
var x = verticeCopy.x;
var y = verticeCopy.y;
var z = verticeCopy.z;
var A = planCopy.A;
var B = planCopy.B;
var C = planCopy.C;
var D = planCopy.D;
var numerator = Math.abs(A*x+B*y+C*z+D);
var denominator = Math.sqrt(A*A+B*B+C*C);
var length = numerator / denominator;
return length;
},
/**
* 已验证正确
* 从vertice向平面plan做垂线,计算垂点坐标
* @param vertice
* @param plan
* @return {World.Vertice}
*/
getVerticeVerticalIntersectPointWidthPlan(vertice: Vertice, plan: Plan){
var verticeCopy = vertice.clone();
var planCopy = plan.clone();
var x0 = verticeCopy.x;
var y0 = verticeCopy.y;
var z0 = verticeCopy.z;
var normalVector = new Vector(planCopy.A,planCopy.B,planCopy.C);
normalVector.normalize();
var a = normalVector.x;
var b = normalVector.y;
var c = normalVector.z;
var d = planCopy.D*a/planCopy.A;
var k = -(a*x0+b*y0+c*z0+d);
var x = k*a+x0;
var y = k*b+y0;
var z = k*c+z0;
var intersectVertice = new Vertice(x,y,z);
return intersectVertice;
},
getIntersectPointByLineAdPlan(line: Line, plan: Plan){
var lineCopy = line.clone();
var planCopy = plan.clone();
lineCopy.vector.normalize();
var A = planCopy.A;
var B = planCopy.B;
var C = planCopy.C;
var D = planCopy.D;
var x0 = lineCopy.vertice.x;
var y0 = lineCopy.vertice.y;
var z0 = lineCopy.vertice.z;
var a = lineCopy.vector.x;
var b = lineCopy.vector.y;
var c = lineCopy.vector.z;
var k = -(A*x0+B*y0+C*z0+D)/(A*a+B*b+C*c);
var x = k*a+x0;
var y = k*b+y0;
var z = k*c+z0;
var intersectVertice = new Vertice(x,y,z);
return intersectVertice;
},
/**
* 已验证正确
* 计算某直线与地球的交点,有可能没有交点,有可能有一个交点,也有可能有两个交点
* @param line 与地球求交的直线
* @return {Array}
*/
getLineIntersectPointWithEarth(line: Line): Vertice[]{
var result:Vertice[] = [];
var lineCopy = line.clone();
var vertice = lineCopy.vertice;
var direction = lineCopy.vector;
direction.normalize();
var r = Kernel.EARTH_RADIUS;
var a = direction.x;
var b = direction.y;
var c = direction.z;
var x0 = vertice.x;
var y0 = vertice.y;
var z0 = vertice.z;
var a2 = a*a;
var b2 = b*b;
var c2 = c*c;
var r2 = r*r;
var ay0 = a*y0;
var az0 = a*z0;
var bx0 = b*x0;
var bz0 = b*z0;
var cx0 = c*x0;
var cy0 = c*y0;
var deltaA = ay0*bx0 + az0*cx0 + bz0*cy0;
var deltaB = ay0*ay0+az0*az0+bx0*bx0+bz0*bz0+cx0*cx0+cy0*cy0;
var deltaC = a2+b2+c2;
var delta = 8*deltaA-4*deltaB+4*r2*deltaC;
if(delta < 0){
result = [];
}
else{
var t = a*x0+b*y0+c*z0;
var A = a2+b2+c2;
if(delta == 0){
var k = - t/A;
var x = k*a+x0;
var y = k*b+y0;
var z = k*c+z0;
var p = new Vertice(x,y,z);
result.push(p);
}
else if(delta > 0){
var sqrtDelta = Math.sqrt(delta);
var k1 = (-2*t+sqrtDelta)/(2*A);
var x1 = k1*a+x0;
var y1 = k1*b+y0;
var z1 = k1*c+z0;
var p1 = new Vertice(x1,y1,z1);
result.push(p1);
var k2 = (-2*t-sqrtDelta)/(2*A);
