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c++ - Haversine公式-数学略有偏离，不确定为什么

转载 作者：行者123 更新时间：2023-12-01 14:58:22 29 4
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我今天早些时候发布了有关此内容的文章，并解决了该问题。我在使用hasversine公式时遇到另一个问题。
我正在尝试计算两个纬度和经度之间的距离。我有公式，我的计算结果确实接近我需要的输出，但是有点差了。我只需要正确地计算数字，而不是小数位。但是有些计算距离太远，以至于它们不是同一英尺。

我经过了尝试，尝试从浮点数更改为 double 数，使用调试器比较了经纬度和长时间，以确保我正确地进行了从DMS到十进制的那些计算。

我不知道怎么了。我必须留下的所有CONST都是不变的。

仅供引用，最后两栏我什么都没做。

朝正确的方向进行的任何帮助将不胜感激!谢谢!

码:

//---------------------------------------------------------------------
//
// Input:   $GPRMC sentence for add (A). Distance traveled (D).
//          Average speed (S). Table of records (T).
//
// Output:  Record added. Table of records. Distance traveled.
//          Average speed.
//          
//---------------------------------------------------------------------

#include<iostream>
#include<string>
#include<iomanip>

using namespace std;

const int MAX_RECS = 5;
const float EARTH_RADIUIS_MILES = 3959;
const int FEET_IN_MILE = 5280;
const float HALF_CIRCLE = 180;
const float PI = 3.14159f;
const int SECS_IN_HR = 3600;
const int SECS_IN_MIN = 60;
const float FPS_PER_KNOT = 1.68781f;
const int ID1 = 2234;
const int ID2 = 5327;
const int ID3 = 7741;

const int TABLEFIRSTSPACE = 51;
const int TABLESECONDSPACE = 6;
const int TABLE8 = 8;
const int TABLE10 = 10;
const int TABLE11 = 11;
const int TABLE13 = 13;

enum FitBitID_Type 
{ 
   ID_FITBIT1 = ID1, ID_FITBIT2 = ID2, ID_FITBIT3 = ID3
};

enum CommandType 
{
   ADD_CMD = 'A', DISTANCE_TRAVELED_CMD = 'D',
   AVG_SPEED_CMD = 'S', TABLE_PRINT_CMD = 'T'
};

void ReadIn(string &time, string &latNum, string &longNum, 
   float &speedFloat);
//void timeBreakdown(int time, int &hours, int &minutes, int &seconds);
//void latLongCalc(float latNum, float longNum, float &latD, float &longD);
//float DegreesToRadians(float degrees);

class FitBit
{
private:
   string strTime[MAX_RECS];
   int totalSecs[MAX_RECS];
   float latitude[MAX_RECS];
   float longitude[MAX_RECS];
   float speed[MAX_RECS];
   int numRecs;//num of records currently stored in the parallel arrays

   void timeBreakdown(string time, int &hours, int &minutes, int &seconds)
   {
      hours = stoi(time.substr(0, 2));
      minutes = stoi(time.substr(2, 2));
      seconds = stoi(time.substr(4, 2));
   }

   void latLongCalc(string latNum, string longNum, float &latD, float &longD)
   {
      float degreeLa = stof(latNum.substr(0, 2));
      float minuteLa = stof(latNum.substr(2, 2));
      float secondLa = stof(latNum.substr(5, 3));
      latD = degreeLa + (minuteLa / SECS_IN_MIN) +
         (((secondLa / 1000) * SECS_IN_MIN) / SECS_IN_HR);
      float degreeLo = stof(longNum.substr(0, 3));
      float minuteLo = stof(longNum.substr(3, 2));
      float secondLo = stof(longNum.substr(6, 3));
      longD = degreeLo + (minuteLo / SECS_IN_MIN) +
         (((secondLo / 1000) * SECS_IN_MIN) / SECS_IN_HR); longD = -longD;
   }

