Finding 3rd point if 2points and 2 distance are known.
hi friends,
I got a problem to find out the unknown point in a polygon with 5 points. when 2 points let A(a,b) and B(p,q) and distance r1 from A to unknown point E(X1, Y1), and distance r2 from B to E are given I have to find point E.
I try to solve this by considering as 2 circles, 1st circle with A as center, and radii as r1, and 2nd circle with B as center and r2 as radii.
The real proble is whether the method i followed is correct or not i dont know. any interested person please check my code and, can tell me about the mistakes i am doing, whther the method i followed wrong or not, or is there any easy method to solve this.
basically my project is a GIS related web application, here it is the manipulated necessary code.
/*
* CirclesIntersectionPoints.java
*
* Created on March 15, 2007, 4:25 PM
*
* Vemula KiranKumar,
* Associate ID - 1997.
* GeoSpace Integrated Solutions,
* Hyderabad.
*
*/
package com.org.Demarcation.importcoord;
/**
*
* @author Vemula KiranKumar.
*/
import java.lang.Math;
/*class CalculatePoints1 {
public static void main(String[] args) {
CirclesIntersectionPoints newPoints = new CirclesIntersectionPoints(-9, 1, 7, 5, -5, 18);
System.out.println("In the main program-x1>"+newPoints.getX1());
System.out.println("In the main program-y1>"+newPoints.getY1());
System.out.println("In the main program-x2>"+newPoints.getX2());
System.out.println("In the main program-y2>"+newPoints.getY2());
}
}*/
/*
*This class is used to find the intersection points of two circles
*Let Circle1 have a center point A(a,b), and Circle 2 have a center point B(p,q)
* and radious of circle 1 is r1, radious of circle 2 is r2,
* intersection points of circle 1 and circle 2 are E(X1, Y1) and (X2, Y2) that have to calculated by this program.
* procedure: -
* K = (1/4)squreroot(((r1+r2)^-d^)(d^-(r1-r2)^))
*d^ = (x2-x1)^ + (y2-y1)^
*
* K is the area of the triangle formed by the centers of the two circles and one of their points of intersection;
* d is the distance between the circles centers;
*r1, r2 are the circles' radii; (x1,y1) and (x2,y2) are the circles' centers
* The two solutions, then, are
*x = (1/2)(x2+x1) + (1/2)(x2-x1)(r1^-r2^)/d^ ?2(y2-y1)K/d^
*y = (1/2)(y2+y1) + (1/2)(y2-y1)(r1^-r2^)/d^ ?-2(x2-x1)K/d^
*/
class CirclesIntersectionPoints{
/* Default Constructor */
public CirclesIntersectionPoints(){
this.a=0;
this.b=0;
this.r1=0;
this.p=0;
this.q=0;
this.r2=0;
this.X1=0;
this.Y1=0;
this.X2=0;
this.Y2=0;
}
/* Parameterised constructor*/
public CirclesIntersectionPoints(double x1,double y1,double d1,double x2,double y2,double d2){
setA(x1);
setB(y1);
setR1(d1);
setP(x2);
setQ(y2);
setR2(d2);
System.out.println(this.a+", "+this.b+", "+this.r1+", "+this.p+", "+this.q+", "+this.r2 +" --> Real values ");
try{
interSectionPoints();// finding the intersection points.
}catch (Exception ex){
ex.printStackTrace();
}// finding the intersection points.
}
/*-Given Point 1(x1, y1) distance d1-*/
publicdouble getA(){
return this.a;
}
privatevoid setA(double x1){
this.a = x1;
}
publicdouble getB(){
return this.b;
}
privatevoid setB(double y1){
this.b = y1;
}
publicdouble getR1(){
return this.r1;
}
privatevoid setR1(double d1){
this.r1 = d1;
}
/*-Given Point 2(x2, y2) distance d2-*/
publicdouble getP(){
return this.p;
}
privatevoid setP(double x2){
this.p = x2;
}
publicdouble getQ(){
return this.q;
}
privatevoid setQ(double y2){
this.q = y2;
}
publicdouble getR2(){
return this.r2;
}
privatevoid setR2(double d2){
this.r2 = d2;
}
/*-New Point (X1, Y1) -*/
publicdouble getX1(){
return this.p;
}
privatevoid setX1(double newx1){
this.X1 = newx1;
}
publicdouble getY1(){
return this.Y1;
}
privatevoid setY1(double newy1){
this.Y1 = newy1;
}
/*-New Point (X2, Y2) -*/
publicdouble getX2(){
return this.X2;
}
privatevoid setX2(double newx2){
this.X2 = newx2;
}
publicdouble getY2(){
return this.Y2;
}
privatevoid setY2(double newy2){
this.Y2 = newy2;
}
/*-end of the getter setter -*/
/*
* finding the Intersection points.
