// rotate_prime.java  given y=f(x) and point xc, rotate function and derivative

import java.awt.*;
import java.awt.event.*;
import java.io.*;

public class rotate_prime extends Frame
{
  double xmin = 0.005;
  double xmax = 1.0;
  double xoff = 50.0;
  double yoff = 600.0;
  double scale = 900.0; // for plotting
  double xtop, ytop, xbot, ybot, xfront, yfront; // special points 
  int height = 1000; // upper part for title 
  int width = 1000; // upper part for title 
  double Pi = 3.14159265358979323846;

  double angle_deg = 22.0; // may be read in 
  String angle_ch = "22";
  double angle;
  double xc = 0.3; // rotate about point
  int n = 0;

  rotate_prime()
  {
    System.out.println("rotate_prime.java running");
    angle = Pi*angle_deg/180.0;

    setTitle("rotate_prime"+angle_ch);
    setSize(width,height);
    setBackground(Color.white);
    setForeground(Color.black);
    addWindowListener(new WindowAdapter()
    {
      public void windowClosing(WindowEvent e)
      {
        System.exit(0);
      }
    });
    setVisible(true);
  } // end constructor rotate_prime

  public void paint(Graphics g)
  {
    double x1, y1, x2, y2, dx;

    g.setColor(Color.black);
    g.drawString("rotate_prime "+angle_ch, 20, 50);
    g.drawLine((int)(xoff),height,(int)(xoff),0);
    g.drawLine(0,height-(int)(yoff),width,height-(int)(yoff));

    g.setColor(Color.green);
    g.drawString("rotated function fry "+angle_ch, 20, 70);

    g.setColor(Color.red);
    g.drawString("rotated prime top "+angle_ch, 20, 90);

    g.setColor(Color.blue);
    g.drawString("rotated prime bottom "+angle_ch, 20, 110);

    g.setColor(Color.black);
    g.drawString("slope top "+angle_ch, 20, 130);

    n = 40;
    dx = (xmax-xmin)/(double)(n-1);
    for(int j=0; j<n; j++)
    {
      x1=xmin+j*dx;
      y1=fry(x1);
      if(j==0)
          System.out.println("in paint, x1="+((int)(scale*x1+xoff))+
                             ", y1="+(height-(int)(scale*y1+yoff)));
      g.setColor(Color.green);
      g.drawOval((int)(scale*x1+xoff)-1, height-(int)(scale*y1+yoff)-1, 2, 2);
      g.setColor(Color.black);
      x2 = x1+0.01*Math.cos(Math.atan(fryp(x1)));
      y2 = y1+0.01*Math.sin(Math.atan(fryp(x1)));
      g.drawLine((int)(scale*x1+xoff),
                 height-(int)(scale*y1+yoff),
                 (int)(scale*x2+xoff),
                 height-(int)(scale*y2+yoff));

      g.setColor(Color.green);
      y1=fryn(x1);
      g.drawOval((int)(scale*x1+xoff)-1, height-(int)(scale*y1+yoff)-1, 2, 2);
      g.setColor(Color.black);
      x2 = x1+0.01*Math.cos(Math.atan(frynp(x1)));
      y2 = y1+0.01*Math.sin(Math.atan(frynp(x1)));
      g.drawLine((int)(scale*x1+xoff),
                 height-(int)(scale*y1+yoff),
                 (int)(scale*x2+xoff),
                 height-(int)(scale*y2+yoff));

      g.setColor(Color.red);
      y1 = fryp(x1);
      g.drawOval((int)(scale*x1+xoff)-1, height-(int)(scale*y1+yoff)-1, 2, 2);

      g.setColor(Color.blue);
      y1 = frynp(x1);
      g.drawOval((int)(scale*x1+xoff)-1, height-(int)(scale*y1+yoff)-1, 2, 2);
    }
    g.drawOval((int)(scale*xc+xoff)-2, height-(int)(scale*0.0+yoff)-2, 4, 4);
  } // end paint


  double f(double x) // function 0015 expanded
  {
      return 0.222675*Math.sqrt(x)-0.0945*x-0.2637*x*x+0.213225*x*x*x
             -0.076125*x*x*x*x;
  } // end f 

  double fry(double x) // f rotated  y=-(x-xc)*sin(angle)+f(x)*cos(angle)
  {
      return -(x-0.3)*Math.sin(angle)+f(x)*Math.cos(angle);
  } // end fry  top

  double fryn(double x) // -f rotated  y=-(x-xc)*sin(angle)-f(x)*cos(angle)
  {
      return -(x-xc)*Math.sin(angle)-f(x)*Math.cos(angle);
  } // end fryn  bottom


  double fryp(double x) // deriv fry  y=-(x-xc)*sin(angle)+f(x)*cos(angle)
  {
      return -Math.sin(angle)+(0.1113375/Math.sqrt(x)-0.0945-0.5274*x
             +0.639675*x*x-0.3045*x*x*x)*Math.cos(angle);
  } // end fryp  slope top

  double frynp(double x) // driv fryn  y=-(x-xc)*sin(angle)-f(x)*cos(angle)
  {
      return -Math.sin(angle)-(0.1113375/Math.sqrt(x)-0.0945-0.5274*x
             +0.639675*x*x-0.3045*x*x*x)*Math.cos(angle);
  } // end frynp  slope bottom


  // rotate  unused
  void pitch(double angle, double x, double y, double ax[], double ay[])
  {
    ax[0] = xc+(x-xc)*Math.cos(angle)+y*Math.sin(angle);
    ay[0] = -(x-xc)*Math.sin(angle)+y*Math.cos(angle);
  } // end pitch 

  public static void main(String args[])
  {
    new rotate_prime();
    System.out.println("rotate_prime.java ends ");
  }
} // end class rotate_prime