var x2 = k2*a+x0;
var y2 = k2*b+y0;
var z2 = k2*c+z0;
var p2 = new Vertice(x2,y2,z2);
result.push(p2);
}
}
return result;
},
/**
* 计算过P点且垂直于向量V的平面
* @param vertice P点
* @param direction 向量V
* @return {Object} World.Plan 返回平面表达式中Ax+By+Cz+D=0的A、B、C、D的信息
*/
getCrossPlaneByLine(vertice: Vertice, direction: Vector): Plan{
var verticeCopy = vertice.clone();
var directionCopy = direction.clone();
directionCopy.normalize();
var a = directionCopy.x;
var b = directionCopy.y;
var c = directionCopy.z;
var x0 = verticeCopy.x;
var y0 = verticeCopy.y;
var z0 = verticeCopy.z;
var d = -(a*x0+b*y0+c*z0);
var plan = new Plan(a,b,c,d);
return plan;
},
///////////////////////////////////////////////////////////////////////////////////////////
//点变换: Canvas->NDC
convertPointFromCanvasToNDC(canvasX: number, canvasY: number): number[]{
if(!(Utils.isNumber(canvasX))){
throw "invalid canvasX";
}
if(!(Utils.isNumber(canvasY))){
throw "invalid canvasY";
}
var ndcX = 2 * canvasX / Kernel.canvas.width - 1;
var ndcY = 1 - 2 * canvasY / Kernel.canvas.height;
return [ndcX,ndcY];
},
//点变换: NDC->Canvas
convertPointFromNdcToCanvas(ndcX: number, ndcY: number): number[]{
if(!(Utils.isNumber(ndcX))){
throw "invalid ndcX";
}
if(!(Utils.isNumber(ndcY))){
throw "invalid ndcY";
}
var canvasX = (1 + ndcX) * Kernel.canvas.width / 2.0;
var canvasY = (1 - ndcY) * Kernel.canvas.height / 2.0;
return [canvasX,canvasY];
},
/**
* 根据层级计算出摄像机应该放置到距离地球表面多远的位置
* @param level
* @return {*}
*/
getLengthFromCamera2EarthSurface(level: number): number{
return 7820683/Math.pow(2,level);
},
/**将经纬度转换为笛卡尔空间直角坐标系中的x、y、z
* @lon 经度(角度单位)
* @lat 纬度(角度单位)
* @r optional 可选的地球半径
* @p 笛卡尔坐标系中的坐标
*/
geographicToCartesianCoord(lon:number, lat: number, r: number = Kernel.EARTH_RADIUS): Vertice{
if(!(lon >= -(180+0.001) && lon <= (180+0.001))){
throw "invalid lon";
}
if(!(lat >= -(90+0.001) && lat <= (90+0.001))){
throw "invalid lat";
}
var radianLon = this.degreeToRadian(lon);
var radianLat = this.degreeToRadian(lat);
var sin1 = Math.sin(radianLon);
var cos1 = Math.cos(radianLon);
var sin2 = Math.sin(radianLat);
var cos2 = Math.cos(radianLat);
var x = r*sin1*cos2;
var y = r*sin2;
var z = r*cos1*cos2;
return new Vertice(x,y,z);
},
/**
* 将笛卡尔空间直角坐标系中的坐标转换为经纬度,以角度表示
* @param vertice
* @return {Array}
*/
cartesianCoordToGeographic(vertice: Vertice): number[]{
var verticeCopy = vertice.clone();
var x = verticeCopy.x;
var y = verticeCopy.y;
var z = verticeCopy.z;
var sin2 = y/Kernel.EARTH_RADIUS;
if(sin2 > 1){
sin2 = 2;
}
else if(sin2 < -1){
sin2 = -1;
}
var radianLat = Math.asin(sin2);
var cos2 = Math.cos(radianLat);
var sin1 = x / (Kernel.EARTH_RADIUS * cos2);
if(sin1 > 1){
sin1 = 1;
}
