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or_relativ.hpp
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or_relativ.hpp
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#include <iostream>
#include <armadillo>
#include <fstream>
#include <string>
#include <vector>
#include <math.h>
#include <iomanip>
using namespace std;
using namespace arma;
struct GMS
{
int G,M,S;
GMS(int,int,int);
double gdec();
double rad();
};
struct topoPoint
{
double Hz,Ze,Di;
vec3 XYZ;
bool rad;
topoPoint(double,double,double,bool);
void cart();
void translate(vec3 tvec);
void Rotate(mat R);
};
GMS::GMS (int g,int m,int s)
{
G=g;
M=m;
S=s;
}
double GMS::gdec ()
{
return double(G)+ (double(M)/60) + (double(S)/3600);
}
double GMS::rad()
{
double radd = gdec() * (datum::pi/180);
return radd;
}
struct SMMTleverARM
{
//to handle with the base from the file
vector<vector<string>> data;
vector<vector<GMS>> hor,zen;
vector<vector<double>> dists;
//the arbitrary-frame surveyed points
vector<vector<topoPoint>> points;
//the planes of the process (coefficients a,b,c,d)
vec4 Hplan,Vplan;
vec4 CEin,CEout,CDin,CDout;
//aux1 is parallel to Hplan
//matrices containing points
mat ptsH,ptsV; //at the sides of the IMU
mat ptsCEin,ptsCEout,ptsCDin,ptsCDout; //points on the parallel circular patterns, on the lens of the cameras
mat ptsOnCEin,ptsOnCEout,ptsOnCDin,ptsOnCDout; //adjusted points
//rotation matrices
mat Rot1 = eye<mat>(3,3);
//the principal vectors, to define the cannonical system
vec3 u,v,w; //u for x,v for y,w for z
//the axis direction of each camera system, in the same convention of the IMU
vec3 xE,yE,zE,xD,yD,zD;
//the axis of each camera system, with the z axis pointing backwards
vec3 Xe,Ye,Ze,Xd,Yd,Zd;
//the difference between the antena top and the center of phase
vec3 PhC = {0,0,-0.0071};
//the lever-arm vectors
vec3 antLA,LcamLA,RcamLA;
//temporary, and auxiliar vectors
vec3 tempE,tempD,aux1e,aux1d,aux_E0,aux_D0;
//the boresight matrices
mat Rimu_LC = eye(3,3),Rimu_RC = eye(3,3),Rimu_LC2 = eye(3,3),Rimu_RC2 = eye(3,3),Rimu_LC3 = eye(3,3),Rimu_RC3 = eye(3,3);
//center of the IMU, the mark on the H plane, the mark on the v plane
vec3 imuC,Hm,Vm;
double planesAngle;
SMMTleverARM (string fileName);
vector<vector<string>> readLAFile(string filename);
//the member functions
void horiz();
void zenit();
void distanc();
void avgOBS();
void pointsPrint(string filename);
void translateAll(vec3 tvec);
void rotAll (mat R);
void report();
};
vec3 onPlanePoint(vec4 plCoef,double x,double y);
//all the function propotypes:
double pdpiH(double,double);
double pdpiV(double,double);
void TptMat (mat *M,vec Tvec);
void RptMat (mat *M,mat R);
vec4 plane3points(vec3 u,vec3 v,vec3 w);
mat topoPointsMat (vector<topoPoint> points,uword first,uword last);
vec4 parallelPlane(vec4 plane1,vec3 pointOnPlane);
vec3 ProjPtOrtPlane(vec3 pt2Proj,vec3 plNorm,vec3 ptOnPlane);
