超简单的道路坐标计算

高速公路的一些线路坐标、高程计算公式(缓和曲线、竖曲线、圆曲线、匝道) 一、缓和曲线上的点坐标计算已知：①缓和曲线上任一点离ZH点的长度：l②圆曲线的半径：R③缓和曲线的长度：l0④转向角系数：K(1或－1)⑤过ZH点的切线方位角：α⑥点ZH的坐标：xZ，yZ计算过程：说明：当曲线为左转向时，K=1，为右转向时，K=-1，公式中n的取值如下：当计算第二缓和曲线上的点坐标时，则：l为到点HZ的长度α为过点HZ的切线方位角再加上180°K值与计算第一缓和曲线时相反xZ，yZ为点HZ的坐标切线角计算公式：二、圆曲线上的点坐标计算已知：①圆曲线上任一点离ZH点的长度：l②圆曲线的半径：R③缓和曲线的长度：l0④转向角系数：K(1或－1)⑤过ZH点的切线方位角：α⑥点ZH的坐标：xZ，yZ计算过程：说明：当曲线为左转向时，K=1，为右转向时，K=-1，公式中n的取值如下：当只知道HZ点的坐标时，则：l为到点HZ的长度α为过点HZ的切线方位角再加上180°K值与知道ZH点坐标时相反xZ，yZ为点HZ的坐标三、曲线要素计算公式公式中各符号说明：l——任意点到起点的曲线长度（或缓曲上任意点到缓曲起点的长度）l1——第一缓和曲线长度l2——第二缓和曲线长度l0——对应的缓和曲线长度R——圆曲线半径R1——曲线起点处的半径R2——曲线终点处的半径P1——曲线起点处的曲率P2——曲线终点处的曲率α——曲线转角值四、竖曲线上高程计算已知：①第一坡度：i1(上坡为“＋”，下坡为“－”)②第二坡度：i2(上坡为“＋”，下坡为“－”)③变坡点桩号：SZ④变坡点高程：HZ⑤竖曲线的切线长度：T⑥待求点桩号：S计算过程：五、超高缓和过渡段的横坡计算已知：如图，第一横坡：i1第二横坡：i2过渡段长度：L待求处离第二横坡点（过渡段终点）的距离：x 求：待求处的横坡：i解：d=x/Li=(i2-i1)(1-3d2+2d3)+i1六、匝道坐标计算已知：①待求点桩号：K②曲线起点桩号：K0③曲线终点桩号：K1④曲线起点坐标：x0，y0⑤曲线起点切线方位角：α0⑥曲线起点处曲率：P0(左转为“－”，右转为“＋”)⑦曲线终点处曲率：P1(左转为“－”，右转为“＋”)求：①线路匝道上点的坐标：x,y②待求点的切线方位角：αT计算过程：。

