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+/* 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/6.0;
+ double d = 1.0;
+ double h = sqrt(2.0 * d*d * (1.0 - sin(theta)));
+ double y, z;
+
+ double zmax = h; double zmin = -0.5;
+ double ymax = capillary(0.03*h,h,d);
+
+ cout << "picture capillary.fplot; capillary.fplot := nullpicture;\n";
+ cout << "addto capillary.fplot contour " << mpoint(0.0,1.0);
+ for(int i=99;i>2;i--) {
+ z = (i/100.0) * h;
+ y = capillary(z,h,d);
+ cout << " .. " << mpoint(y/ymax,(z-zmin)/(zmax-zmin));
+ }
+ cout << " -- " << mpoint(1.0,0.0);
+ cout << " -- " << mpoint(0.0,0.0);
+ cout << " -- cycle;\n\n";
+
+ cout << "picture capillary.lplot; capillary.lplot := nullpicture;\n";
+ cout << "addto capillary.lplot doublepath " << mpoint(0.0,1.0);
+ for(int i=99;i>2;i--) {
+ z = (i/100.0) * h;
+ y = capillary(z,h,d);
+ cout << " .. " << mpoint(y/ymax,(z-zmin)/(zmax-zmin));
+ }
+ cout << ";\n\n";
+
+ cout.setf(ios_base::fixed,ios_base::floatfield);
+ cout.precision(5);
+ cout << "numeric capillary.xleft; ";
+ cout << "capillary.xleft = 0.0;\n";
+ cout << "numeric capillary.xright; ";
+ cout << "capillary.xright = " << ymax << ";\n";
+ cout << "numeric capillary.ybot; ";
+ cout << "capillary.ybot = " << zmin << ";\n";
+ cout << "numeric capillary.ytop; ";
+ cout << "capillary.ytop = " << zmax << ";\n\n";
+
+ cout << "pair capillary.contactpoint; ";
+ cout << "capillary.contactpoint = (0.0, 1.0);\n";
+ cout << "numeric capillary.contactangle; ";
+ cout << "capillary.contactangle = " << theta * 180/pi << ";\n";
+}