/* Simple capillary surface */

#include<sstream>
#include<iostream>
#include<cmath>

using namespace std;

string mpoint(double x, double y) {
 ostringstream pointstring;
 pointstring.setf(ios_base::fixed,ios_base::floatfield);
 pointstring.precision(5);
 pointstring << '(' << x << ',' << y << ')';
 return pointstring.str();
}

double arccosh(double x) {
 return log(x + sqrt(x*x-1));
}

double capillary(double z, double h, double d) {
 return arccosh(2.0*d/z) - arccosh(2.0*d/h)
        + sqrt(4.0 - h*h/(d*d)) - sqrt(4.0 - z*z/(d*d));
}

const double pi = 3.1415926535897932384626433832795;

int main() {
 double theta = pi/4.0;
 double d = 1.0;
 double h = sqrt(2.0 * d*d * (1.0 - sin(theta)));
 double y, z;

 cout << "picture capillary; capillary := nullpicture;\n";
 cout << "addto capillary contour " << mpoint(0.0,h);

 for(int i=99;i>2;i--) {
   z = (i/100.0) * h;
   y = capillary(z,h,d);
   cout << " .. " << mpoint(y,z);
 }

 cout << " -- " << mpoint(y,-0.5);
 cout << " -- " << mpoint(0.0,-0.5);
 cout << " -- cycle;\n";
}