两相交的直线段夹角平分的直线上过交点距离为d的另一点求解公式

两相交的直线段夹角平分的直线上过交点距离为d的另一点求解公式
问题描述：
已知p0,p1,pN三个点，p0到p1走向直线段，pN到p0走向直线段，相交于p0点，
则pN到p0到p1夹角为a,平分夹角为a/2,求经过p0点方向角为平分线上距离p0点距离为d的点p(x,y）坐标值。

平分线点斜式方程为：
y-y0=k(x-x0)

两点距离公式为：
(y-y0)^2 +
（x-x0)^2
=d^2

斜率k=tg(a)

联合解方程组：
y-y0=k(x-x0)
(y-y0)^2 +
（x-x0)^2
=d^2

Mathematica 9 解公式表达式：

In[4]:= Solve[{d^2==(x-x0)^2+(y-y0)^2,(y-y0)==k*(x-x0)},{x,y}]

解结果：

文本公式：

In[4]:= Solve[{d^2==(x-x0)^2+(y-y0)^2,(y-y0)==k*(x-x0)},{x,y}]2    2  2          2-Sqrt[d  + d  k ] + x0 + k  x0
Out[4]= {{x -> ------------------------------, 21 + k2       2                       3k Sqrt[d  (1 + k )]            k x0    k  x0
>     y -> -(-------------------) - k x0 + ------ + ------ + y0}, 2                       2        21 + k                   1 + k    1 + k2    2  2          2                  2       2                      3Sqrt[d  + d  k ] + x0 + k  x0       k Sqrt[d  (1 + k )]           k x0    k  x0
>    {x -> -----------------------------, y -> ------------------- - k x0 + ------ + ------ + y0}}2                              2                      2        21 + k                          1 + k                  1 + k    1 + kIn[5]:=

//创建界址点注记  宗地 如:J1,J2private void createZJ_JZD_JX(ZHFeaturePolyLine from_zhFeat, IFeatureClass toFc){IGeometry geo = from_zhFeat.pFeature.ShapeCopy;if (geo != null && geo is IPolygon){IPolygon pn = geo as IPolygon;IPoint[] pointArray = zjTool.getPoints(pn).ToArray();if (pointArray != null && pointArray.Length <= 2){   //跳过 不能构面的线return;}string jNR = "";IPoint p0 = null;IPoint p1 = null;IPoint pN = null;//长度注记for (int i = 0; i < pointArray.Length; i++){//int lastIndex = i + 1;if (lastIndex >= pointArray.Length-1){break;}if(i==0){p0 = pointArray[i];p1 = pointArray[i + 1];pN= pointArray[pointArray.Length-2];}else if(i== pointArray.Length-2){p0 = pointArray[i];p1 = pointArray[0];pN = pointArray[i - 3];}else{p0 = pointArray[i];p1 = pointArray[i + 1];pN = pointArray[i-1];}                    double A_P0_1 = zjTool.getAngleOfLine(p0, p1);double A_PN_0= zjTool.getAngleOfLine(pN, p0);double A_delta = zjTool.getAngleLine2Line(p0, pN, p1);// Math.Atan(Math.Abs(Math.Tan(A_PN_0) - Math.Tan(A_P0_1))/1+ Math.Tan(A_PN_0)* Math.Tan(A_P0_1));double A_delta_2 = A_delta / 2.0;//平分线方向角a               double A_lineMid = A_PN_0 + A_delta_2;  //凸多边形if(Math.Abs(A_PN_0- A_P0_1)<0.0001){//三点共线 //凸多边形}else{double Area_delta = zjTool.getAreaLine2Line(p0, pN, p1);if (Area_delta < 0){   //凹多边形A_lineMid = A_PN_0 - A_delta_2;}}//修正角度                 if (A_lineMid>=360){   A_lineMid = A_lineMid - 360;   }if (A_lineMid<0){A_lineMid = A_lineMid + 360;}//jNR = "J" + (i + 1).ToString();//double newAngleZJ = zjTool.newAngleZJ(AofLine);//获取注记文字长度ITextSymbol txtSymbol = zjTool.getTestTextSymbol(this.zjFontName, this.zjFontSize);double zj_width = zjTool.getTextSize(txtSymbol, jNR, true);//获取注记起始点IPoint zjPoint = zjTool.getZJPoint_JZP(p0, A_lineMid, this.zjDistance, zj_width);double A_P0_Pzj = zjTool.getAngleOfLine(p0, zjPoint);if (Math.Abs(A_lineMid - A_P0_Pzj) < 0.0001){   //注记方向与线走向一致                        }else{   //注记方向与线走向 相反zjPoint = zjTool.getZJPoint_JZP_1(p0, A_lineMid, this.zjDistance, zj_width);}//this.writeZJPoint(zjPoint, jNR, 0, from_zhFeat, toFc);this.writeZJPoint(zjPoint, ".", 0, from_zhFeat, toFc);}//}}//-----