vec4 leasqPlane2(vector<topoPoint> pointList,mat *ptOnPlane,string repNam,uword ijpt=0)
{
vec4 res,Xo;
mat data,P,Pinf,A,B,M,mvcXa,mvcLa,mvcV,mvcW;
vec Lb,W,X,Xa,K,V,La;
double vp;
if (pointList.size() >= 3)
{
Xo = plane3points(pointList.at(0).XYZ,pointList.at(1).XYZ,pointList.at(2).XYZ);
}
Pinf = eye(3,3)*10000;
if (pointList.size() < 3)
{
res = {0,0,1,0};
}
else if (pointList.size() == 3)
{
res = Xo;
}
else
{
ofstream out(repNam);
//vetor Lb
data = ones(pointList.size(),3);
for (uword i0 = 0; i0 < pointList.size(); i0++)
{
data.row(i0) = pointList.at(i0).XYZ.t();
}
Lb = vectorise(data.t());
//matriz dos pesos
P = eye(Lb.n_elem,Lb.n_elem);
if (ijpt != 0)
{
//em caso de que haja um ponto a ser injuncionado
// P.submat(ijpt*3-2,ijpt*3-2,ijpt*3,ijpt*3) = Pinf;
P.submat(ijpt*3-3,ijpt*3-3,ijpt*3-1,ijpt*3-1) = Pinf;
}
//matriz jacobiana A (parametros)
A = ones<mat>(pointList.size(),4);
for (uword i = 0; i < pointList.size(); i++)
{
A(i,0)=data(i,0);
A(i,1)=data(i,1);
A(i,2)=data(i,2);
}
//matriz jacobiana B (observacoes)
B = zeros<mat>(pointList.size(),Lb.n_elem);
uword j = 0;
for (uword i2 = 0; i2 < pointList.size(); i2++)
{
B(i2,0+j)=Xo(0);
B(i2,1+j)=Xo(1);
B(i2,2+j)=Xo(2);
j += 3;
}
W = zeros<vec>(pointList.size());
for (uword i3 = 0; i3 < pointList.size(); i3++)
{
W(i3) = dot(A.row(i3),Xo);
}
M = B * P.i() * B.t();
X = - inv(A.t()*M.i()*A)*(A.t()*M.i()*W);
Xa = Xo + X;
K = -M.i()*(A*X+W);
V = P.i() * B.t() * K;
La = Lb+V;
*ptOnPlane = trans(reshape(La,3,pointList.size()));
vp = as_scalar( V.t() * P * V / (Lb.n_elem - Xo.n_elem) );
mvcXa = vp * inv(A.t()*M.i()*A);
mvcLa = vp*(inv(P)+inv(P)*B.t()*inv(M)*A*inv(A.t()*inv(M)*A)*A.t()*inv(M)*B*inv(P)-inv(P)*B.t()*inv(M)*B*inv(P));
mvcV = vp*P.i()-mvcLa;
mvcW = vp*M;
out.precision(30);
res = Xa;
// Xo.raw_print(out,"Xo");
// X.raw_print(out,"X");
// Xa.raw_print(out,"Xa:");
// res.raw_print(out," b ");
// out <<"Xo+X: "<<endl<<std::setprecision(30)<< Xo+X<<endl;
//normalizing the plane equations
res.rows(0,2) = normalise(Xa.rows(0,2));
res(3) = - dot(normalise(Xa.rows(0,2)),La.rows(0,2));
// res.print(out," a ");
data.print(out,"dados de entrada: ");
out<<endl;
res.print(out,"coeficientes do plano estimado: ");
out<<endl;
V.print(out,"resíduos: ");
out<<endl;
La.print(out,"La:");
out<<endl;
out << "var. posteriori: " << vp << endl<<endl;
mvcXa.print(out,"MVC dos parametros ajustados");
out<<endl;
mvcLa.print(out,"MVC das observações ajustadas");
out<<endl;
}
//cout<< res<<endl;
return res;
}
void leasq2ParallelPlanes(vec4 *plane1,vec4 *plane2,mat points1,mat points2,mat *ptOnPlane1,mat *ptOnPlane2,string repNam,uword n=5,double e=.000001)
{
vec5 Xo,X,Xa;
mat data,P,A,B,M,mvcXa,mvcLa,mvcV,mvcW,ptsOnPlanes;
vec Lb,W,K,V,La,temp5,temp6;
double vp;
vec4 temp1,temp2,temp3,temp4;
temp1.ones();
temp2.zeros();
uword iter;
ofstream out(repNam);