else if(sin1 < -1){
sin1 = -1;
}
var cos1 = z / (Kernel.EARTH_RADIUS * cos2);
if(cos1 > 1){
cos1 = 1;
}
else if(cos1 < -1){
cos1 = -1;
}
var radianLog = Math.asin(sin1);
if(sin1 >= 0){//经度在[0,π]
if(cos1 >= 0){//经度在[0,π/2]之间
radianLog = radianLog;
}
else{//经度在[π/2,π]之间
radianLog = Math.PI - radianLog;
}
}
else{//经度在[-π,0]之间
if(cos1 >= 0){//经度在[-π/2,0]之间
radianLog = radianLog;
}
else{//经度在[-π,-π/2]之间
radianLog = -radianLog - Math.PI;
}
}
var degreeLat = this.radianToDegree(radianLat);
var degreeLog = this.radianToDegree(radianLog);
return [degreeLog, degreeLat];
},
/**
* 角度转弧度
* @param degree
* @return {*}
*/
degreeToRadian(degree: number){
return degree * this.ONE_DEGREE_EQUAL_RADIAN;
},
/**
* 弧度转角度
* @param radian
* @return {*}
*/
radianToDegree(radian: number){
return radian * this.ONE_RADIAN_EQUAL_DEGREE;
},
/**
* 将投影坐标x转换为以弧度表示的经度
* @param x 投影坐标x
* @return {Number} 返回的经度信息以弧度表示
*/
webMercatorXToRadianLog(x: number){
return x / Kernel.EARTH_RADIUS;
},
/**
* 将投影坐标x转换为以角度表示的经度
* @param x 投影坐标x
* @return {*} 返回的经度信息以角度表示
*/
webMercatorXToDegreeLog(x: number): number{
var radianLog = this.webMercatorXToRadianLog(x);
return this.radianToDegree(radianLog);
},
/**
* 将投影坐标y转换为以弧度表示的纬度
* @param y 投影坐标y
* @return {Number} 返回的纬度信息以弧度表示
*/
webMercatorYToRadianLat(y: number): number{
if(!(Utils.isNumber(y))){
throw "invalid y";
}
var a = y / Kernel.EARTH_RADIUS;
var b = Math.pow(Math.E,a);
var c = Math.atan(b);
var radianLat = 2*c - Math.PI/2;
return radianLat;
},
/**
* 将投影坐标y转换为以角度表示的纬度
* @param y 投影坐标y
* @return {*} 返回的纬度信息以角度表示
*/
webMercatorYToDegreeLat(y: number): number{
var radianLat = this.webMercatorYToRadianLat(y);
return this.radianToDegree(radianLat);
},
/**
* 将投影坐标x、y转换成以弧度表示的经纬度
* @param x 投影坐标x
* @param y 投影坐标y
* @return {Array} 返回的经纬度信息以弧度表示
*/
webMercatorToRadianGeographic(x: number, y: number): number[]{
var radianLog = this.webMercatorXToRadianLog(x);
var radianLat = this.webMercatorYToRadianLat(y);
return [radianLog,radianLat];
},
/**
* 将投影坐标x、y转换成以角度表示的经纬度
* @param x 投影坐标x
* @param y 投影坐标y
* @return {Array} 返回的经纬度信息以角度表示
*/
webMercatorToDegreeGeographic(x: number, y: number): number[]{
var degreeLog = this.webMercatorXToDegreeLog(x);
var degreeLat = this.webMercatorYToDegreeLat(y);
return [degreeLog,degreeLat];
},
/**
* 将以弧度表示的经度转换为投影坐标x
* @param radianLog 以弧度表示的经度
* @return {*} 投影坐标x
*/
radianLogToWebMercatorX(radianLog: number): number{
if(!(Utils.isNumber(radianLog) && radianLog <= (Math.PI+0.001) && radianLog >= -(Math.PI+0.001))){
throw "invalid radianLog";
}
return Kernel.EARTH_RADIUS * radianLog;
},
/**
* 将以角度表示的纬度转换为投影坐标y
* @param degreeLog 以角度表示的经度
* @return {*} 投影坐标x
*/
degreeLogToWebMercatorX(degreeLog: number): number{