逐 桩 坐 标 表ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离8525.8823590080.3521849.9370.000173.78-909083.8263.780 3.033 1.46 4.60412 8525.8823590080.3521849.93714.120.324173.78-909083.8263.780.0056 3.033 1.46 4.60412 8525.8823590080.3521849.93734.120.782173.78-909083.8263.780.0136 3.033 1.46 4.60412 8525.8823590080.3521849.93754.12 1.24173.78-909083.8263.780.0216 3.033 1.46 4.60412 8525.8823590080.3521849.93774.12 1.699173.78-909083.8263.780.0296 3.033 1.46 4.60412 8525.8823590080.3521849.93794.12 2.157173.78-909083.8263.780.0376 3.033 1.46 4.60412 8525.8823590080.3521849.937114.12 2.615173.78-909083.8263.780.0456 3.033 1.46 4.60412 8525.8823590080.3521849.937134.12 3.074173.78-909083.8263.780.0536 3.033 1.46 4.60412 8525.8823590080.3521849.937154.12 3.532173.78-909083.8263.780.0616 3.033 1.46 4.60412 8525.8823590080.3521849.937174.12 3.99173.78-909083.8263.780.0696 3.033 1.46 4.60412 8525.8823590080.3521849.937194.12 4.449173.78-909083.8263.780.0776 3.033 1.46 4.60412 8525.8823590080.3521849.937214.12 4.907173.78-909083.8263.780.0856 3.033 1.46 4.60412 8525.8823590080.3521849.937234.12 5.366173.78-909083.8263.780.0936 3.033 1.46 4.60412 8525.8823590080.3521849.937254.12 5.824173.78-909083.8263.780.1016 3.033 1.46 4.60412 8525.8823590080.3521849.937274.12 6.282173.78-909083.8263.780.1096 3.033 1.46 4.60412 8525.8823590080.3521849.937294.12 6.741173.78-909083.8263.780.1176 3.033 1.46 4.60412 8525.8823590080.3521849.937314.127.199173.78-909083.8263.780.1256 3.033 1.46 4.60412 8525.8823590080.3521849.937334.127.657173.78-909083.8263.780.1336 3.033 1.46 4.60412 8525.8823590080.3521849.937354.128.116173.78-909083.8263.780.1416 3.033 1.46 4.60412 8525.8823590080.3521849.937374.128.574173.78-909083.8263.780.1496 3.033 1.46 4.6047.995 8525.8823590080.3521849.937394.129.033173.78-909083.8263.780.1576 3.033 1.46 4.6047.995 8525.8823590080.3521849.937414.129.491173.78-909083.8263.780.1656 3.033 1.46 4.6047.995 8525.8823590080.3521849.937434.129.949173.78-909083.8263.780.1736 3.033 1.46 4.6047.995 8525.8823590080.3521849.937454.1210.41173.78-909083.8263.780.1816 3.033 1.46 4.6047.995 8525.8823590080.3521849.937474.1210.87173.78-909083.8263.780.1896 3.033 1.46 4.6047.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离8525.8823590080.3521849.937494.1211.32173.78-909083.8263.780.1976 3.033 1.46 4.6047.995 8525.8823590080.3521849.937514.1211.78173.78-909083.8263.780.2056 3.033 1.46 4.6047.995 8525.8823590080.3521849.937534.1212.24173.78-909083.8263.780.2136 3.033 1.46 4.6047.995 8525.8823590080.3521849.937554.1212.7173.78-909083.8263.780.2216 3.033 1.46 4.6047.995 8525.8823590080.3521849.937574.1213.16173.78-909083.8263.780.2296 3.033 1.46 4.6047.995 8525.8823590080.3521849.937594.1213.62173.78-909083.8263.780.2376 3.033 1.46 4.6047.995 8525.8823590080.3521849.937614.1214.07173.78-909083.8263.780.2456 3.033 1.46 4.6047.995 8525.8823590080.3521849.937634.1214.53173.78-909083.8263.780.2536 3.033 1.46 4.6047.995 8525.8823590080.3521849.937654.1214.99173.78-909083.8263.780.2616 3.033 1.46 4.6047.995 8525.8823590080.3521849.937674.1215.45173.78-909083.8263.780.2696 3.033 1.46 4.6047.995 8525.8823590080.3521849.937694.1215.91173.78-909083.8263.780.2776 3.033 1.46 4.6047.995 8525.8823590080.3521849.937714.1216.37173.78-909083.8263.780.2856 3.033 1.46 4.6047.995 8525.8823590080.3521849.937734.1216.82173.78-909083.8263.780.2936 3.033 1.46 4.6047.995 8525.8823590080.3521849.937754.1217.28173.78-909083.8263.780.3016 3.033 1.46 4.6047.995 8525.8823590080.3521849.937774.1217.74173.78-909083.8263.780.3096 3.033 1.46 4.6047.995 8525.8823590080.3521849.937775.4817.77173.78-909083.8263.780.3102 3.033 1.46 4.6047.995 ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离9301.3663589309.378521933.927300018.6340.356173.781-909084.1264.140.0062 3.033 1.47 4.617.995 9301.3663589309.378521933.927300038.6340.738173.781-909084.5264.520.0129 3.033 1.48 4.6177.995 9301.3663589309.378521933.927300058.634 1.12173.781-909084.9264.90.0195 3.033 1.48 4.6237.995 9301.3663589309.378521933.927300078.634 1.502173.781-909085.3265.280.0262 3.033 1.49 4.637.995 9301.3663589309.378521933.927300098.634 1.884173.781-909085.7265.670.0329 3.033 1.5 4.6377.995 9301.3663589309.378521933.9273000118.634 2.266173.781-909086266.050.0395 3.033 1.5 4.6437.995 9301.3663589309.378521933.9273000138.634 2.648173.781-909086.4266.430.0462 3.033 1.51 4.657.995 9301.3663589309.378521933.9273000158.634 3.03173.781-909086.8266.810.0529 3.033 1.52 4.6577.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离9301.3663589309.378521933.9273000178.634 3.412173.781-909087.2267.190.0595 3.033 1.52 4.6637.995 9301.3663589309.378521933.9273000198.634 3.794173.781-909087.6267.580.0662 3.033 1.53 4.677.995 9301.3663589309.378521933.9273000218.634 4.176173.781-909088267.960.0729 3.033 1.54 4.6777.995 9301.3663589309.378521933.9273000238.634 4.558173.781-909088.3268.340.0795 3.033 1.54 4.6837.995 9301.3663589309.378521933.9273000258.634 4.94173.781-909088.7268.720.0862 3.033 1.55 4.697.995 9301.3663589309.378521933.9273000278.634 5.322173.781-909089.1269.10.0929 3.033 1.56 4.6977.995 9301.3663589309.378521933.9273000298.634 5.703173.781-909089.5269.490.0995 3.033 1.56 4.7037.995 9301.3663589309.378521933.9273000318.634 6.085173.781-909089.9269.870.1062 3.033 1.57 4.717.995 9301.3663589309.378521933.9273000338.634 6.467173.781-909090.2270.250.1129 3.033 1.58 4.7177.995 9301.3663589309.378521933.9273000353.727 6.756173.781-909090.5270.540.1179 3.033 1.58 4.7227.995 9655.0933588956.29521951.441 4.910.112180.54-909090.5270.540.002 3.151 1.58 4.7227.995 9655.0933588956.29521951.44124.910.571180.54-909090.5270.540.01 3.151 1.58 4.7227.995 9655.0933588956.29521951.44144.91 1.029180.54-909090.5270.540.018 3.151 1.58 4.7227.995 9655.0933588956.29521951.44164.91 1.488180.54-909090.5270.540.026 3.151 1.58 4.7227.995 9655.0933588956.29521951.44184.91 1.946180.54-909090.5270.540.034 3.151 1.58 4.7227.995 9655.0933588956.29521951.441104.91 2.404180.54-909090.5270.540.042 3.151 1.58 4.7227.995 9655.0933588956.29521951.441124.91 2.863180.54-909090.5270.540.05 3.151 1.58 4.7227.995 9655.0933588956.29521951.441144.91 3.321180.54-909090.5270.540.058 3.151 1.58 4.7227.995 9655.0933588956.29521951.441164.91 3.779180.54-909090.5270.540.066 3.151 1.58 4.7227.995 9655.0933588956.29521951.441171.51 3.931180.54-909090.5270.540.0686 3.151 1.58 4.7227.995 9826.6083588784.782521949.831150013.392-0.02180.54-1-909090.5270.56201.67-0.01 1.58 4.7227.995 9826.6083588784.782521949.831150033.392-0.11180.54-1-909090.4270.64201.67-0.04 1.58 4.7247.995 9826.6083588784.782521949.831150053.392-0.27180.54-1-909090.3270.81201.67-0.09 1.58 4.7267.995 9826.6083588784.782521949.831150073.392-0.51180.54-1-909090271.05201.67-0.17 1.57 4.7317.995 9826.6083588784.782521949.831150093.392-0.83180.54-1-909089.7271.36201.67-0.28 1.57 4.7367.995 9826.6083588784.782521949.8311500113.392-1.22180.54-1-909089.3271.76201.67-0.41 1.56 4.7437.995 9826.6083588784.782521949.8311500133.392-1.69180.54-1-909088.9272.22201.67-0.56 1.55 4.7517.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离9826.6083588784.782521949.8311500153.392-2.23180.54-1-909088.3272.77201.67-0.74 1.54 4.7617.995 9826.6083588784.782521949.8311500173.392-2.85180.54-1-909087.7273.39201.67-0.95 1.53 4.7717.995 9826.6083588784.782521949.8311500193.392-3.54180.54-1-909087274.08201.67-1.18 1.52 4.7847.995 9826.6083588784.782521949.8311500201.667-3.85180.54-1-909086.7274.39201.67-1.28 1.51 4.7897.995 ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离10028.2753588583.173521952.455150011.7250.448176.69-1-909086.2266.240.0078 3.084 1.51 4.6477.995 10028.2753588583.173521952.455150031.725 1.212176.69-1-909085.5265.470.0212 3.084 1.49 4.6337.995 10028.2753588583.173521952.455150051.725 1.976176.69-1-909084.7264.710.0345 3.084 1.48 4.627.995 10028.2753588583.173521952.455150071.725 2.74176.69-1-909083.9263.950.0478 3.084 1.47 4.6077.995 10028.2753588583.173521952.455150091.725 3.504176.69-1-909083.2263.180.0612 3.084 1.45 4.5937.995 10028.2753588583.173521952.4551500111.725 4.268176.69-1-909082.4262.420.0745 3.084 1.44 4.587.995 10028.2753588583.173521952.4551500131.725 5.032176.69-1-909081.7261.650.0878 3.084 1.43 4.5677.995 10028.2753588583.173521952.4551500151.725 5.795176.69-1-909080.9260.890.1012 3.084 1.41 4.5537.995 10028.2753588583.173521952.4551500171.725 6.559176.69-1-909080.1260.130.1145 3.084 1.4 4.547.995 10028.2753588583.173521952.4551500191.7257.323176.69-1-909079.4259.360.1278 3.084 1.39 4.5277.995 10028.2753588583.173521952.4551500211.7258.087176.69-1-909078.6258.60.1412 3.084 1.37 4.5137.995 10028.2753588583.173521952.4551500231.7258.851176.69-1-909077.8257.840.1545 3.084 1.36 4.57.995 10028.2753588583.173521952.4551500251.7259.615176.69-1-909077.1257.070.1678 3.084 1.35 4.4877.995 10028.2753588583.173521952.4551500269.1610.28176.69-1-909076.4256.410.1794 3.084 1.33 4.4757.995 9301.3663589309.378521933.9273000998.63419.07173.781-9090103282.850.3329 3.033 1.8 4.9377.995 9301.3663589309.378521933.92730001018.63419.45173.781-9090103283.240.3395 3.033 1.8 4.9437.995 9301.3663589309.378521933.92730001038.63419.84173.781-9090104283.620.3462 3.033 1.81 4.957.9959301.3663589309.378521933.9271098.63420.98173.78-909083.8263.780.3662 3.033 1.46 4.6047.995 9301.3663589309.378521933.9271118.63421.36173.78-909083.8263.780.3729 3.033 1.46 4.6047.995 9301.3663589309.378521933.9271138.63421.75173.78-909083.8263.780.3795 3.033 1.46 4.6047.995 9301.3663589309.378521933.9271158.63422.13173.78-909083.8263.780.3862 3.033 1.46 4.6047.995ZY点或YZ点RL E N 左右偏左侧右侧F F弧度E 弧度N 弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离ZY点或YZ点坐标9301.3663589309.378521933.9271178.63422.51173.78-909083.8263.780.3929 3.033 1.46 4.6047.9959301.3663589309.378521933.9271197.73622.88173.78-909083.8263.780.3992 3.033 1.46 4.6047.995ZY点或YZ点R LEN左右偏左侧右侧FF弧度E 弧度N 弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离10499.1023588123.637522048.0980.900.021162.55-909072.6252.550.0004 2.837 1.27 4.4087.99510499.1023588123.637522048.09820.900.479162.55-909072.6252.550.0084 2.837 1.27 4.4087.99510499.1023588123.637522048.09840.900.937162.55-909072.6252.550.0164 2.837 1.27 4.4087.99510499.1023588123.637522048.09860.90 1.396162.55-909072.6252.550.0244 2.837 1.27 4.4087.99510499.1023588123.637522048.09880.90 1.854162.55-909072.6252.550.0324 2.837 1.27 4.4087.99510499.1023588123.637522048.098100.90 2.312162.55-909072.6252.550.0404 2.837 1.27 4.4087.99510499.1023588123.637522048.098120.90 2.771162.55-909072.6252.550.0484 2.837 1.27 4.4087.99510499.1023588123.637522048.098140.90 3.229162.55-909072.6252.550.0564 2.837 1.27 4.4087.99510499.1023588123.637522048.098160.90 3.688162.55-909072.6252.550.0644 2.837 1.27 4.4087.99510499.1023588123.637522048.098180.90 4.146162.55-909072.6252.550.0724 2.837 1.27 4.4087.99510499.1023588123.637522048.098200.90 4.604162.55-909072.6252.550.0804 2.837 1.27 4.4087.99510499.1023588123.637522048.098220.90 5.063162.55-909072.6252.550.0884 2.837 1.27 4.4087.99510499.1023588123.637522048.098240.90 5.521162.55-909072.6252.550.0964 2.837 1.27 4.4087.99510499.1023588123.637522048.098260.90 5.979162.55-909072.6252.550.1044 2.837 1.27 4.4087.99510499.1023588123.637522048.098280.90 6.438162.55-909072.6252.550.1124 2.837 1.27 4.4087.99510499.1023588123.637522048.098300.90 6.896162.55-909072.6252.550.1204 2.837 1.27 4.4087.99510499.1023588123.637522048.098320.907.354162.55-909072.6252.550.1284 2.837 1.27 4.4087.99510499.1023588123.637522048.098340.907.813162.55-909072.6252.550.1364 2.837 1.27 4.4087.99510499.1023588123.637522048.098360.908.271162.55-909072.6252.550.1444 2.837 1.27 4.4087.99510499.1023588123.637522048.098380.908.73162.55-909072.6252.550.1524 2.837 1.27 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4.7587.995 12424.3753586234.023522364.158395.639.067182.63-909092.6272.630.1583 3.187 1.62 4.7587.995 12424.3753586234.023522364.158415.639.525182.63-909092.6272.630.1663 3.187 1.62 4.7587.995 12424.3753586234.023522364.158435.639.984182.63-909092.6272.630.1743 3.187 1.62 4.7587.995 12424.3753586234.023522364.158455.6310.44182.63-909092.6272.630.1823 3.187 1.62 4.7587.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离12424.3753586234.023522364.158475.6310.9182.63-909092.6272.630.1903 3.187 1.62 4.7587.995 12424.3753586234.023522364.158495.6311.36182.63-909092.6272.630.1983 3.187 1.62 4.7587.995 12424.3753586234.023522364.158515.6311.82182.63-909092.6272.630.2063 3.187 1.62 4.7587.995 12424.3753586234.023522364.158535.6312.28182.63-909092.6272.630.2143 3.187 1.62 4.7587.995 12424.3753586234.023522364.158555.6312.73182.63-909092.6272.630.2223 3.187 1.62 4.7587.995 12424.3753586234.023522364.158575.6313.19182.63-909092.6272.630.2303 3.187 1.62 4.7587.995 12424.3753586234.023522364.158595.6313.65182.63-909092.6272.630.2383 3.187 1.62 4.7587.995 12424.3753586234.023522364.158615.6314.11182.63-909092.6272.630.2463 3.187 1.62 4.7587.995 12424.3753586234.023522364.158635.6314.57182.63-909092.6272.630.2543 3.187 1.62 4.7587.995 12424.3753586234.023522364.158655.6315.03182.63-909092.6272.630.2623 3.187 1.62 4.7587.995 12424.3753586234.023522364.158675.6315.48182.63-909092.6272.630.2703 3.187 1.62 4.7587.995 12424.3753586234.023522364.158695.6315.94182.63-909092.6272.630.2783 3.187 1.62 4.7587.995 12424.3753586234.023522364.158715.6316.4182.63-909092.6272.630.2863 3.187 1.62 4.7587.995 12424.3753586234.023522364.158735.6316.86182.63-909092.6272.630.2943 3.187 1.62 4.7587.995 12424.3753586234.023522364.158755.6317.32182.63-909092.6272.630.3023 3.187 1.62 4.7587.995 12424.3753586234.023522364.158775.6317.78182.63-909092.6272.630.3103 3.187 1.62 4.7587.995 12424.3753586234.023522364.158795.6318.23182.63-909092.6272.630.3183 3.187 1.62 4.7587.995 12424.3753586234.023522364.158815.6318.69182.63-909092.6272.630.3263 3.187 1.62 4.7587.995 12424.3753586234.023522364.158835.6319.15182.63-909092.6272.630.3343 3.187 1.62 4.7587.995 12424.3753586234.023522364.158855.6319.61182.63-909092.6272.630.3423 3.187 1.62 4.7587.995 12424.3753586234.023522364.158875.6320.07182.63-909092.6272.630.3503 3.187 1.62 4.7587.995 12424.3753586234.023522364.158895.6320.53182.63-909092.6272.630.3583 3.187 1.62 4.7587.995 12424.3753586234.023522364.158915.6320.98182.63-909092.6272.630.3663 3.187 1.62 4.7587.995 12424.3753586234.023522364.158935.6321.44182.63-909092.6272.630.3743 3.187 1.62 4.7587.995 12424.3753586234.023522364.158955.6321.9182.63-909092.6272.630.3823 3.187 1.62 4.7587.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离12424.3753586234.023522364.158975.6322.36182.63-909092.6272.630.3903 3.187 1.62 4.7587.995 12424.3753586234.023522364.158995.6322.82182.63-909092.6272.630.3983 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,015.6323.28182.63-909092.6272.630.4063 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,035.6323.73182.63-909092.6272.630.4143 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,055.6324.19182.63-909092.6272.630.4223 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,075.6324.65182.63-909092.6272.630.4303 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,095.6325.11182.63-909092.6272.630.4383 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,115.6325.57182.63-909092.6272.630.4463 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,135.6326.03182.63-909092.6272.630.4543 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,155.6326.48182.63-909092.6272.630.4623 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,175.6326.94182.63-909092.6272.630.4703 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,195.6327.4182.63-909092.6272.630.4783 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,215.6327.86182.63-909092.6272.630.4863 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,235.6328.32182.63-909092.6272.630.4943 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,255.6328.78182.63-909092.6272.630.5023 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,275.6329.24182.63-909092.6272.630.5103 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,295.6329.69182.63-909092.6272.630.5183 3.187 1.62 4.7587.995 12424.3753586234.023522364.1581,302.9729.86182.63-909092.6272.630.5212 3.187 1.62 4.7587.995 13727.343584932.426522304.462260012.660.279182.631-909092.9272.90.0049 3.187 1.62 4.7637.995 13727.343584932.426522304.462260032.660.72182.631-909093.3273.350.0126 3.187 1.63 4.7717.995 13727.343584932.426522304.462260052.66 1.16182.631-909093.8273.790.0203 3.187 1.64 4.7787.995 13727.343584932.426522304.462260072.66 1.601182.631-909094.2274.230.0279 3.187 1.64 4.7867.995 13727.343584932.426522304.462260092.66 2.042182.631-909094.7274.670.0356 3.187 1.65 4.7947.995 13727.343584932.426522304.4622600112.66 2.483182.631-909095.1275.110.0433 3.187 1.66 4.8027.995 13727.343584932.426522304.4622600132.66 2.923182.631-909095.5275.550.051 3.187 1.67 4.8097.995 13727.343584932.426522304.4622600152.66 3.364182.631-909096275.990.0587 3.187 1.68 4.8177.995ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F S 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧横向距离13727.343584932.426522304.4622600172.66 3.805182.631-909096.4276.430.0664 3.187 1.68 4.8257.995 13727.343584932.426522304.4622600192.66 4.246182.631-909096.9276.870.0741 3.187 1.69 4.8327.995 13727.343584932.426522304.4622600212.66 4.686182.631-909097.3277.310.0818 3.187 1.7 4.847.995 13727.343584932.426522304.4622600232.66 5.127182.631-909097.8277.750.0895 3.187 1.71 4.8487.995 13727.343584932.426522304.4622600252.66 5.568182.631-909098.2278.190.0972 3.187 1.71 4.8557.995 13727.343584932.426522304.4622600272.66 6.009182.631-909098.6278.630.1049 3.187 1.72 4.8637.995 13727.343584932.426522304.4622600292.66 6.449182.631-909099.1279.080.1126 3.187 1.73 4.8717.995 13727.343584932.426522304.4622600312.66 6.89182.631-909099.5279.520.1203 3.187 1.74 4.8787.995 13727.343584932.426522304.4622600332.667.331182.631-9090100279.960.1279 3.187 1.74 4.8867.995 13727.343584932.426522304.4622600352.667.772182.631-9090100280.40.1356 3.187 1.75 4.8947.995 13727.343584932.426522304.4622600372.668.212182.631-9090101280.840.1433 3.187 1.76 4.9027.995 13727.343584932.426522304.4622600392.668.653182.631-9090101281.280.151 3.187 1.77 4.9097.995 13727.343584932.426522304.4622600412.669.094182.631-9090102281.720.1587 3.187 1.78 4.9177.995 13727.343584932.426522304.4622600432.669.534182.631-9090102282.160.1664 3.187 1.78 4.9257.995 13727.343584932.426522304.4622600452.669.975182.631-9090103282.60.1741 3.187 1.79 4.9327.995 13727.343584932.426522304.4622600472.6610.42182.631-9090103283.040.1818 3.187 1.8 4.947.995 13727.343584932.426522304.4622600492.6610.86182.631-9090103283.480.1895 3.187 1.81 4.9487.995 13727.343584932.426522304.4622600512.6611.3182.631-9090104283.920.1972 3.187 1.81 4.9557.995 13727.343584932.426522304.4622600532.6611.74182.631-9090104284.360.2049 3.187 1.82 4.96312 13727.343584932.426522304.4622600552.6612.18182.631-9090105284.80.2126 3.187 1.83 4.97112 13727.343584932.426522304.4622600572.6612.62182.631-9090105285.250.2203 3.187 1.84 4.97812 13727.343584932.426522304.4622600592.6613.06182.631-9090106285.690.2279 3.187 1.84 4.98612 13727.343584932.426522304.4622600612.6613.5182.631-9090106286.130.2356 3.187 1.85 4.99412 13727.343584932.426522304.4622600632.6613.94182.631-9090107286.570.2433 3.187 1.86 5.00212 13727.343584932.426522304.4622600652.6614.38182.631-9090107287.010.251 3.187 1.87 5.00912 13727.343584932.426522304.4622600672.6614.82182.631-9090107287.450.2587 3.187 1.88 5.01712 13727.343584932.426522304.4622600692.6615.26182.631-9090108287.890.2664 3.187 1.88 5.02512 13727.343584932.426522304.4622600712.6615.7182.631-9090108288.330.2741 3.187 1.89 5.03212 13727.343584932.426522304.4622600732.6616.15182.631-9090109288.770.2818 3.187 1.9 5.0412。