Xo.rows(0,3) = plane3points(trans(points1.row(0)),trans(points1.row(1)),trans(points1.row(2)) );
Xo(4) = - dot(Xo.rows(0,2),points2.row(0));
//vetor Lb
data = join_vert(points1,points2);
Lb = vectorise(data.t());
//matriz dos pesos
P = eye(Lb.n_elem,Lb.n_elem);
//matriz jacobiana A (parametros)
A = zeros<mat>(data.n_rows,Xo.n_elem);
B = zeros<mat>(data.n_rows,Lb.n_elem);
W = zeros<vec>(data.n_rows);
A.submat(0,0,data.n_rows-1,data.n_cols-1) = data;
for (uword i = 0; i < data.n_rows; i++)
{
if (i < points1.n_rows)
{
A(i,3) = 1;
}
else
{
A(i,4) = 1;
}
}
for(uword it = 0; it < n; it ++)
{
uword j = 0;
for (uword i2 = 0; i2 < data.n_rows; i2++)
{
B(i2,0+j)=Xo(0);
B(i2,1+j)=Xo(1);
B(i2,2+j)=Xo(2);
j += 3;
temp1.rows(0,2) = trans( data.row(i2) );
temp2.rows(0,2) = Xo.rows(0,2);
if(i2 < points1.n_rows)
{
temp2(3)=Xo(3);
}
else
{
temp2(3)=Xo(4);
}
W(i2) = dot(temp1,temp2);
}
M = B * P.i() * B.t();
X = - inv(A.t()*M.i()*A)*(A.t()*M.i()*W);
Xa = Xo + X;
Xo = Xa;
iter = it;
if (arma::max(arma::abs(X)) < e)
{
break;
}
}
K = -M.i()*(A*X+W);
V = P.i() * B.t() * K;
La = Lb+V;
ptsOnPlanes = trans(reshape(La,data.n_cols,data.n_rows));
*ptOnPlane1 = ptsOnPlanes.rows(0,points1.n_rows-1);
*ptOnPlane2 = ptsOnPlanes.rows(points1.n_rows,data.n_rows-1);
temp3.rows(0,2) = normalise(Xa.rows(0,2));
temp3(3)= - dot(La.rows(0,2),normalise(Xa.rows(0,2)));
temp4 = temp3;
temp4(3)= - dot(La.rows(La.n_elem-3,La.n_elem-1),normalise(Xa.rows(0,2)));
*plane1 = temp3;
*plane2 = temp4;
vp = as_scalar( V.t() * P * V / (Lb.n_elem - Xo.n_elem) );
mvcXa = vp * inv(A.t()*M.i()*A);
mvcLa = vp*(inv(P)+inv(P)*B.t()*inv(M)*A*inv(A.t()*inv(M)*A)*A.t()*inv(M)*B*inv(P)-inv(P)*B.t()*inv(M)*B*inv(P));
mvcV = vp*P.i()-mvcLa;
mvcW = vp*M;
out.precision(20);
points1.raw_print(out,"dados de entrada (primeiro plano): ");
out<<endl;
points2.raw_print(out,"dados de entrada (segundo plano): ");
out<<endl;
out << iter <<" iterações necessárias" <<endl<<endl;
Xa.raw_print(out," vetor Xa (pré-normalização)");
out<<endl;
temp3.raw_print(out,"coeficientes do primeiro plano estimado: ");
out<<endl;
temp4.raw_print(out,"coeficientes do segundo plano estimado: ");
out<<endl;
V.raw_print(out,"resíduos: ");
out<<endl;
ptsOnPlanes.raw_print(out,"La:");
out<<endl;
out << "var. posteriori: " << vp << endl<<endl;
mvcXa.raw_print(out,"MVC dos parametros ajustados");
out<<endl;
mvcLa.raw_print(out,"MVC das observações ajustadas");
out<<endl;
}
struct Sphere
{
vec3 center;
double r;
mat onSpherePts;
Sphere(mat points,string repNam,uword n=20,double e=.000001);
};
Sphere::Sphere(mat data,string repNam,uword n,double e)
{
vec4 Xo,X,Xa;
mat P,A,B,M,mvcXa,mvcLa,mvcV,mvcW,ptsOnPlanes;
vec Lb,W,K,V,La,temp5,temp6,aux;
double vp;
vec4 temp1,temp2,temp3,temp4;
temp1.ones();
temp2.zeros();
uword iter;
ofstream out(repNam);
aux=zeros(data.n_rows);
for (uword i = 0; i < aux.n_rows; i++)
{
aux(i) = norm(data.row(i) - mean(data));
}
Xo.rows(1,3) = trans(mean(data));