if(!(Utils.isNumber(degreeLog) && degreeLog <= (180+0.001) && degreeLog >= -(180+0.001))){
throw "invalid degreeLog";
}
var radianLog = this.degreeToRadian(degreeLog);
return this.radianLogToWebMercatorX(radianLog);
},
/**
* 将以弧度表示的纬度转换为投影坐标y
* @param radianLat 以弧度表示的纬度
* @return {Number} 投影坐标y
*/
radianLatToWebMercatorY(radianLat: number): number{
if(!(radianLat <= (Math.PI/2+0.001) && radianLat >= -(Math.PI/2+0.001))){
throw "invalid radianLat";
}
var a = Math.PI/4 + radianLat/2;
var b = Math.tan(a);
var c = Math.log(b);
var y = Kernel.EARTH_RADIUS * c;
return y;
},
/**
* 将以角度表示的纬度转换为投影坐标y
* @param degreeLat 以角度表示的纬度
* @return {Number} 投影坐标y
*/
degreeLatToWebMercatorY(degreeLat: number): number{
if(!(degreeLat <= (90+0.001) && degreeLat >= -(90+0.001))){
throw "invalid degreeLat";
}
var radianLat = this.degreeToRadian(degreeLat);
return this.radianLatToWebMercatorY(radianLat);
},
/**
* 将以弧度表示的经纬度转换为投影坐标
* @param radianLog 以弧度表示的经度
* @param radianLat 以弧度表示的纬度
* @return {Array} 投影坐标x、y
*/
radianGeographicToWebMercator(radianLog: number, radianLat: number): number[]{
var x = this.radianLogToWebMercatorX(radianLog);
var y = this.radianLatToWebMercatorY(radianLat);
return [x,y];
},
/**
* 将以角度表示的经纬度转换为投影坐标
* @param degreeLog 以角度表示的经度
* @param degreeLat 以角度表示的纬度
* @return {Array}
*/
degreeGeographicToWebMercator(degreeLog: number, degreeLat: number): number[]{
var x = this.degreeLogToWebMercatorX(degreeLog);
var y = this.degreeLatToWebMercatorY(degreeLat);
return [x,y];
},
//根据切片的level、row、column计算该切片所覆盖的投影区域的范围
getTileWebMercatorEnvelopeByGrid(level: number, row: number, column: number): any{
var k = Kernel.MAX_PROJECTED_COORD;
var size = 2*k / Math.pow(2,level);
var minX = -k + column * size;
var maxX = minX + size;
var maxY = k - row * size;
var minY = maxY - size;
var Eproj = {
"minX":minX,
"minY":minY,
"maxX":maxX,
"maxY":maxY
};
return Eproj;
},
//根据切片的level、row、column计算该切片所覆盖的经纬度区域的范围,以经纬度表示返回结果
getTileGeographicEnvelopByGrid(level: number, row: number, column: number): any{
var Eproj = this.getTileWebMercatorEnvelopeByGrid(level,row,column);
var pMin = this.webMercatorToDegreeGeographic(Eproj.minX,Eproj.minY);
var pMax = this.webMercatorToDegreeGeographic(Eproj.maxX,Eproj.maxY);
var Egeo = {
"minLon":pMin[0],
"minLat":pMin[1],
"maxLon":pMax[0],
"maxLat":pMax[1]
};
return Egeo;
},
//根据切片的level、row、column计算该切片所覆盖的笛卡尔空间直角坐标系的范围,以x、y、z表示返回结果
getTileCartesianEnvelopByGrid(level: number, row: number, column: number): Object{
var Egeo = this.getTileGeographicEnvelopByGrid(level,row,column);
var minLon = Egeo.minLon;
var minLat = Egeo.minLat;
var maxLon = Egeo.maxLon;
var maxLat = Egeo.maxLat;