用Excel程序快速计算公路工程逐桩坐标H现代公路IGHWAY用Excel程序快速计算公路工程逐桩坐标文/左卿引言在公路工程设计及施工过程中，逐桩坐标的计算是一项必不可少的工作，尤其近些年随着全站仪的普及使用，坐标放样法因速度快、精度高而被广泛应用，逐桩坐标计算的工程量也因此而大大增加。

例如：某高速公路某一合同段有20公里的路基，按照常规的设计及施工方法，不考虑曲线加桩，按每20m一个断面，每个断面左右幅2个点，那么需要计算1000个点2000个坐标。

如此大的计算量假如采用传统的计算器计算，不仅费时，还难免出错。

笔者从事多年施工工作，针对这一情况，利用Microsoft Office中的Excel电子表格的编程计算功能，设计了一套包括直线、缓和曲线和圆曲线的坐标计算程序，该计算程序具有快速、精确、程序简单、使用方便等优点，较其他编程软件编制的计算程序更灵活、更适用。

坐标计算直线段逐桩坐标首先介绍函数Value（MIDB（“ZH”，2，n）MIDB(“ZH”，n+3，7)），n表示公里数的位数，当里程公里数为1位数，那么n=1，当公里数为2位数，n=2，当里程公里数为3位数时，n=3……。

如ZH=K136+700，运行该函数，n=3，结果=136700，其目的为将K136+700文本数据（字符串）去掉“K”和“+”，并转换成数字格式。

那么里程≤ZH的前直线上任意桩号坐标计算：在Excel某一单元格中，坐标计算编辑公式为：X= Xj+（T+Value（MIDB （“ZH”，2，n）MIDB(“ZH”，n+3，7)）－Value（MIDB（“K”，2，n）MIDB(“K”，n+3，7)））*cos((A1+180)*PI()/180)Y= Yj+（T+Value（MIDB（“ZH”，2，n）MIDB(“ZH”， n+3，7)）－Value（MIDB（“K”，2，程序设计程序设计初步打开Microsoft Office Excel2022，新建工作表book1，并将其命名为“公路工程逐桩坐标计算表”。

gps坐标测距计算公式GPS坐标测距计算公式1. 计算两个点之间的直线距离直线距离是最常见的测距方式，计算两个点的经纬度坐标之间的直线距离可以使用几何学中的直线距离公式：Distance = √[(X2-X1)^2 + (Y2-Y1)^2]其中，X1和Y1是第一个点的经纬度坐标，X2和Y2是第二个点的经纬度坐标。

这个公式适用于小范围的测距，对于大范围的测距可能存在误差。

例如，计算两个点之间的直线距离：•点A的经纬度坐标：(, )•点B的经纬度坐标：(, )按照上述公式计算：Distance = √[()^2 + ()^2] = √[(-)^2 + ()^2] ≈因此，点A和点B之间的直线距离约为。

2. 计算两个点之间的球面距离GPS坐标表示的是地球上的位置，在地球表面上两点之间的距离必须考虑地球的曲率。

采用球面距离公式可以更精确地计算两个点之间的距离。

Haversine公式是一种常用的计算球面距离的方式，适用于小范围和大范围的距离计算。

Distance = 2 * R * arcsin(√[sin^2((lat2-lat1)/2) + cos(lat1) * cos(lat2) * sin^2((lon2-lon1)/2)] )其中，R是地球的半径（一般取平均半径），lat1和lon1是第一个点的纬度和经度，lat2和lon2是第二个点的纬度和经度。

这个公式能够准确地计算两个点之间的球面距离，无论距离多远。

举个例子，计算两个点之间的球面距离：•点A的经纬度坐标：(, )•点B的经纬度坐标：(, )按照Haversine公式计算：Distance = 2 * 6371 * arcsin(√[sin^2(()/2) + cos() * cos() * sin^2(()/2)] )= 2 * 6371 * arcsin(√[sin^2(-) + cos() * cos() * sin^2()] )≈因此，点A和点B之间的球面距离约为公里。

ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧218003581208.168485683.7650.000183.4-909093.4273.390 3.201 1.63 4.772 218003581208.168485683.76520.000.121183.4-909093.4273.390.0021 3.201 1.63 4.772 218003581208.168485683.76540.000.241183.4-909093.4273.390.0042 3.201 1.63 4.772 218003581208.168485683.76560.000.362183.4-909093.4273.390.0063 3.201 1.63 4.772 218003581208.168485683.76580.000.482183.4-909093.4273.390.0084 3.201 1.63 4.772 218003581208.168485683.765100.000.603183.4-909093.4273.390.0105 3.201 1.63 4.772 218003581208.168485683.765120.000.724183.4-909093.4273.390.0126 3.201 1.63 4.772 218003581208.168485683.765140.000.844183.4-909093.4273.390.0147 3.201 1.63 4.772 218003581208.168485683.765145.49 1.852183.4-909093.4273.390.0323 3.201 1.63 4.772 21945.4853581062.938485675.152950014.510.088183.41-909093.5273.480.0015 3.201 1.63 4.773 21945.4853581062.938485675.152950034.510.208183.41-909093.6273.60.0036 3.201 1.63 4.775 21945.4853581062.938485675.152950054.510.329183.41-909093.7273.720.0057 3.201 1.64 4.777 21945.4853581062.938485675.152950074.510.449183.41-909093.8273.840.0078 3.201 1.64 4.779ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧21945.4853581062.938485675.152950094.510.57183.41-909094273.960.0099 3.201 1.64 4.782 21945.4853581062.938485675.1529500114.510.691183.41-909094.1274.080.0121 3.201 1.64 4.784 21945.4853581062.938485675.1529500134.510.811183.41-909094.2274.210.0142 3.201 1.64 4.786 21945.4853581062.938485675.1529500154.510.932183.41-909094.3274.330.0163 3.201 1.65 4.788 21945.4853581062.938485675.1529500174.51 1.053183.41-909094.4274.450.0184 3.201 1.65 4.79 21945.4853581062.938485675.1529500194.51 1.173183.41-909094.6274.570.0205 3.201 1.65 4.792 21945.4853581062.938485675.1529500214.51 1.294183.41-909094.7274.690.0226 3.201 1.65 4.794 21945.4853581062.938485675.1529500234.51 1.414183.41-909094.8274.810.0247 3.201 1.65 4.796 21945.4853581062.938485675.1529500254.51 1.535183.41-909094.9274.930.0268 3.201 1.66 4.798 21945.4853581062.938485675.1529500274.51 1.656183.41-909095275.050.0289 3.201 1.66 4.801 21945.4853581062.938485675.1529500294.51 1.776183.41-909095.2275.170.031 3.201 1.66 4.803 21945.4853581062.938485675.1529500314.51 1.897183.41-909095.3275.290.0331 3.201 1.66 4.805 21945.4853581062.938485675.1529500334.51 2.018183.41-909095.4275.410.0352 3.201 1.67 4.807ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧21945.4853581062.938485675.1529500354.51 2.138183.41-909095.5275.530.0373 3.201 1.67 4.809 21945.4853581062.938485675.1529500374.51 2.259183.41-909095.7275.650.0394 3.201 1.67 4.811 21945.4853581062.938485675.1529500394.51 2.379183.41-909095.8275.770.0415 3.201 1.67 4.813 21945.4853581062.938485675.1529500414.51 2.5183.41-909095.9275.890.0436 3.201 1.67 4.815 21945.4853581062.938485675.1529500434.51 2.621183.41-909096276.010.0457 3.201 1.68 4.817 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23904.023579110.677485588.429575.9813.2186.5-909096.5276.460.2304 3.254 1.68 4.825 23904.023579110.677485588.429595.9813.66186.5-909096.5276.460.2384 3.254 1.68 4.825 23904.023579110.677485588.429615.9814.12186.5-909096.5276.460.2464 3.254 1.68 4.825 23904.023579110.677485588.429632.03914.49186.5-909096.5276.460.2528 3.254 1.68 4.825 24536.0593578482.657485517.269250023.9410.549186.5-1-909095.9275.920.0096 3.254 1.67 4.816 24536.0593578482.657485517.269250043.941 1.007186.5-1-909095.5275.460.0176 3.254 1.67 4.808ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧24536.0593578482.657485517.269250063.941 1.465186.5-1-9090952750.0256 3.254 1.66 4.8 24536.0593578482.657485517.269250083.941 1.924186.5-1-909094.5274.540.0336 3.254 1.65 4.792 24536.0593578482.657485517.2692500103.941 2.382186.5-1-909094.1274.080.0416 3.254 1.64 4.784 24536.0593578482.657485517.2692500123.941 2.841186.5-1-909093.6273.620.0496 3.254 1.63 4.776 24536.0593578482.657485517.2692500143.941 3.299186.5-1-909093.2273.170.0576 3.254 1.63 4.768 24536.0593578482.657485517.2692500163.941 3.757186.5-1-909092.7272.710.0656 3.254 1.62 4.76 24536.0593578482.657485517.2692500183.941 4.216186.5-1-909092.2272.250.0736 3.254 1.61 4.752 24536.0593578482.657485517.2692500203.941 4.674186.5-1-909091.8271.790.0816 3.254 1.6 4.744 24536.0593578482.657485517.2692500223.941 5.132186.5-1-909091.3271.330.0896 3.254 1.59 4.736 24536.0593578482.657485517.2692500243.941 5.591186.5-1-909090.9270.870.0976 3.254 1.59 4.728 24536.0593578482.657485517.2692500263.941 6.049186.5-1-909090.4270.420.1056 3.254 1.58 4.72 24536.0593578482.657485517.2692500283.941 6.507186.5-1-909090269.960.1136 3.254 1.57 4.712 24536.0593578482.657485517.2692500303.941 6.966186.5-1-909089.5269.50.1216 3.254 1.56 4.704ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧24536.0593578482.657485517.2692500323.9417.424186.5-1-909089269.040.1296 3.254 1.55 4.696 24536.0593578482.657485517.2692500343.9417.883186.5-1-909088.6268.580.1376 3.254 1.55 4.688 24536.0593578482.657485517.2692500363.9418.341186.5-1-909088.1268.120.1456 3.254 1.54 4.68 24536.0593578482.657485517.2692500383.9418.799186.5-1-909087.7267.670.1536 3.254 1.53 4.672 24536.0593578482.657485517.2692500403.9419.258186.5-1-909087.2267.210.1616 3.254 1.52 4.664 24536.0593578482.657485517.2692500423.9419.716186.5-1-909086.7266.750.1696 3.254 1.51 4.656 24536.0593578482.657485517.2692500443.94110.17186.5-1-909086.3266.290.1776 3.254 1.51 4.648 24536.0593578482.657485517.2692500463.94110.63186.5-1-909085.8265.830.1856 3.254 1.5 4.64 24536.0593578482.657485517.2692500483.94111.09186.5-1-909085.4265.370.1936 3.254 1.49 4.632 24536.0593578482.657485517.2692500503.94111.55186.5-1-909084.9264.920.2016 3.254 1.48 4.624 24536.0593578482.657485517.2692500523.94112.01186.5-1-909084.5264.460.2096 3.254 1.47 4.616 24536.0593578482.657485517.2692500543.94112.47186.5-1-9090842640.2176 3.254 1.47 4.608 24536.0593578482.657485517.2692500563.94112.92186.5-1-909083.5263.540.2256 3.254 1.46 4.6ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧24536.0593578482.657485517.2692500583.94113.38186.5-1-909083.1263.080.2336 3.254 1.45 4.592 24536.0593578482.657485517.2692500603.94113.84186.5-1-909082.6262.620.2416 3.254 1.44 4.584 24536.0593578482.657485517.2692500624.64514.32186.5-1-909082.1262.150.2499 3.254 1.43 4.575 25160.7043577859.68485524.809250019.2960.442172.11-909082.6262.590.0077 3.005 1.44 4.583 25160.7043577859.68485524.809250039.2960.901172.11-909083263.050.0157 3.005 1.45 4.591 25160.7043577859.68485524.809250059.296 1.359172.11-909083.5263.510.0237 3.005 1.46 4.599 25160.7043577859.68485524.809250079.296 1.817172.11-909084263.970.0317 3.005 1.47 4.607 25160.7043577859.68485524.809250099.296 2.276172.11-909084.4264.420.0397 3.005 1.47 4.615 25160.7043577859.68485524.8092500119.296 2.734172.11-909084.9264.880.0477 3.005 1.48 4.623 25160.7043577859.68485524.8092500139.296 3.192172.11-909085.3265.340.0557 3.005 1.49 4.631 25160.7043577859.68485524.8092500159.296 3.651172.11-909085.8265.80.0637 3.005 1.5 4.639 25160.7043577859.68485524.8092500179.296 4.109172.11-909086.3266.260.0717 3.005 1.51 4.647 25160.7043577859.68485524.8092500199.296 4.568172.11-909086.7266.720.0797 3.005 1.51 4.655ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25160.7043577859.68485524.8092500219.296 5.026172.11-909087.2267.170.0877 3.005 1.52 4.663 25160.7043577859.68485524.8092500239.296 5.484172.11-909087.6267.630.0957 3.005 1.53 4.671 25160.7043577859.68485524.8092500259.296 5.943172.11-909088.1268.090.1037 3.005 1.54 4.679 25160.7043577859.68485524.8092500279.296 6.401172.11-909088.5268.550.1117 3.005 1.55 4.687 25160.7043577859.68485524.8092500299.296 6.859172.11-909089269.010.1197 3.005 1.55 4.695 25160.7043577859.68485524.8092500319.2967.318172.11-909089.5269.470.1277 3.005 1.56 4.703 25160.7043577859.68485524.8092500339.2967.776172.11-909089.9269.920.1357 3.005 1.57 4.711 25160.7043577859.68485524.8092500359.2968.234172.11-909090.4270.380.1437 3.005 1.58 4.719 25160.7043577859.68485524.8092500379.2968.693172.11-909090.8270.840.1517 3.005 1.59 4.727 25160.7043577859.68485524.8092500390.938.959172.11-909091.1271.110.1564 3.005 1.59 4.732 25160.7043577859.68485524.8092500399.309.151172.11-909091.3271.30.1597 3.005 1.59 4.735 