Xo(0) = mean(aux);
//vetor Lb
Lb = vectorise(data.t());
//matriz dos pesos
P = eye(Lb.n_elem,Lb.n_elem);
//matriz jacobiana A (parametros)
A = zeros<mat>(data.n_rows,Xo.n_elem);
B = zeros<mat>(data.n_rows,Lb.n_elem);
W = zeros<vec>(data.n_rows);
for(uword it = 0; it < n; it ++)
{
uword j = 0;
for (uword i2 = 0; i2 < data.n_rows; i2++)
{
A(i2,0) = - 2 * Xo(0);
A(i2,1) = 2 * (Xo(1) - data(i2,0));
A(i2,2) = 2 * (Xo(2) - data(i2,1));
A(i2,3) = 2 * (Xo(3) - data(i2,2));
B(i2,j) = - 2 * (Xo(1) - data(i2,0));
B(i2,1+j)= - 2 * (Xo(2) - data(i2,1));
B(i2,2+j)= - 2 * (Xo(3) - data(i2,2));
j += 3;
W(i2) = std::pow((data(i2,0) - Xo(1)),2) + std::pow((data(i2,1) - Xo(2)),2) +
std::pow((data(i2,2) - Xo(3)),2) - std::pow(Xo(0),2);
}
M = B * P.i() * B.t();
X = - inv(A.t()*M.i()*A)*(A.t()*M.i()*W);
Xa = Xo + X;
Xo = Xa;
iter = it;
if (arma::max(arma::abs(X)) < e)
{
break;
}
}
K = -M.i()*(A*X+W);
V = P.i() * B.t() * K;
La = Lb+V;
onSpherePts = trans(reshape(La,data.n_cols,data.n_rows));
vp = as_scalar( V.t() * P * V / (Lb.n_elem - Xo.n_elem) );
mvcXa = vp * inv(A.t()*M.i()*A);
mvcLa = vp*(inv(P)+inv(P)*B.t()*inv(M)*A*inv(A.t()*inv(M)*A)*A.t()*inv(M)*B*inv(P)-inv(P)*B.t()*inv(M)*B*inv(P));
mvcV = vp*P.i()-mvcLa;
mvcW = vp*M;
out.precision(20);
data.raw_print(out,"dados de entrada :");
out<<endl;
out << iter <<" iterações necessárias" <<endl<<endl;
Xa.raw_print(out,"parametros ajustados (r,XC,YC,ZC)");
out<<endl;
V.raw_print(out,"resíduos: ");
out<<endl;
La.raw_print(out,"La:");
out<<endl;
out << "var. posteriori: " << vp << endl<<endl;
mvcXa.raw_print(out,"MVC dos parametros ajustados");
out<<endl;
mvcLa.raw_print(out,"MVC das observações ajustadas");
out<<endl;
//assignment to the object variables
r = Xo(0);
center = Xo.rows(1,3);
}
vector<vector<string>> SMMTleverARM::readLAFile(string filename)
{
//to read a file of the raw data of the Lever Arm surveying
ifstream in(filename);
vector<vector<string>> res;
vector<string> A,B,C,D,E;
//to control
int state = 0;
string line;
while (std::getline(in,line))
{
if (line.find("COD:[A") != -1)
{
state = 1;
continue;
}
if (line.find("COD:[B") != -1)
{
state = 2;
continue;
}
if (line.find("COD:[C") != -1)
{
state =3 ;
continue;
}
if (line.find("COD:[D") != -1)
{
state =4 ;
continue;
}
if (line.find("COD:[E") != -1)
{
state =5 ;
continue;
}
if (state == 1)
{
A.push_back(line);
//cout << stoi(line.substr(23,3))<<endl;
}
if (state == 2)
{
B.push_back(line);
}
if (state == 3)
{
C.push_back(line);
}
if (state ==4 )
{
D.push_back(line);
}
if (state == 5)
{
E.push_back(line);
}
}
res.push_back(A);
res.push_back(B);
res.push_back(C);
res.push_back(D);
res.push_back(E);
//cout<<A.size()<<" "<< B.size()<<" "<<C.size()<<" "<<D.size()<<" "<<E.size()<<endl;
//cout<<res.size();
return res;
}
SMMTleverARM::SMMTleverARM (string fileName)
{
// the constructor, all the modifying functions must have their calls here.
