/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

double f(double t) { return 0.25*(1-0.25*Sin(2*M_PI*t)+0.75*exp(t)); }
P fy(double t) { return P(t, -f(t), 0); }
P fz(double t) { return P(t, 0, f(t)); }

int main() 
{
  bounding_box(P(-2,-2),P(2,2));
  unitlength("1in");
  picture(5,5);

  begin();

  grid();

  double x_0=0.7, x_tmp;

  label(P(0.5*(x_min+x_max), y_min), P(0,4), 
	"Volume $=\\displaystyle\\pi\\int_a^b f(x)^2\\,dx$",t);
  camera.at(P(2.5,-2.5,1));
  camera.look_at(P(0.5,0,0));
  camera.focus(5);

  blue();
  arrow(P(0,0,0), P(0,0,0.75));
  label(P(0,0,0.75), P(0,4), "$y$",t);
  line(P(0,0,0), P(x_0,0,0));
  black();

  line(P(0,-1,0), P(0,0,0));
  line(P(x_0,-1,0), P(x_0,0,0));

  label(P(0,-1,0), P(-4,-2), "$a$", bl);
  label(P(x_0,-1,0), P(-4,-2), "$x$", bl);

  //  label(P(1,f(1),0), P(0,-4), "$y=f(x)$", b);

  gray(0.1);
  font_size("footnotesize");

  circle section;
  //  fill();
  //  gray(0);
  for (int i=0; i <= 20; ++i)
    {
      x_tmp = 0.05*i;
      //      if (fabs(x_tmp-x_0) < 0.001)
      if (i == 14) //x_tmp==x_0)
	fill();

      if (i == 0)
	pen(1.5);
      section=circle(P(x_tmp,0,0), f(x_tmp), E_1);
      section.draw();

	  //	  label(middle, P(-24,0), "$A(x)=\\pi f(x)^2$", c);
      if (i == 14) //x_tmp==x_0)
	{
	  fill(false);
	  bold(); red();
	  section=circle(P(x_tmp,0,0), f(x_tmp), E_1);
	  section.draw();
	  plain(); black();
	}
      if (i == 0)
	plain();

      /*
      blue();
      line(P(x_tmp,0,0), fz(x_tmp));
      line(P(x_tmp+0.025,0,0), fz(x_tmp+0.025));
      black();
      */
    }

  line(P(1,-1,0), P(1,0,0));
  label(P(1,-1,0), P(-4,-2), "$b$", bl);

  dashed(); red();
  section=circle(P(x_0,0,0), f(x_0), E_1);
  section.draw();
  solid();
  arrow(P(x_0,0,1), fz(x_0), P(0,4), "$A(x)=\\pi f(x)^2$", t, 0.5);
  black(); 

  pen(1.5);
  //  plot(f, x_0, 1, 24);
  plot(fy, 0, 1, 40);

  section=circle(P(1,0,0), f(1), E_1);
  section.draw();

  blue();
  plot(fz, 0, 1, 24);
  plain();
  
  line(P(x_0,0,0), P(1.25,0,0));
  line(P(1,0,0), fz(1));
  // masklabel(P(1.5,0,0), P(6,-2), "$x$", r);

  end();
}