25160.7043577859.68485524.8092500419.309.61172.11-909091.8271.760.1677 3.005 1.6 4.743 25160.7043577859.68485524.8092500439.3010.07172.11-909092.2272.220.1757 3.005 1.61 4.751ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25160.7043577859.68485524.8092500459.3010.53172.11-909092.7272.670.1837 3.005 1.62 4.759 25160.7043577859.68485524.8092500479.3010.98172.11-909093.1273.130.1917 3.005 1.63 4.767 25160.7043577859.68485524.8092500499.3011.44172.11-909093.6273.590.1997 3.005 1.63 4.775 25160.7043577859.68485524.8092500519.3011.9172.11-909094.1274.050.2077 3.005 1.64 4.783 25160.7043577859.68485524.8092500539.3012.36172.11-909094.5274.510.2157 3.005 1.65 4.791 25160.7043577859.68485524.8092500559.3012.82172.11-909095274.970.2237 3.005 1.66 4.799 25160.7043577859.68485524.8092500579.3013.28172.11-909095.4275.430.2317 3.005 1.67 4.807 25160.7043577859.68485524.8092500599.3013.73172.11-909095.9275.880.2397 3.005 1.67 4.815 25160.7043577859.68485524.8092500619.3014.19172.11-909096.3276.340.2477 3.005 1.68 4.823 25160.7043577859.68485524.8092500639.3014.65172.11-909096.8276.80.2557 3.005 1.69 4.831 25160.7043577859.68485524.8092500659.3015.11172.11-909097.3277.260.2637 3.005 1.7 4.839 25160.7043577859.68485524.8092500672.0715.4172.11-909097.6277.550.2688 3.005 1.7 4.844 25832.7763577189.633485526.5637.220.166187.6-909097.6277.550.0029 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.56327.220.624187.6-909097.6277.550.0109 3.273 1.7 4.844 25832.7763577189.633485526.56347.224 1.082187.6-909097.6277.550.0189 3.273 1.7 4.844 25832.7763577189.633485526.56367.224 1.541187.6-909097.6277.550.0269 3.273 1.7 4.844 25832.7763577189.633485526.56387.224 1.999187.6-909097.6277.550.0349 3.273 1.7 4.844 25832.7763577189.633485526.563107.224 2.457187.6-909097.6277.550.0429 3.273 1.7 4.844 25832.7763577189.633485526.563127.224 2.916187.6-909097.6277.550.0509 3.273 1.7 4.844 25832.7763577189.633485526.563147.224 3.374187.6-909097.6277.550.0589 3.273 1.7 4.844 25832.7763577189.633485526.563167.224 3.832187.6-909097.6277.550.0669 3.273 1.7 4.844 25832.7763577189.633485526.563187.224 4.291187.6-909097.6277.550.0749 3.273 1.7 4.844 25832.7763577189.633485526.563207.224 4.749187.6-909097.6277.550.0829 3.273 1.7 4.844 25832.7763577189.633485526.563227.224 5.208187.6-909097.6277.550.0909 3.273 1.7 4.844 25832.7763577189.633485526.563247.224 5.666187.6-909097.6277.550.0989 3.273 1.7 4.844 25832.7763577189.633485526.563267.224 6.124187.6-909097.6277.550.1069 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.563287.224 6.583187.6-909097.6277.550.1149 3.273 1.7 4.844 25832.7763577189.633485526.563307.2247.041187.6-909097.6277.550.1229 3.273 1.7 4.844 25832.7763577189.633485526.563327.2247.499187.6-909097.6277.550.1309 3.273 1.7 4.844 25832.7763577189.633485526.563347.2247.958187.6-909097.6277.550.1389 3.273 1.7 4.844 25832.7763577189.633485526.563367.2248.416187.6-909097.6277.550.1469 3.273 1.7 4.844 25832.7763577189.633485526.563387.2248.875187.6-909097.6277.550.1549 3.273 1.7 4.844 25832.7763577189.633485526.563407.2249.333187.6-909097.6277.550.1629 3.273 1.7 4.844 25832.7763577189.633485526.563427.2249.791187.6-909097.6277.550.1709 3.273 1.7 4.844 25832.7763577189.633485526.563447.22410.25187.6-909097.6277.550.1789 3.273 1.7 4.844 25832.7763577189.633485526.563467.22410.71187.6-909097.6277.550.1869 3.273 1.7 4.844 25832.7763577189.633485526.563487.22411.17187.6-909097.6277.550.1949 3.273 1.7 4.844 25832.7763577189.633485526.563507.22411.62187.6-909097.6277.550.2029 3.273 1.7 4.844 25832.7763577189.633485526.563527.22412.08187.6-909097.6277.550.2109 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.563547.22412.54187.6-909097.6277.550.2189 3.273 1.7 4.844 25832.7763577189.633485526.563567.22413187.6-909097.6277.550.2269 3.273 1.7 4.844 25832.7763577189.633485526.563587.22413.46187.6-909097.6277.550.2349 3.273 1.7 4.844 25832.7763577189.633485526.563607.22413.92187.6-909097.6277.550.2429 3.273 1.7 4.844 25832.7763577189.633485526.563627.22414.37187.6-909097.6277.550.2509 3.273 1.7 4.844 25832.7763577189.633485526.563647.22414.83187.6-909097.6277.550.2589 3.273 1.7 4.844 25832.7763577189.633485526.563667.22415.29187.6-909097.6277.550.2669 3.273 1.7 4.844 25832.7763577189.633485526.563687.22415.75187.6-909097.6277.550.2749 3.273 1.7 4.844 25832.7763577189.633485526.563707.22416.21187.6-909097.6277.550.2829 3.273 1.7 4.844 25832.7763577189.633485526.563727.22416.67187.6-909097.6277.550.2909 3.273 1.7 4.844 25832.7763577189.633485526.563747.22417.13187.6-909097.6277.550.2989 3.273 1.7 4.844 25832.7763577189.633485526.563767.22417.58187.6-909097.6277.550.3069 3.273 1.7 4.844 25832.7763577189.633485526.563787.22418.04187.6-909097.6277.550.3149 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.563807.22418.5187.6-909097.6277.550.3229 3.273 1.7 4.844 25832.7763577189.633485526.563827.22418.96187.6-909097.6277.550.3309 3.273 1.7 4.844 25832.7763577189.633485526.563847.22419.42187.6-909097.6277.550.3389 3.273 1.7 4.844 25832.7763577189.633485526.563867.22419.88187.6-909097.6277.550.3469 3.273 1.7 4.844 25832.7763577189.633485526.563887.22420.33187.6-909097.6277.550.3549 3.273 1.7 4.844 25832.7763577189.633485526.563907.22420.79187.6-909097.6277.550.3629 3.273 1.7 4.844 25832.7763577189.633485526.563927.22421.25187.6-909097.6277.550.3709 3.273 1.7 4.844 25832.7763577189.633485526.563947.22421.71187.6-909097.6277.550.3789 3.273 1.7 4.844 25832.7763577189.633485526.563967.22422.17187.6-909097.6277.550.3869 3.273 1.7 4.844 25832.7763577189.633485526.563987.22422.63187.6-909097.6277.550.3949 3.273 1.7 4.844 25832.7763577189.633485526.5631007.22423.08187.6-909097.6277.550.4029 3.273 1.7 4.844 25832.7763577189.633485526.5631027.22423.54187.6-909097.6277.550.4109 3.273 1.7 4.844 25832.7763577189.633485526.5631047.22424187.6-909097.6277.550.4189 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.5631067.22424.46187.6-909097.6277.550.4269 3.273 1.7 4.844 25832.7763577189.633485526.5631087.22424.92187.6-909097.6277.550.4349 3.273 1.7 4.844 25832.7763577189.633485526.5631107.22425.38187.6-909097.6277.550.4429 3.273 1.7 4.844 25832.7763577189.633485526.5631127.22425.83187.6-909097.6277.550.4509 3.273 1.7 4.844 25832.7763577189.633485526.5631147.22426.29187.6-909097.6277.550.4589 3.273 1.7 4.844 25832.7763577189.633485526.5631167.22426.75187.6-909097.6277.550.4669 3.273 1.7 4.844 25832.7763577189.633485526.5631187.22427.21187.6-909097.6277.550.4749 3.273 1.7 4.844 25832.7763577189.633485526.5631207.22427.67187.6-909097.6277.550.4829 3.273 1.7 4.844 25832.7763577189.633485526.5631227.22428.13187.6-909097.6277.550.4909 3.273 1.7 4.844 25832.7763577189.633485526.5631247.22428.58187.6-909097.6277.550.4989 3.273 1.7 4.844 25832.7763577189.633485526.5631267.22429.04187.6-909097.6277.550.5069 3.273 1.7 4.844 25832.7763577189.633485526.5631287.22429.5187.6-909097.6277.550.5149 3.273 1.7 4.844 25832.7763577189.633485526.5631307.22429.96187.6-909097.6277.550.5229 3.273 1.7 4.844ZY点或YZ点坐标ZY点或YZ点R L E N左右偏左侧右侧F F弧度E弧度N弧度F弧度F 桩号X Y半径长度切线角方位角方向左侧右侧左侧右侧25832.7763577189.633485526.5631327.22430.42187.6-909097.6277.550.5309 3.273 1.7 4.844 25832.7763577189.633485526.5631347.22430.88187.6-909097.6277.550.5389 3.273 1.7 4.844 25832.7763577189.633485526.5631367.22431.33187.6-909097.6277.550.5469 3.273 1.7 4.844 25832.7763577189.633485526.5631387.22431.79187.6-909097.6277.550.5549 3.273 1.7 4.844 25832.7763577189.633485526.5631407.22432.25187.6-909097.6277.550.5629 3.273 1.7 4.844 25832.7763577189.633485526.5631427.22432.71187.6-909097.6277.550.5709 3.273 1.7 4.844 25832.7763577189.633485526.5631447.22433.17187.6-909097.6277.550.5789 3.273 1.7 4.844 25832.7763577189.633485526.5631467.22433.63187.6-909097.6277.550.5869 3.273 1.7 4.844 25832.7763577189.633485526.5631487.22434.08187.6-909097.6277.550.5949 3.273 1.7 4.844 25832.7763577189.633485526.5631507.22434.54187.6-909097.6277.550.6029 3.273 1.7 4.844 25832.7763577189.633485526.5631527.22435187.6-909097.6277.550.6109 3.273 1.7 4.844 25832.7763577189.633485526.5631531.34935.1187.6-909097.6277.550.6125 3.273 1.7 4.844S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85S横向距离14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85 14.85。