   float DegreesToRadians(float degrees) const
   {
      return degrees * PI / HALF_CIRCLE;
   }

public:
   FitBit()
   {
      numRecs = 0;
   }
   void addRecord(string time, string latNum, string longNum, 
      float speedFloat)
   {
      int hours, minutes, seconds;
      timeBreakdown(time, hours, minutes, seconds);
      float latD, longD;
      latLongCalc(latNum, longNum, latD, longD);
      hours *= SECS_IN_MIN; minutes += hours; minutes *= SECS_IN_MIN;
      seconds += minutes; speedFloat *= FPS_PER_KNOT;
      if (numRecs < MAX_RECS)
      {
         strTime[numRecs] = time; totalSecs[numRecs] = seconds;
         latitude[numRecs] = latD; longitude[numRecs] = longD;
         speed[numRecs] = speedFloat;
         numRecs++;
      }
      else
      {
         for (int i = 1; i < numRecs; i++)
         {
            strTime[i - 1] = strTime[i]; totalSecs[i - 1] = totalSecs[i];
            latitude[i - 1] = latitude[i];
            longitude[i - 1] = longitude[i]; speed[i - 1] = speed[i];
         }
         strTime[numRecs] = time; totalSecs[numRecs] = seconds;
         latitude[numRecs] = latD; longitude[numRecs] = longD;
         speed[numRecs] = speedFloat;
      }
   }
   float distanceBetweenEarthCoordinates(float lat1, float lon1, 
                                       float lat2, float lon2) const
   {
      float dLat, dLon, a, c;
      lat1 = DegreesToRadians(lat1);
      lon1 = DegreesToRadians(lon1);
      lat2 = DegreesToRadians(lat2);
      lon2 = DegreesToRadians(lon2);
      lon1 = -lon1;
      lon2 = -lon2;
      dLat = (lat2 - lat1);
      dLon = (lon2 - lon1);

      a = (sin(dLat / 2) * sin(dLat / 2)) + cos(lat1) * cos(lat2) 
         * (sin(dLon / 2) * sin(dLon / 2));
      c = 2 * atan2(sqrt(a), sqrt(1 - a));

      //return ((EARTH_RADIUIS_MILES * c) * FEET_IN_MILE);
      return EARTH_RADIUIS_MILES * c * FEET_IN_MILE;
   }
   float Distance()
   {
      if (!(numRecs <= 1))
      {
         float total = 0;
         for (int i = 1; i < numRecs; i++)
         {
            float x = distanceBetweenEarthCoordinates(latitude[i-1],
               longitude[i-1], latitude[i], longitude[i]);
            total += x;
         }
         return total;
      }
      return 0;
   }
   float DistanceForTable(int i) const
   {
      if (!(i < 1))
      {
         return distanceBetweenEarthCoordinates(latitude[i - 1],
            longitude[i - 1], latitude[i], longitude[i]);
      }
      return 0;
   }
   void PrintTable()
   {
      cout << left << setw(TABLE8) << "Time" << setw(TABLE10)
         << "Latitude" << setw(TABLE10) << "Longitude" << setw(TABLE11)
         << "Speed" << setw(TABLE13) << "Distance" << setw(TABLE10)
         << "Average" << setw(TABLE13) << "Acceleration" << endl << right
         << setw(TABLEFIRSTSPACE) << "Traveled(ft)" 
         << setw(TABLESECONDSPACE) << "Speed" << endl;
      if (numRecs > 0)
      {
         for (int i = 0; i < numRecs; i++)
         {
            cout << left << setw(TABLE8) << strTime[i];
            cout << left << setw(TABLE10) << latitude[i];
            cout << left << setw(TABLE10) << longitude[i];
            cout << left << setw(TABLE11) << speed[i];
            if (i < 1)
               cout << left << setw(TABLE13) << " ";
            else
               cout << left << setw(TABLE13) << DistanceForTable(i);
            cout << left << setw(TABLE10) << 200.0;
            cout << left << setw(TABLE13) << 1.0101 << endl;
         }
      }
   }
};

void ProcessCommandForFitBit(FitBit & bit, CommandType command,
   FitBitID_Type FitBitID);

int main()
{
   cout << fixed << showpoint << setprecision(4);
   char cmd; int id;