var pLeftBottom = this.geographicToCartesianCoord(minLon,minLat);
var pLeftTop = this.geographicToCartesianCoord(minLon,maxLat);
var pRightTop = this.geographicToCartesianCoord(maxLon,maxLat);
var pRightBottom = this.geographicToCartesianCoord(maxLon,minLat);
var Ecar = {
"pLeftBottom":pLeftBottom,
"pLeftTop":pLeftTop,
"pRightTop":pRightTop,
"pRightBottom":pRightBottom,
"minLon":minLon,
"minLat":minLat,
"maxLon":maxLon,
"maxLat":maxLat
};
return Ecar;
},
/**
* 获取切片的中心点,以经纬度数组形式返回
* @param level
* @param row
* @param column
* @return {Array}
*/
getGeographicTileCenter(level: number, row: number, column: number): number[]{
var Egeo = this.getTileGeographicEnvelopByGrid(level,row,column);
var minLon = Egeo.minLon;
var minLat = Egeo.minLat;
var maxLon = Egeo.maxLon;
var maxLat = Egeo.maxLat;
var centerLon = (minLon+maxLon)/2;//切片的经度中心
var centerLat = (minLat+maxLat)/2;//切片的纬度中心
var lonlatTileCenter = [centerLon,centerLat];
return lonlatTileCenter;
},
getCartesianTileCenter(level: number, row: number, column: number): Vertice{
var lonLat = this.getGeographicTileCenter(level,row,column);
var vertice = this.geographicToCartesianCoord(lonLat[0],lonLat[1]);
return vertice;
},
/**
* 计算TRIANGLES的平均法向量
* @param vs 传入的顶点坐标数组 array
* @param ind 传入的顶点的索引数组 array
* @return {Array} 返回每个顶点的平均法向量的数组
*/
calculateNormals(vs: number[], ind: number[]): number[]{
var x=0;
var y=1;
var z=2;
var ns:number[] = [];
//对于每个vertex,初始化normal x, normal y, normal z
for(var i=0;i<vs.length;i=i+3){
ns[i+x]=0.0;
ns[i+y]=0.0;
ns[i+z]=0.0;
}
//用三元组vertices计算向量,所以i = i+3,i表示索引
for(var i=0;i<ind.length;i=i+3){
var v1:number[] = [];
var v2:number[] = [];
var normal:number[] = [];
//p2 - p1,得到向量Vp1p2
v1[x] = vs[3*ind[i+2]+x] - vs[3*ind[i+1]+x];
v1[y] = vs[3*ind[i+2]+y] - vs[3*ind[i+1]+y];
v1[z] = vs[3*ind[i+2]+z] - vs[3*ind[i+1]+z];
//p0 - p1,得到向量Vp0p1
v2[x] = vs[3*ind[i]+x] - vs[3*ind[i+1]+x];
v2[y] = vs[3*ind[i]+y] - vs[3*ind[i+1]+y];
v2[z] = vs[3*ind[i]+z] - vs[3*ind[i+1]+z];
//两个向量叉乘得到三角形的法线向量,注意三角形的正向都是逆时针方向,此处要注意两个向量相乘的顺序,要保证法线向量是从背面指向正面的
normal[x] = v1[y]*v2[z] - v1[z]*v2[y];
normal[y] = v1[z]*v2[x] - v1[x]*v2[z];
normal[z] = v1[x]*v2[y] - v1[y]*v2[x];
//更新三角形的法线向量:向量的和
for(var j=0;j<3;j++){
ns[3*ind[i+j]+x] = ns[3*ind[i+j]+x] + normal[x];
ns[3*ind[i+j]+y] = ns[3*ind[i+j]+y] + normal[y];
ns[3*ind[i+j]+z] = ns[3*ind[i+j]+z] + normal[z];
}
}
//对法线向量进行归一化
for(var i=0;i<vs.length;i=i+3){
var nn:number[]=[];
nn[x] = ns[i+x];
nn[y] = ns[i+y];
nn[z] = ns[i+z];
var len = Math.sqrt((nn[x]*nn[x])+(nn[y]*nn[y])+(nn[z]*nn[z]));
if (len == 0) len = 1.0;
nn[x] = nn[x]/len;
nn[y] = nn[y]/len;
nn[z] = nn[z]/len;
ns[i+x] = nn[x];
ns[i+y] = nn[y];
ns[i+z] = nn[z];
}
return ns;
}
};
export = MathUtils;