Polar imaging

Question

Hi everyone. I've a set of images in parallel format and another set of images in polar format.
I want to draw control points directly on the polar images. But, i want to convert curve created from the control points to parallel format.
I understand about the polar coordinate system. Implementing? Help!!!
Thank you!

Answer 1

I needed polar coordinates for my recent math project so I wrote this class that represents a point in cartesian as well as polar coords.
Watch out, i'm not formatting the code.
import java.awt.geom.*;
public class ExtendedPt extends Point2D
     private double x, y;          //rectangular coordinates
     private double r, theta;     //polar coordinates. theta pvr: [0,2PI)
     public ExtendedPt()
     //if no flag is specified, it is assumend the coordinates passed are cartesian
     public ExtendedPt(double coord1, double coord2)
          setLocation(coord1, coord2);
     //the flag 'cartesian' specifies if the passed coordinates are in rectangular or polar form
     public ExtendedPt(double coord1, double coord2, boolean cartesian)
          if(cartesian)
               setLocation(coord1, coord2);
          else
               setPolarCoords(coord1, coord2);
     public void setLocation(double xval, double yval)
          x = xval;
          y = yval;
          calcPolarCoords();
     public void setCartesianCoords(double xval, double yval)
          setLocation(xval, yval);
     //This function sets the polar coodinates of the point:
     public void setPolarCoords(double rval, double tval)
          r = rval;
          theta = tval;
          calcCartesianCoords();
     public void setX(double xval)
          x = xval;
          //recalculate polar coordinates:
          calcPolarCoords();
     public void setY(double yval)
          y = yval;
          //re-calculate polar coordinates:
          calcPolarCoords();
     public void setR(double rval)
          r = rval;
          //re-calculate the cartesian coordinates:
          calcCartesianCoords();
     public void setTheta(double tval)
          theta = tval;
          //re-calculate the cartesian coordiates:
          calcCartesianCoords();
     //accessors:
     public double getX()
          return x;
     public double getY()
          return y;
     public double getR()
          return r;
     public double getTheta()
          return theta;
     //helper functions:
     private void calcPolarCoords()
          r = radiusCoord(x,y);
          theta = angleCoord(x,y,2);
     private void calcCartesianCoords()
          x = xCoord(r,theta);
          y = yCoord(r,theta);
     //The next two function can be used to convert cartesian to polar coordinates     
     //gives the radius coordinate of cartesian point (x,y)
     public static double radiusCoord(double x, double y)
          return Math.sqrt(Math.pow(x,2) + Math.pow(y,2));
     //gives the angle coordinate of cartesian point (x,y).
     //typeofPVR indicates in what range theta should be returned: 1 indicates a theta range of (-PI, PI] and a value of 2 returns theta in the range of [0,2PI)
     public static double angleCoord(double x, double y, int typeOfPVR)
          double t = Math.atan2(y, x);  //returns theta in P.V.R = (-PI, PI]
          if(typeOfPVR == 2)     //change the pvr from -PI, PI to [0,2PI).
               //Only the lower half (-PI, 0) has to be adjusted
               if((t > -Math.PI)&&(t < 0))
                    t = t + 2*Math.PI;
          return t;
     //The next two functions can be used to convert polar coordinates to cartesian
     //gives the x (abscissa) coordinate given r and theta
     public static double xCoord(double r, double theta)
          return r*Math.cos(theta);
     //gives the y (ordinate) coordinate given r and theta
     public static double yCoord(double r, double theta)
          return r*Math.sin(theta);
     public String toString()
          return "Cartesian: (" + x + ", " + y + "). Polar: (" + r + ", " + theta + ")";
     //small driver
     public static void main(String[] args)
          ExtendedPt P = new ExtendedPt(5,0,true);
          System.out.println(P);
}ciao,
nikita