#include <iostream>
#include <fstream>
#include <sstream>
#include <math.h>
#include <vector>
using namespace std;
struct point
{
float x,y;
};
float norm (point p) // get the norm of a vector
{
return pow(pow(p.x,2)+pow(p.y,2),.5);
}
point trilateration(point point1, point point2, point point3, double r1, double r2, double r3) {
point resultPose;
//unit vector in a direction from point1 to point 2
double p2p1Distance = pow(pow(point2.x-point1.x,2) + pow(point2.y- point1.y,2),0.5);
point ex = {(point2.x-point1.x)/p2p1Distance, (point2.y-point1.y)/p2p1Distance};
point aux = {point3.x-point1.x,point3.y-point1.y};
//signed magnitude of the x component
double i = ex.x * aux.x + ex.y * aux.y;
//the unit vector in the y direction.
point aux2 = { point3.x-point1.x-i*ex.x, point3.y-point1.y-i*ex.y};
point ey = { aux2.x / norm (aux2), aux2.y / norm (aux2) };
//the signed magnitude of the y component
double j = ey.x * aux.x + ey.y * aux.y;
//coordinates
double x = (pow(r1,2) - pow(r2,2) + pow(p2p1Distance,2))/ (2 * p2p1Distance);
double y = (pow(r1,2) - pow(r3,2) + pow(i,2) + pow(j,2))/(2*j) - i*x/j;
//result coordinates
double finalX = point1.x+ x*ex.x + y*ey.x;
double finalY = point1.y+ x*ex.y + y*ey.y;
resultPose.x = finalX;
resultPose.y = finalY;
return resultPose;
}
int main(int argc, char* argv[]){
point finalPose;
point p1 = {4.0,4.0};
point p2 = {9.0,7.0};
point p3 = {9.0,1.0};
double r1,r2,r3;
r1 = 4;
r2 = 3;
r3 = 3.25;
finalPose = trilateration(p1,p2,p3,r1,r2,r3);
cout<<"X::: "<<finalPose.x<<endl;
cout<<"Y::: "<<finalPose.y<<endl;
}
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