data = readLAFile(fileName);
horiz();
zenit();
distanc();
avgOBS();
//the two planes
Vplan = leasqPlane2(points.at(1),&ptsV,"plano_vert.txt",2);
Hplan = leasqPlane2(points.at(2),&ptsH,"plano_hor.txt",2);
//the angle between them
planesAngle = std::acos(dot(Vplan.rows(0,2),Hplan.rows(0,2))) * (180/datum::pi);
//the marks on the IMU surface
Hm = trans(ptsH.row(2));
Vm = trans(ptsV.row(2));
//the normal of the Hplan, is also the third direction (w),
//but at first, is needed some test
w = Hplan.rows(0,2);
if(w(2)<0) //the z component, needs to be positive, due to the z axis of the total station
{
w *= -1;
}
//the aux1 plane
//aux1.rows(0,2) = w;
//aux1(3) = - dot(w,Vm);
//IMU center with the intersection of the plane (aux1) and the line (point Hm and direction w)
//imuC = Hm + (dot(w,(Vm-Hm)))* w; //do not delete the old implementation
imuC = ProjPtOrtPlane(Hm,w,Vm);
//the first principal direction (u)
u = normalise(Vm - imuC);
//the second principal direction(v)
v = normalise(cross(w,u));
//first, translating the origin to the calculated center of the IMU
TptMat(&ptsH,-imuC);
TptMat(&ptsV,-imuC);
translateAll(-imuC);
pointsPrint("points1.txt");
//composing the first rotation matrice
Rot1.col(0)=u;
Rot1.col(1)=v;
Rot1.col(2)=w;
Rot1 = Rot1.t();
//rotating all to the imu BF
RptMat(&ptsH,Rot1);
RptMat(&ptsV,Rot1);
rotAll(Rot1);
pointsPrint("points2.txt");
//imuC += -imuC;
//creating matrices with the points, from topoPoints;
ptsCDin = topoPointsMat(points.at(3),0,4);
ptsCDout = topoPointsMat(points.at(3),5,9);
ptsCEin = topoPointsMat(points.at(4),0,4);
ptsCEout = topoPointsMat(points.at(4),5,9);
//the pair of parallel planes, one for each camera
leasq2ParallelPlanes(&CDin,&CDout,ptsCDin,ptsCDout,&ptsOnCDin,&ptsOnCDout,"RcamPlanes.txt");
leasq2ParallelPlanes(&CEin,&CEout,ptsCEin,ptsCEout,&ptsOnCEin,&ptsOnCEout,"LcamPlanes.txt");
//creating a sphere for each camera, to measure the center
Sphere Rsphere(join_vert(ptsOnCDin,ptsOnCDout),"Rsphere.txt");
Sphere Lsphere(join_vert(ptsOnCEin,ptsOnCEout),"Lsphere.txt");
//Y of each camera direction (with same convention)
//due to the IMU bf and the cameras position, the y component needs to be positive
// to point forward the camera axis
yE = normalise(CEin.rows(0,2));
if (yE(1) < 0 )
{
yE *= -1;
}
yD = normalise(CDin.rows(0,2));
if (yD(1) < 0 )
{
yD *= -1;
}
//yD.print();cout<<endl;
//yE.print();cout<<endl;