关于高速公路施工测量中的坐标计算摘要：在高速公路施工测量中经常遇会到关于坐标的计算问题，本文主要介绍路线中桩坐标、与已知点左右幅有一定距离的点的坐标计算，两套坐标系的旋转与平移计算。

关键词：方位角、直线、圆曲线、缓和曲线、坐标计算一、方位角：即路线某一直线方向与正北方向的夹角（由正北方向起按顺时针方向旋转到该直线方向的夹角），通常用θ表示。

N(X)如图所示：JD1～JD2的方位角用θ1表示；JD2～JD3的方位角用θ2表示；路线的转角α等于后一方位角与前一方位角之差。

α＝θ2－θ 1 2当α为正时路线右转即α=αy；当α为负时，路线左转即α＝αz，方位角α在大地直角坐标中也称为坐标方位角。

直线的方向(即方位角)按下式计算：β＝tan-1（Δy /Δx）＝tan-1((y2－y2)/ （x2－x1）)路线的方位角θ按下式计算：第一象限：Δx＞0，Δy＞0，θ=β第二象限：Δx＜0，Δy＞0，θ=180°－β第三象限：Δx＜0，Δy＜0，θ=180°+β第四象限：Δx＜0，Δy＜0，θ=360°－β二、直线段上各桩号点坐标的计算：1、已知在直线段上A点桩号、B点桩号两点的坐标A（X A，Y A）、B（X B，Y B）,求C点桩号的坐标。

根据（一）式可求出AB 的方位角θ,即X C=X B+S*cosθ A B C 路线前进方向Y C=Y B+S*sinθ其中S为C点桩号与B点桩号之间的距离。

2、已知A,C1,C2都在直线段上,A点桩号坐标（X A，Y A），A点的坐标方位角为θA，求C1、C2点桩号的坐标及方位角。

C2 A C1 路线前进方向其中AC1=S1，AC2=S2；则C1点的坐标：X C1=X A+S1*cosθAY C1=Y A+S1*sinθAC2点的坐标：X C2=X A+S1*cos (θA+180°)Y C2=Y A+S1*sin (θA +180°)3、已知在直线段上A点桩号的坐标A（X A，Y A）及其坐标方位角θ，B点在A点的左侧,距A点的距离为S1, C点在A点的右侧,距A点的距离为S2,如图示：求已知:AB=S1，AC=S2, 则: CC点的坐标：X C=X A+S2*cos (θ+θ 2 )Y C=Y A+S2*sin (θ+θ 2 )B点的坐标：X b=X A+S1*cos(θ－θ 1 )Y b=Y A+S1*sin(θ－θ 1 )三、圆曲线上各桩号点坐标的计算：1、已知圆曲线上任一点坐标A（X A，Y A），坐标方位角θA,B点桩号，圆曲线半径R。

