例题-圆曲线坐标计算
1、该路线为一圆曲线，R=500,请将上表补充完整
解：JD1方位角=arctan（（3192.8803-3145.8062）/（1000.1723-1285.1157））
=170.6191759（可用Arg（X+Yi）或者Pol（X，Y）得出，在excel中，使用DEGREES（ATAN2（X,Y））得出
JD2里程=JD1里程+√（（1000.1723-1285.1157）^2+(3192.8803-3145.8062)^2))
=100000+288.805665(可用Abs（X+Yi）或者Pol（X,Y）得出，在Excel中，可使用SQRT(X^2+Y^2)得出
JD2方位角因为和JD1在一条直线上，所以方位角相等
JD3里程=√（（739.4631-1000.1723）^2+(3108.2597-3192.8803)^2))
=100288.805665+274.098435
JD3方位角=arctan((3108.2597-3192.8803)/(739.4631-1000.1723))
=197.9823157
ZY点里程=JD1里程+√（（1120.2611-1285.1157）^2+(3173.041-3145.8062)^2))
=100000+167.0891
YZ点里程=ZY点里程+圆曲线长
∵ 圆曲线转角=YZ点方位角-ZY点方位角
∵ ZY点方位角=JD3方位角
∴ YZ点里程=ZY点里程+（π*R*（YZ点方位角-ZY点方位角）/180
=100167.0891+（π*500*（197.9823157-170.6191759））/180
=100617.0891+238.7884=100405.8775
YZ点坐标等于
X YZ =X ZY +弦长*cos(α弦长）弦长=2R*sin（△YZ ）△YZ =（ZY点方位角-YZ点方位角）/2
Y YZ =Y ZY +弦长*sin(α弦长）=2*500*SIN(RADIANS((197.9823157-170.6191759)/2))
=236.525619570512
X YZ =1120.2611+236.5256196*cos(RADIANS（184.3007458）)α弦长=αZY +△YZ
Y YZ =3173.041+236.5256196*sin(RADIANS（184.3007458）)=170.6191759+(197.9823157-170.6191759)/2
X =884.401499=184.3007458
Y =3155.303540
QZ点里程为圆曲线长度二分之一加ZY点里程
∵圆曲线L=238.7884
∴QZ点里程=238.7884/2+100167.0891
=100286.4833
方位角αQZ =αZY +α圆曲/2
=170.6191759+(197.9823157-170.6191759)/2
=184.3007458
QZ点坐标等于
X QZ =X ZY +弦长QZ *cos(αQZ ）
弦长QZ =2R*sin(α圆曲/4）Y QZ =Y ZY +弦长QZ *sin(αQZ ）
=2*500*SIN(RADIANS(197.9823157-170.6191759)/4)X QZ =1120.2611+119.11076*cos(177.45996085)
=119.11076253761Y QZ =3173.041+119.11076*sin(177.45996085)
αQZ =αZY +α圆曲/4=1001.267367
=170.6191759+（(197.9823157-170.6191759)/4)=3178.319694=177.45996085
2、若待测点i坐标为
求该点里程；若道路净宽10.5m，测设基线为路线中心往左4.375m，求i点的偏距，以及左右边桩坐标。解：ZY点到圆曲线圆心方位角=αZY +90°
=170.6191759+90
=260.6191759
则有，圆心坐标为：
X 圆心=X ZY +R*cos（α圆心）
Y 圆心=Y ZY +R*sin（α圆心）
X =1120.2611+500*COS(RADIANS(260.6191759))
Y =3173.041+500*SIN(RADIANS(260.6191759))
X =1038.763218
Y =2679.727616
以圆心为坐标原点，则有圆心到ZY点方位角为αZY-圆心-180°
=260.6191759-180
=80.619176
待测点i至圆心方位角等于
αi=arctan（（3147.3126-2679.727616）/（939.3381-1038.763218））
αi =DEGREES(ATAN2((939.3381-1038.763218),(3147.3126-2679.727616)))
αi =102.004322
待测点i所对应的角度=αi -αO-ZY
△i =102.004322-80.619176
△i =21.385146
该段弧长Li=π*R*△i/180
Li =(PI()*500*21.385146/180)
Li =186.620604i点所对应的路线到ZY点的弦的方位角αi=αZY+△i/2该段弦长Ci=2R*sin（△i/2）=170.6191759+21.385146/2
Ci =2*500*SIN(RADIANS(21.385146/2))=181.3117489
Ci =185.53924
i点对应里程位于测设基线的里程为：
Ki=186.620604+100167.0891
Ki
=K100+353.7097
i点对应里程位于测设基线的坐标为：
X i =X ZY +C i *cos（αi ）
Y i =Y ZY +C i *sin（αi ）
=1120.2611+185.53924*COS(RADIANS(181.3117489))
=3173.041+185.53924*SIN(RADIANS(181.3117489))
=934.770483
=3168.793573
=170.6191759+21.385146
=192.0043219
左偏角为αi-90°=192.0043219-90=102.0043219
右偏角为αi+90°=192.0043219+90=282.0043219
左边桩距测设基线距离为：10.5/2-4.375=0.875m
右边桩距测设基线距离为：10.5/2+4.375=9.625m
左右边桩坐标：
X左=Xi+M*cos α左=934.770483+0.875*COS(RADIANS(102.0043219))=934.588496
Y左=Yi+M*sin α左=3168.793573+0.875*SIN(RADIANS(102.0043219))=3169.649438
X右=Xi+M*cos α右=934.770483+9.625*COS(RADIANS(282.0043219))=936.772343
Y右=Yi+M*sinα右=3168.793573+9.625*SIN(RADIANS(282.0043219))=3159.37905