   FitBit bit1, bit2, bit3;

   while (cin)
   {
      cin >> cmd >> id;
      FitBitID_Type FitBitID = FitBitID_Type(id);
      CommandType command = CommandType(cmd); 
      if (FitBitID == ID_FITBIT1)
         ProcessCommandForFitBit(bit1, command, FitBitID);
      else if (FitBitID == ID_FITBIT2)
         ProcessCommandForFitBit(bit2, command, FitBitID);
      else if (FitBitID == ID_FITBIT3)
         ProcessCommandForFitBit(bit3, command, FitBitID);
   }

   cout << "Normal Termination of Program 5.";
   return 0;
}

void ProcessCommandForFitBit(FitBit & bit, CommandType command,
                             FitBitID_Type FitBitID)
{
   int returnedDistance = 0;  float returnedAvgSpeed = 0;
   string time, latNum, longNum; float speedFloat = 0;

   switch (command)
   {
   case ADD_CMD:
      ReadIn(time, latNum, longNum, speedFloat);
      bit.addRecord(time, latNum, longNum, speedFloat);
      cout << "Record added for FitBit with ID " << FitBitID << endl;
      break;
   case DISTANCE_TRAVELED_CMD:
      returnedDistance = bit.Distance();
      cout << "Distance Traveled in feet for FitBit with ID "
           << FitBitID << " is " << returnedDistance << endl;
      break;
   case AVG_SPEED_CMD:

      cout << "Average Speed for FitBit with ID " << FitBitID
           << " is " << returnedAvgSpeed << endl;
      break;
   case TABLE_PRINT_CMD:
      cout << "Records for FitBit with ID " << FitBitID << endl;
      bit.PrintTable();
      break;
   }
}

void ReadIn(string &time, string &latNum, string &longNum, float &speedFloat)
{
   string trash;
   cin >> trash >> time >> trash >> latNum >> trash >> longNum
      >> trash >> speedFloat >> trash >> trash >> trash >> trash;
}

输入文件: 
A 2234 $GPRMC 204849 A 4243.636 N 09028.597 W 000.0 065.5 091297 000.2 W*7F
A 2234 $GPRMC 204851 A 4243.636 N 09028.594 W 006.4 074.4 091297 000.2 W*76
A 2234 $GPRMC 204853 A 4243.638 N 09028.586 W 011.7 067.9 091297 000.2 W*73
A 2234 $GPRMC 204855 A 4243.641 N 09028.574 W 014.2 067.5 091297 000.2 W*7A
T 2234
D 2234
S 2234
A 2234 $GPRMC 204903 A 4243.662 N 09028.593 W 018.7 066.2 090108 000.2 W*7A
T 2234
D 2234
S 2234
T 5327
D 5327
S 5327
A 5327 $GPRMC 204905 A 4273.667 N 09047.499 W 021.6 064.5 090108 000.2 W*78
T 5327
D 5327
S 5327
A 5327 $GPRMC 204907 A 4273.671 N 09047.480 W 027.3 065.4 090108 000.2 W*73
T 5327
D 5327
S 5327
A 7741 $GPRMC 204909 A 4273.679 N 09047.459 W 026.5 066.8 090108 000.2 W*77
A 7741 $GPRMC 204913 A 4273.689 N 09047.418 W 031.7 068.6 090108 000.2 W*7F
T 7741
D 7741
S 7741