//we'll need points perfectly on the plane, and to have this guarantee:
//each one are obtained by the plane equation, with z=f(x,y)
aux1d = onPlanePoint(CDin,ptsOnCDin(ptsOnCDin.n_rows-1,0),ptsOnCDin(ptsOnCDin.n_rows-1,1));
aux1e = onPlanePoint(CEin,ptsOnCEin(ptsOnCEin.n_rows-1,0),ptsOnCEin(ptsOnCEin.n_rows-1,1));
aux_D0 = onPlanePoint(CDin,ptsOnCDin(0,0),ptsOnCDin(0,1));
aux_E0 = onPlanePoint(CEin,ptsOnCEin(0,0),ptsOnCEin(0,1));
//projecting the center of spheres on the inner plane of the rings on the camera lenses
tempD = ProjPtOrtPlane(Rsphere.center,yD,aux1d);
tempE = ProjPtOrtPlane(Lsphere.center,yE,aux1e);
//calculating the z direction, for each camera
zE = normalise(aux_E0 - tempE);
zD = normalise(aux_D0 - tempD);
//and, finally the x direction
xE = normalise(cross(yE,zE));
xD = normalise(cross(yD,zD));
vec3 Xe2,Ye2,Ze2,Xd2,Yd2,Zd2;
//////formerly:
//////we can describe the axes in the camera conventional convention (z axis pointing from the CP to the focal plane)
////Xe = xE;Ye = zE;Ze = -yE;
////Xd = xD;Yd = zD;Zd = -yD;
//we can describe the axes in the camera modern convention (z axis pointing from the principle point to CP)
Xe = xE;
Ye = -zE;
Ze = yE;
Xd = xD;
Yd = -zD;
Zd = yD;
//conventional convention
Xe2 = xE;Ye2 = zE;Ze2 = -yE;
Xd2 = xD;Yd2 = zD;Zd2 = -yD;
//with the axis, we can have the boresight matrices:
//first with the same convention of the IMU:
Rimu_LC2.row(0) = trans(xE);
Rimu_LC2.row(1) = trans(yE);
Rimu_LC2.row(2) = trans(zE);
Rimu_RC2.row(0) = trans(xD);
Rimu_RC2.row(1) = trans(yD);
Rimu_RC2.row(2) = trans(zD);
//with the camera modern convention
Rimu_LC.row(0) = trans(Xe);
Rimu_LC.row(1) = trans(Ye);
Rimu_LC.row(2) = trans(Ze);
Rimu_RC.row(0) = trans(Xd);
Rimu_RC.row(1) = trans(Yd);
Rimu_RC.row(2) = trans(Zd);
//then with the camera conventional convention
Rimu_LC3.row(0) = trans(Xe2);
Rimu_LC3.row(1) = trans(Ye2);
Rimu_LC3.row(2) = trans(Ze2);
Rimu_RC3.row(0) = trans(Xd2);
Rimu_RC3.row(1) = trans(Yd2);
Rimu_RC3.row(2) = trans(Zd2);
//now, the lever-arm
//antenna lever-arm: just the point at the antena top, and the offset from there to the PhC
antLA = (points.at(0).at(0).XYZ) + PhC;
//the lever-arm of the two cameras:
RcamLA = Rsphere.center;
LcamLA = Lsphere.center;
report();
}
void SMMTleverARM::avgOBS()
{
vector<topoPoint> temp;
double hA,zA,dA=0,hB,zB,dB,hC,zC,dC,hD,zD,dD,hE,zE,dE,hF,zF,dF,hG,zG,dG,hH,zH,dH,hI,zI,dI,hJ,zJ,dJ;
//std::setprecision(8);
for (unsigned int i = 0; i < hor.size(); i++)