道路之星坐标正算格式道路之星正算是一种常用的测量方法，用于确定道路、建筑物或其他地物的坐标。

它可以帮助我们准确地描述和定位地理空间中的各个要素，为道路规划、交通管理以及地理信息系统等领域提供可靠的数据支持。

道路之星坐标正算的过程可以简单概括为以下几个步骤：测量，计算，校正和存储。

第一步是测量。

在进行道路之星坐标正算之前，我们需要使用测量仪器进行实地测量，包括测量角度和距离。

这些测量数据可以通过全站仪、GPS定位仪或其他测量设备获得，确保测量数据的准确性和可靠性。

第二步是计算。

在获得测量数据后，我们需要进行计算，将测量数据转换成坐标值。

一般来说，我们可以利用三角测量原理或者其他测量方法来计算坐标值。

这涉及到一系列的数学计算，包括三角函数、向量运算等。

通过计算，我们可以得到道路或地物的准确坐标。

第三步是校正。

在计算坐标后，我们需要对其进行校正。

校正是为了排除测量误差和系统误差，保证测量数据和计算结果的准确性和一致性。

在校正过程中，我们可以使用不同的校正方法和技术，包括平差法、误差检测和分析等。

通过校正，我们可以提高测量数据的精度和可靠性。

最后一步是存储。

在完成道路之星坐标正算后，我们需要将所得的坐标值进行存储。

存储可以采用不同的方式，如数据库、地理信息系统等，并将坐标值与地物属性进行关联。

这样可以方便我们在日后的道路规划、交通管理等工作中进行查询和使用。

总之，道路之星坐标正算是一项重要的测量技术，对于道路规划和地理空间信息的准确描述具有非常重要的意义。

通过测量、计算、校正和存储的步骤，我们可以获取准确的道路坐标信息，为城市交通管理和地理信息系统的建设提供有力的支持。

EXCEL快速计算任何难度的道路中线、边线坐标主程序Public i As IntegerPublic pi As DoubleSub TP()Dim ii As IntegerDim k(1000) As DoubleDim xzq, yzq, kq, xzh, yzh, kzh, xjd, yjd, kjd, khy, kyh As Double'直线区域pi = 3.14159265358979xzq = 71862.642yzq = 63474.651kq = 0 '因为直线连接终点为ZH点，与圆曲线起点为同一点，所以在直线区域不定义ZH点参数'直线区域'曲线区域xzh = 71858.3267yzh = 63375.2684kzh = 99.4763xhz = 71909.3687yhz = 63283.8076 '曲线区域定义内容有：ZH（坐标、里程）、HZ（坐标、里程）、JD（坐标、里程）khz = 212.3392 'R（半径）、LS（缓和曲线长度）、HY（里程）、YH（里程）xjd = 71855.658yjd = 63313.806kjd = 160.9966ls = 30r = 75khy = 129.4763kyh = 182.3385'曲线区域i = 2 '从第二格开始读取数据所以定义I=2ii = 1 '桩号从第一个开始启用，所以定义II=2Dok(ii) = Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 1) '定义桩号等于读取数据If Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 1) = "" Then Exit Do '当没有数据读取时退出循环If k(ii) < kq Then '若计算点超过计算起点给予提示并退出程序MsgBox ("猪啊！！你的输入的桩号居然超过计算起点桩号")Exit SubElseIf k(ii) <= kzh Then '若计算点在ZH点前，则进入直线程序Call zx(xzq, yzq, kq, xzh, yzh, kzh, k(ii))ElseIf kzh < k(ii) And k(ii) <= khy Then '若计算点在ZH和HY之间则调入前段缓和曲线程序Call qhhqx(xzh, yzh, kzh, xhz, yhz, khz, xjd, yjd, kjd, ls, r, k(ii))ElseIf khy < k(ii) And k(ii) <= kyh Then '若计算点在HY和YH之间则调入圆曲线程序Call yqx(xzh, yzh, kzh, xhz, yhz, khz, xjd, yjd, kjd, ls, r, k(ii))ElseIf kyh < k(ii) And k(ii) <= khz Then '若计算点在YH和HZ之间则调入后段缓和曲线程序Call hhhqx(xzh, yzh, kzh, xhz, yhz, khz, xjd, yjd, kjd, ls, r, k(ii))ElseMsgBox ("笨啊！！数据已超出计算范围了") '若出现超出范围的桩号则给与提示并退出程序Exit SubEnd Ifi = i + 1ii = ii + 1LoopEnd Sub直线模块Sub zx(ByV al xzq As Double, ByV al yzq As Double, ByV al kq As Double, ByV al xzh As Double, ByV al yzh As Double, ByV al kzh As Double, ParamArray k())fw = fwj(xzh, xzq, yzh, yzq) '首先调入方位角程序计算直线方位角x = xzq + (k(ii) - kq) * Cos(fw) '然后根据桩号和长度计算出坐标值y = yzq + (k(ii) - kq) * Sin(fw)zdfm = dfm(fw) '将弧度形式的前进方位角转换度分秒形式'输出坐标值以弧度和度分秒形式的前进方位角Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 2) = xWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 3) = yWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 4) = fwWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 5) = zdfmEnd Sub圆曲线模块Sub yqx(ByV al xzh As Double, ByV al yzh As Double, ByV al kzh As Double, ByV al xhz As Double, ByV al yhz As Double, ByV al khz As Double, ByV al xjd As Double, ByV al yjd As Double, ByV al kjd As Double, ByV al ls As Double, ByV al r As Double, ParamArray k())l = Abs(k(ii) - kzh) '计算ZH点（因为以直缓点起算）到待求桩号的弧度长度ly = l - ls / 2 '计算圆弧长度p = ls ^ 2 / 24 / r - ls ^ 4 / 2688 / r ^ 3 '曲线内移值m = ls / 2 - ls ^ 3 / 240 / r ^ 2 '曲线切线长增量u = r * Sin(ly / r) + m '偏量坐标计算v = r * (1 - Cos(ly / r)) + p'调入方位角fwq = fwj(xjd, xzh, yjd, yzh) '计算ZH点方位角fwh = fwj(xhz, xjd, yhz, yjd) '计算HZ点方位角（此角作用是用来推算曲线是左偏还是右偏）'调入偏角判定nq = n(fwq, fwh) '计算偏角方向，左偏为-1右偏为1'计算坐标x = u * Cos(fwq) - nq * v * Sin(fwq) + xzhy = u * Sin(fwq) + nq * v * Cos(fwq) + yzhd = (90 * (2 * l - ls) / pi / r) * pi / 180 '计算圆曲线上的偏角（此句要点为角度必须转换为弧度即：pi/180）fw = fwq + d * nq '计算前进方位角zdfm = dfm(fw) '将弧度形式的前进方位角转换度分秒形式'输出坐标值以弧度和度分秒形式的前进方位角Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 2) = xWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 3) = yWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 4) = fwWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 5) = zdfmEnd Sub前缓和段Sub qhhqx(ByV al xzh As Double, ByV al yzh As Double, ByV al kzh As Double, ByV al xhz As Double, ByV al yhz As Double, ByV al khz As Double, ByV al xjd As Double, ByV al yjd As Double, ByV al kjd As Double, ByV al ls As Double, ByV al r As Double, ParamArray k())l = Abs(k(ii) - kzh) '计算测点到ZH点的距离u = l - l ^ 5 / 40 / r ^ 2 / ls ^ 2 + l ^ 9 / r ^ 4 / ls ^ 4 / 3456 '计算偏量v = l ^ 3 / 6 / r / ls - l ^ 7 / 336 / r ^ 3 / ls ^ 3'用公式二则以下两计算可省略(圆曲线和后缓和曲线也同理)Rem t = Atn(v / u)Rem s = Sqr(u ^ 2 + v ^ 2)'调入方位角计算fwq = fwj(xjd, xzh, yjd, yzh) '计算ZH点方位角fwh = fwj(xhz, xjd, yhz, yjd) '计算HZ点方位角（此角作用是用来推算曲线是左偏还是右偏）'调入偏角判定nq = n(fwq, fwh) '计算偏角方向，左偏为-1右偏为1'结果计算Rem x = xzh + s * Cos(fwq + nq * t)Rem y = yzh + s * Sin(fwq + nq * t)x = u * Cos(fwq) - nq * v * Sin(fwq) + xzh '经过测试，计算结果中的两种公式计算结果是一样的y = u * Sin(fwq) + nq * v * Cos(fwq) + yzhd = (90 * l * l / pi / r / ls) * pi / 180 '计算缓和曲线上的偏角（此句要点为角度必须转换为弧度即：pi/180）fw = fwq + d * nq '计算前进方位角zdfm = dfm(fw) '将弧度形式的前进方位角转换度分秒形式'输出坐标值以弧度和度分秒形式的前进方位角Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 2) = xWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 3) = yWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 4) = fwWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 5) = zdfmEnd Sub后缓和段模块Sub hhhqx(ByV al xzh As Double, ByV al yzh As Double, ByV al kzh As Double, ByV al xhz As Double, ByV al yhz As Double, ByV al khz As Double, ByV al xjd As Double, ByV al yjd As Double, ByV al kjd As Double, ByV al ls As Double, ByV al r As Double, ParamArray k())l = Abs(k(ii) - khz) '计算测点到HZ点的距离（后缓和曲线是以HZ点为起点）u = l - l ^ 5 / 40 / r ^ 2 / ls ^ 2 + l ^ 9 / r ^ 4 / ls ^ 4 / 3456 '计算偏量v = l ^ 3 / 6 / r / ls - l ^ 7 / 336 / r ^ 3 / ls ^ 3Rem t = Atn(v / u)Rem s = Sqr(u ^ 2 + v ^ 2)'调入方位角计算fwq = fwj(xjd, xzh, yjd, yzh) '计算ZH点方位角fwh = fwj(xhz, xjd, yhz, yjd) '计算HZ点方位角（此角作用是用来推算曲线是左偏还是右偏）'调入偏角判定nh = n(fwh, fwq) '计算偏角方向，左偏为-1右偏为1（注意：因为是从后HZ点起算，所以必须将HZ点方位角放在前ZH放在后）'结果计算Rem x = xzh + s * Cos(fwq + nq * t)Rem y = yzh + s * Sin(fwq + nq * t)x = xhz - (u * Cos(fwh) - nh * v * Sin(fwh)) '经过测试，计算结果中的两种公式计算结果是一样的y = yhz - (u * Sin(fwh) + nh * v * Cos(fwh))d = (90 * l * l / pi / r / ls) * pi / 180 '计算缓和曲线上的偏角（此句要点为角度必须转换为弧度即：pi/180）fw = fwh + d * nh '计算前进方位角zdfm = dfm(fw) '将弧度形式的前进方位角转换度分秒形式'输出坐标值以弧度和度分秒形式的前进方位角Workbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 2) = xWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 3) = yWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 4) = fwWorkbooks("单交点平曲线.xls").Worksheets("sheet1").Cells(i, 5) = zdfmEnd Sub偏角模块Function n(ByV al fw1 As Double, ByV al fw2 As Double) As Doublepj = fw1 + pi - fw2 '前进的右角pjIf pj - pi > 0 Then '当右角pj-pi 〉0时为左偏否则为右偏n = -1Else: n = 1End IfEnd Function方位角模块Function fwj(ByV al x1 As Double, ByV al x2 As Double, ByV al y1 As Double, ByV al y2 As Double) As Double'计算增量x0 = x1 - x2y0 = y1 - y2'由增量判断方位角所在象限，不同象限取不同的值If x0 = 0 And y0 > 0 Thenfwj = pi / 2 '当在大地坐标中偏量在X轴上的值时ElseIf x0 = 0 And y0 < 0 Thenfwj = 3 * pi / 2 '当在大地坐标中偏量在负X轴上的值时ElseIf x0 < 0 Thenfwj = Atn(y0 / x0) + pi '当在大地坐标中偏量在第二第三象限上的值时ElseIf x0 > 0 And y0 < 0 Thenfwj = Atn(y0 / x0) + 2 * pi '当在大地坐标中偏量在第四象限上的值时Elsefwj = Atn(y0 / x0) '当在大地坐标中偏量在第一象限上的值时End IfEnd Function度分秒模块Function dfm(ByV al ao As Double) As V ariantao = ao * 180 / pi '将弧度转化为度jd = Int(ao) '计算度jf = Int(ao * 60 - jd * 60) '计算分jmx = (ao - jd - jf / 60) * 3600 '计算秒jm = Left(jmx, 8) '因为拆分出来的秒数经常占到十多位，所以只取秒数的前八位dfm = jd & "°" & jf & "′" & jm & "″" '连接度分秒End Function边桩公式(此公式在电子表格中直接输入)：=B2+J2*COS(D2+RADIANS(L2)+PI()) =C2+J2*SIN(D2+RADIANS(L2)+PI()) =B2+K2*COS(D2+RADIANS(M2)) =C2+K2*SIN(D2+RADIANS(M2))=B3+J3*COS(D3+RADIANS(L3)+PI()) =C3+J3*SIN(D3+RADIANS(L3)+PI()) =B3+K3*COS(D3+RADIANS(M3)) =C3+K3*SIN(D3+RADIANS(M3))=B4+J4*COS(D4+RADIANS(L4)+PI()) =C4+J4*SIN(D4+RADIANS(L4)+PI()) =B4+K4*COS(D4+RADIANS(M4)) =C4+K4*SIN(D4+RADIANS(M4))=B5+J5*COS(D5+RADIANS(L5)+PI()) =C5+J5*SIN(D5+RADIANS(L5)+PI()) =B5+K5*COS(D5+RADIANS(M5)) =C5+K5*SIN(D5+RADIANS(M5))=B6+J6*COS(D6+RADIANS(L6)+PI()) =C6+J6*SIN(D6+RADIANS(L6)+PI()) =B6+K6*COS(D6+RADIANS(M6)) =C6+K6*SIN(D6+RADIANS(M6))=B7+J7*COS(D7+RADIANS(L7)+PI()) =C7+J7*SIN(D7+RADIANS(L7)+PI()) =B7+K7*COS(D7+RADIANS(M7)) =C7+K7*SIN(D7+RADIANS(M7))=B8+J8*COS(D8+RADIANS(L8)+PI()) =C8+J8*SIN(D8+RADIANS(L8)+PI()) =B8+K8*COS(D8+RADIANS(M8)) =C8+K8*SIN(D8+RADIANS(M8))=B9+J9*COS(D9+RADIANS(L9)+PI()) =C9+J9*SIN(D9+RADIANS(L9)+PI()) =B9+K9*COS(D9+RADIANS(M9)) =C9+K9*SIN(D9+RADIANS(M9))=B10+J10*COS(D10+RADIANS(L10)+PI()) =C10+J10*SIN(D10+RADIANS(L10)+PI()) =B10+K10*COS(D10+RADIANS(M10)) =C10+K10*SIN(D10+RADIANS(M10))=B11+J11*COS(D11+RADIANS(L11)+PI()) =C11+J11*SIN(D11+RADIANS(L11)+PI()) =B11+K11*COS(D11+RADIANS(M11)) =C11+K11*SIN(D11+RADIANS(M11))=B12+J12*COS(D12+RADIANS(L12)+PI()) =C12+J12*SIN(D12+RADIANS(L12)+PI()) =B12+K12*COS(D12+RADIANS(M12)) =C12+K12*SIN(D12+RADIANS(M12))=B13+J13*COS(D13+RADIANS(L13)+PI()) =C13+J13*SIN(D13+RADIANS(L13)+PI()) =B13+K13*COS(D13+RADIANS(M13)) =C13+K13*SIN(D13+RADIANS(M13))=B14+J14*COS(D14+RADIANS(L14)+PI()) =C14+J14*SIN(D14+RADIANS(L14)+PI()) =B14+K14*COS(D14+RADIANS(M14)) =C14+K14*SIN(D14+RADIANS(M14))=B15+J15*COS(D15+RADIANS(L15)+PI()) =C15+J15*SIN(D15+RADIANS(L15)+PI()) =B15+K15*COS(D15+RADIANS(M15)) =C15+K15*SIN(D15+RADIANS(M15))=B16+J16*COS(D16+RADIANS(L16)+PI()) =C16+J16*SIN(D16+RADIANS(L16)+PI()) =B16+K16*COS(D16+RADIANS(M16)) =C16+K16*SIN(D16+RADIANS(M16))=B17+J17*COS(D17+RADIANS(L17)+PI()) =C17+J17*SIN(D17+RADIANS(L17)+PI()) =B17+K17*COS(D17+RADIANS(M17)) =C17+K17*SIN(D17+RADIANS(M17))=B18+J18*COS(D18+RADIANS(L18)+PI()) =C18+J18*SIN(D18+RADIANS(L18)+PI()) =B18+K18*COS(D18+RADIANS(M18)) =C18+K18*SIN(D18+RADIANS(M18))=B19+J19*COS(D19+RADIANS(L19)+PI()) =C19+J19*SIN(D19+RADIANS(L19)+PI()) =B19+K19*COS(D19+RADIANS(M19)) =C19+K19*SIN(D19+RADIANS(M19))=B20+J20*COS(D20+RADIANS(L20)+PI()) =C20+J20*SIN(D20+RADIANS(L20)+PI()) =B20+K20*COS(D20+RADIANS(M20)) =C20+K20*SIN(D20+RADIANS(M20))=B21+J21*COS(D21+RADIANS(L21)+PI()) =C21+J21*SIN(D21+RADIANS(L21)+PI()) =B21+K21*COS(D21+RADIANS(M21)) =C21+K21*SIN(D21+RADIANS(M21))=B22+J22*COS(D22+RADIANS(L22)+PI()) =C22+J22*SIN(D22+RADIANS(L22)+PI()) =B22+K22*COS(D22+RADIANS(M22)) =C22+K22*SIN(D22+RADIANS(M22))=B23+J23*COS(D23+RADIANS(L23)+PI()) =C23+J23*SIN(D23+RADIANS(L23)+PI()) =B23+K23*COS(D23+RADIANS(M23)) =C23+K23*SIN(D23+RADIANS(M23))呵呵，这个就是传说已久的EXCEL自动计算曲线坐标．给大家研究研究．欢迎在此基础上开发增加新模块。