我的输出: 
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
204849  42.7273   -90.4766  0.0000                  200.0000  1.0101       
204851  42.7273   -90.4766  10.8020    12.8137      200.0000  1.0101       
204853  42.7273   -90.4764  19.7474    37.9431      200.0000  1.0101       
204855  42.7274   -90.4762  23.9669    54.9950      200.0000  1.0101       
Distance Traveled in feet for FitBit with ID 2234 is 105
Average Speed for FitBit with ID 2234 is 0.0000
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
204849  42.7273   -90.4766  0.0000                  200.0000  1.0101       
204851  42.7273   -90.4766  10.8020    12.8137      200.0000  1.0101       
204853  42.7273   -90.4764  19.7474    37.9431      200.0000  1.0101       
204855  42.7274   -90.4762  23.9669    54.9950      200.0000  1.0101       
204903  42.7277   -90.4765  31.5620    151.4476     200.0000  1.0101       
Distance Traveled in feet for FitBit with ID 2234 is 257
Average Speed for FitBit with ID 2234 is 0.0000
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
204905  43.2278   -90.7916  36.4567                 200.0000  1.0101       
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
204905  43.2278   -90.7916  36.4567                 200.0000  1.0101       
204907  43.2279   -90.7913  46.0772    87.9045      200.0000  1.0101       
Distance Traveled in feet for FitBit with ID 5327 is 87
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 7741
Record added for FitBit with ID 7741
Records for FitBit with ID 7741
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed
204909  43.2280   -90.7910  44.7270                 200.0000  1.0101       
204913  43.2281   -90.7903  53.5036    193.2789     200.0000  1.0101       
Distance Traveled in feet for FitBit with ID 7741 is 193
Average Speed for FitBit with ID 7741 is 0.0000
Average Speed for FitBit with ID 7741 is 0.0000
Normal Termination of Program 5.

我需要匹配的输出: 
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
204849  42.7273   -90.4766  0.0000     
204851  42.7273   -90.4766  10.8020    12           5.4010    5.4010       
204853  42.7273   -90.4764  19.7474    36           10.1831   4.4727       
204855  42.7274   -90.4762  23.9669    56           13.6291   2.1098       
Distance Traveled in feet for FitBit with ID 2234 is 104
Average Speed for FitBit with ID 2234 is 13.6291
Record added for FitBit with ID 2234
Records for FitBit with ID 2234
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
204849  42.7273   -90.4766  0.0000     
204851  42.7273   -90.4766  10.8020    12           5.4010    5.4010       
204853  42.7273   -90.4764  19.7474    36           10.1831   4.4727       
204855  42.7274   -90.4762  23.9669    56           13.6291   2.1098       
204903  42.7277   -90.4765  31.5620    153          17.2157   0.9494       
Distance Traveled in feet for FitBit with ID 2234 is 257
Average Speed for FitBit with ID 2234 is 17.2157
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 0.0000
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
204905  43.2278   -90.7916  36.4567    
Distance Traveled in feet for FitBit with ID 5327 is 0
Average Speed for FitBit with ID 5327 is 36.4567
Record added for FitBit with ID 5327
Records for FitBit with ID 5327
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
204905  43.2278   -90.7916  36.4567    
204907  43.2278   -90.7913  46.0772    84           41.2670   4.8103       
Distance Traveled in feet for FitBit with ID 5327 is 84
Average Speed for FitBit with ID 5327 is 41.2670
Record added for FitBit with ID 7741
Record added for FitBit with ID 7741
Records for FitBit with ID 7741
Time    Latitude  Longitude Speed      Distance     Average   Acceleration 
                                       Traveled(ft) Speed     
204909  43.2280   -90.7910  44.7270    
204913  43.2281   -90.7903  53.5036    192          49.1153   2.1942       
Distance Traveled in feet for FitBit with ID 7741 is 192
Average Speed for FitBit with ID 7741 is 49.1153
Normal Termination of Program 5.

最佳答案

解决了
我不得不重用我们的教授从未告诉过我们的旧代码，我们需要复制。这是度数秒转换器的另一种实现方式，与haversine公式无关。
感谢您的所有帮助!

关于c++ - Haversine公式-数学略有偏离，不确定为什么，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/59313976/

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