{
if (i == 0)
{
hA = (pdpiH(hor[i][0].gdec(),hor[i][1].gdec()) +
pdpiH(hor[i][2].gdec(),hor[i][3].gdec()) +
pdpiH(hor[i][4].gdec(),hor[i][5].gdec())) / 3;
zA = (pdpiV(zen[i][0].gdec(),zen[i][1].gdec()) +
pdpiV(zen[i][2].gdec(),zen[i][3].gdec()) +
pdpiV(zen[i][4].gdec(),zen[i][5].gdec())) / 3;
for (unsigned int j = 0; j < dists[i].size(); j++)
{
dA += dists[i][j]/6;
}
topoPoint ANT(hA,zA,dA,false);
temp.push_back(ANT);
//cout <<hA<<" "<<zA<<" "<<dA<<endl;
//cout <<hA<<" "<<zA<<" "<<dA<<endl;
}
if (i == 1)
{
hA = (pdpiH(hor[i][0].gdec(),hor[i][5].gdec()) +
pdpiH(hor[i][10].gdec(),hor[i][15].gdec())) / 2;
hB = (pdpiH(hor[i][1].gdec(),hor[i][6].gdec()) +
pdpiH(hor[i][11].gdec(),hor[i][16].gdec())) / 2;
hC = (pdpiH(hor[i][2].gdec(),hor[i][7].gdec()) +
pdpiH(hor[i][12].gdec(),hor[i][17].gdec())) / 2;
hD = (pdpiH(hor[i][3].gdec(),hor[i][8].gdec()) +
pdpiH(hor[i][13].gdec(),hor[i][18].gdec())) / 2;
hE = (pdpiH(hor[i][4].gdec(),hor[i][9].gdec()) +
pdpiH(hor[i][14].gdec(),hor[i][19].gdec())) / 2;
zA = (pdpiV(zen[i][0].gdec(),zen[i][5].gdec()) +
pdpiV(zen[i][10].gdec(),zen[i][15].gdec())) / 2;
zB = (pdpiV(zen[i][1].gdec(),zen[i][6].gdec()) +
pdpiV(zen[i][11].gdec(),zen[i][16].gdec())) / 2;
zC = (pdpiV(zen[i][2].gdec(),zen[i][7].gdec()) +
pdpiV(zen[i][12].gdec(),zen[i][17].gdec())) / 2;
zD = (pdpiV(zen[i][3].gdec(),zen[i][8].gdec()) +
pdpiV(zen[i][13].gdec(),zen[i][18].gdec())) / 2;
zE = (pdpiV(zen[i][4].gdec(),zen[i][9].gdec()) +
pdpiV(zen[i][14].gdec(),zen[i][19].gdec())) / 2;
dA = (dists[i][0]+dists[i][5]+dists[i][10]+dists[i][15]) / 4;
dB = (dists[i][1]+dists[i][6]+dists[i][11]+dists[i][16]) / 4;
dC = (dists[i][2]+dists[i][7]+dists[i][12]+dists[i][17]) / 4;
dD = (dists[i][3]+dists[i][8]+dists[i][13]+dists[i][18]) / 4;
dE = (dists[i][4]+dists[i][9]+dists[i][14]+dists[i][19]) / 4;
topoPoint A(hA,zA,dA,false);
temp.push_back(A);
topoPoint B(hB,zB,dB,false);
temp.push_back(B);
topoPoint C(hC,zC,dC,false);
temp.push_back(C);
topoPoint D(hD,zD,dD,false);
temp.push_back(D);
topoPoint E(hE,zE,dE,false);
temp.push_back(E);
// cout <<hA<<" "<<zA<<" "<<dA<<endl;
}
if (i == 2)
{
hA = (pdpiH(hor[i][0].gdec(),hor[i][5].gdec()) +
pdpiH(hor[i][10].gdec(),hor[i][15].gdec())) / 2;
hB = (pdpiH(hor[i][1].gdec(),hor[i][6].gdec()) +
pdpiH(hor[i][11].gdec(),hor[i][16].gdec())) / 2;
hC = (pdpiH(hor[i][2].gdec(),hor[i][7].gdec()) +
pdpiH(hor[i][12].gdec(),hor[i][17].gdec())) / 2;