/// <summary>  /// 根据余弦定理求两个线段夹角  /// </summary>  /// <param name="o">端点</param>  /// <param name="s">start点</param>  /// <param name="e">end点</param>  /// <returns></returns>  public static double getAngleLine2Line(IPoint o, IPoint s, IPoint e){double cosfi = 0, fi = 0, norm = 0;double dsx = s.X - o.X;double dsy = s.Y - o.Y;double dex = e.X - o.X;double dey = e.Y - o.Y;cosfi = dsx * dex + dsy * dey;norm = (dsx * dsx + dsy * dsy) * (dex * dex + dey * dey);cosfi /= Math.Sqrt(norm);if (cosfi >= 1.0) return 0;if (cosfi <= -1.0) return Math.PI;fi = Math.Acos(cosfi);if (180 * fi / Math.PI < 180){return 180 * fi / Math.PI;}else{return 360 - 180 * fi / Math.PI;}}//计算三角形面积(负数表示逆时针,正数表示顺时针方向)public static double getAreaLine2Line(IPoint o,IPoint s,IPoint e){List<IPoint> tList = new List<IPoint>();tList.Add(s);tList.Add(o);tList.Add(e);tList.Add(s);IPolygon pn = CreatePolygonNoSimplify(tList.ToArray(),null);return (pn as IArea).Area;}//public static IPoint getZJPoint_JZP(IPoint p0, double A_lineMid, double d, double zj_width){            if (A_lineMid < 1e-13){    //与X轴重叠IPoint pp = new PointClass();pp.X = p0.X + d;   //-dpp.Y = p0.Y;return pp;}double K = Math.Tan(A_lineMid*Math.PI/180.0);  //转为弧度角double KK = K * K;double KKK = KK * K;double KK_1 = 1 + KK;double sqrt_1_kk = Math.Sqrt(1 + KK);//p在直线上p0+A_lineMiddouble x = (-d * sqrt_1_kk + p0.X + KK * p0.X) / KK_1;double y = -1 * K * d * sqrt_1_kk / KK_1  - K * p0.X +(K * p0.X) / KK_1 + (KKK * p0.X) / KK_1+ p0.Y;//IPoint p = new PointClass();p.X = x;p.Y = y;return p;//          }public static IPoint getZJPoint_JZP_1(IPoint p0, double A_lineMid, double d, double zj_width){if (A_lineMid < 1e-13){    //与X轴重叠IPoint pp = new PointClass();pp.X = p0.X + d;   //-dpp.Y = p0.Y;return pp;}double K = Math.Tan(A_lineMid * Math.PI / 180.0);double KK = K * K;double KKK = KK * K;double KK_1 = 1 + KK;double sqrt_1_kk = Math.Sqrt(1 + KK);//p在直线上p0+A_lineMiddouble x = (d * sqrt_1_kk + p0.X + KK * p0.X) / KK_1;double y = K * d * sqrt_1_kk / KK_1 - K * p0.X + (K * p0.X) / KK_1 + (KKK * p0.X) / KK_1 + p0.Y;//IPoint p = new PointClass();p.X = x;p.Y = y;return p;//          }

public static IPolygon CreatePolygonNoSimplify(IPoint[] exteriorRingPoints, IPoint[][] interiorRingPoints){IPolygon r = new PolygonClass();IGeometryCollection geos = r as IGeometryCollection;//添加外环IPointCollection exRing = new RingClass();for(int i=0;i< exteriorRingPoints.Length;i++)// (IPoint p in exteriorRingPoints){IPoint p = exteriorRingPoints[i];exRing.AddPoint(p);}               geos.AddGeometry(exRing as IGeometry);//如果有内环，添加内环if (interiorRingPoints != null){foreach (IPoint[] pc in interiorRingPoints){IPointCollection inRing = new RingClass();foreach (IPoint inP in pc)inRing.AddPoint(inP);geos.AddGeometry(inRing as IGeometry);}}            return r;}

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两相交的直线段夹角平分的直线上过交点距离为d的另一点求解公式

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