hD = (pdpiH(hor[i][3].gdec(),hor[i][8].gdec()) +
pdpiH(hor[i][13].gdec(),hor[i][18].gdec())) / 2;
hE = (pdpiH(hor[i][4].gdec(),hor[i][9].gdec()) +
pdpiH(hor[i][14].gdec(),hor[i][19].gdec())) / 2;
zA = (pdpiV(zen[i][0].gdec(),zen[i][5].gdec()) +
pdpiV(zen[i][10].gdec(),zen[i][15].gdec())) / 2;
zB = (pdpiV(zen[i][1].gdec(),zen[i][6].gdec()) +
pdpiV(zen[i][11].gdec(),zen[i][16].gdec())) / 2;
zC = (pdpiV(zen[i][2].gdec(),zen[i][7].gdec()) +
pdpiV(zen[i][12].gdec(),zen[i][17].gdec())) / 2;
zD = (pdpiV(zen[i][3].gdec(),zen[i][8].gdec()) +
pdpiV(zen[i][13].gdec(),zen[i][18].gdec())) / 2;
zE = (pdpiV(zen[i][4].gdec(),zen[i][9].gdec()) +
pdpiV(zen[i][14].gdec(),zen[i][19].gdec())) / 2;
dA = (dists[i][0]+dists[i][5]+dists[i][10]+dists[i][15]) / 4;
dB = (dists[i][1]+dists[i][6]+dists[i][11]+dists[i][16]) / 4;
dC = (dists[i][2]+dists[i][7]+dists[i][12]+dists[i][17]) / 4;
dD = (dists[i][3]+dists[i][8]+dists[i][13]+dists[i][18]) / 4;
dE = (dists[i][4]+dists[i][9]+dists[i][14]+dists[i][19]) / 4;
topoPoint A(hA,zA,dA,false);
temp.push_back(A);
topoPoint B(hB,zB,dB,false);
temp.push_back(B);
topoPoint C(hC,zC,dC,false);
temp.push_back(C);
topoPoint D(hD,zD,dD,false);
temp.push_back(D);
topoPoint E(hE,zE,dE,false);
temp.push_back(E);
// cout <<hA<<" "<<zA<<" "<<dA<<endl;
}
if (i == 3)
{
topoPoint EXTRA(hor[i][0].gdec(),zen[i][0].gdec(),dists[i][0],false);
hA = pdpiH(hor[i][1].gdec(),hor[i][11].gdec());
hB = pdpiH(hor[i][2].gdec(),hor[i][12].gdec());
hC = pdpiH(hor[i][3].gdec(),hor[i][13].gdec());
hD = pdpiH(hor[i][4].gdec(),hor[i][14].gdec());
hE = pdpiH(hor[i][5].gdec(),hor[i][15].gdec());
hF = pdpiH(hor[i][6].gdec(),hor[i][16].gdec());
hG = pdpiH(hor[i][7].gdec(),hor[i][17].gdec());
hH = pdpiH(hor[i][8].gdec(),hor[i][18].gdec());
hI = pdpiH(hor[i][9].gdec(),hor[i][19].gdec());
hJ = pdpiH(hor[i][10].gdec(),hor[i][20].gdec());
zA = pdpiV(zen[i][1].gdec(),zen[i][11].gdec());
zB = pdpiV(zen[i][2].gdec(),zen[i][12].gdec());
zC = pdpiV(zen[i][3].gdec(),zen[i][13].gdec());
zD = pdpiV(zen[i][4].gdec(),zen[i][14].gdec());
zE = pdpiV(zen[i][5].gdec(),zen[i][15].gdec());
zF = pdpiV(zen[i][6].gdec(),zen[i][16].gdec());
zG = pdpiV(zen[i][7].gdec(),zen[i][17].gdec());
zH = pdpiV(zen[i][8].gdec(),zen[i][18].gdec());
zI = pdpiV(zen[i][9].gdec(),zen[i][19].gdec());
zJ = pdpiV(zen[i][10].gdec(),zen[i][20].gdec());
dA = (dists[i][1]+dists[i][11]) / 2;
dB = (dists[i][2]+dists[i][12]) / 2;
dC = (dists[i][3]+dists[i][13]) / 2;