* x = (1/2)(x2+x1) + (1/2)(x2-x1)(r1^-r2^)/d^ ?2(y2-y1)K/d^
* y = (1/2)(y2+y1) + (1/2)(y2-y1)(r1^-r2^)/d^ ?-2(x2-x1)K/d^
*
*/
publicvoid interSectionPoints(){
double aa = 0, bb = 0, rr1 = 0, pp = 0, qq = 0, rr2 = 0, sqrdistance = 0, areaoftri = 0;
double partx1 = 0, partx2 = 0, partx3 = 0;
double party1 = 0, party2 = 0, party3 = 0;
double _x1 = 0, _x2 = 0, _y1 = 0, _y2 = 0;
aa = getA();
bb = getB();
rr1 = getR1();
pp = getP();
qq = getQ();
rr2 = getR2();
sqrdistance = sqrdistBetweenCenters();// getting the distance between the centers of circles.
areaoftri = areaofTriangle();// getting the area of triangle.
/*
* Now Calculate the partx1, partx2, partx3 for XX1, XX2 coordnates,
* and Calculate the party1, party2, party3 for YY1, YY2 coordnates.
* _x1 = partx1 + partx2 + partx3
* _x2 = partx1 + partx2 - partx3
* _y1 = party1 + party2 + party3
* _y2 = party1 + party2 - party3
*/
sqrdistance = sqrdistBetweenCenters();
areaoftri = areaofTriangle();
/*
* finding the X coordinates.
*/
partx1 = (pp + aa) / 2;
partx2 = ((pp - aa) * ( (Math.pow(rr1,2) ) - (Math.pow(rr2,2)) ))/ (2 * sqrdistance);
partx3 = (2 * (qq - bb) * areaoftri) / sqrdistance;
_x1 = partx1 + partx2 + partx3;
_x2 = partx1 + partx2 - partx3;
/*
* Setting the x coordinates
*/
setX1(_x1);
setX2(_x2);
/*
* finding the Y coordinates.
*/
party1 = (qq + bb) / 2;
party2 = ((qq - bb) * ( (Math.pow(rr1,2) ) - (Math.pow(rr2,2)) ))/ (2 * sqrdistance);;
party3 = -(2 * (pp - aa) * areaoftri) / sqrdistance;
_y1 = party1 + party2 + party3;
_y2 = party1 + party2 - party3;
/*
* Setting the y coordinates
*/
setY1(_y1);
setY2(_y2);
}
/*
* This method will calculate the K, area of the triangle ABE.
* K = (1/4)squreroot(((r1+r2)^-d^)(d^-(r1-r2)^))
* where d is the distance between the two centers.
* (a, b) --> center of circle 1, with radii r1(given distance d1)
* (p, q) --> center of circle 2, with radii r2(given distance d2)
*/
publicdouble areaofTriangle(){
double areaoftri = 0;
double part1 = 0;
double part2 = 0;
double sqrdistance = 0;//distance between
double aa,bb,rr1,pp,qq,rr2;
aa = getA();
bb = getB();
rr1 = getR1();
pp = getP();
qq = getQ();
rr2 = getR2();
System.out.println(aa+", "+bb+", "+rr1+", "+pp+", "+qq+", "+rr2+"-->OK Test Passed.");
/*
* getting the square of distance between
* centers of 2 circles.
*/
sqrdistance= sqrdistBetweenCenters();
System.out.println("squre distance is >"+sqrdistance+"-->OK Test Passed.");
/*
* calculating part1, part 2 and subsitute in formula
* K = (1/4)squreroot((part1)*(part2))
*/
part1 = Math.pow((rr1 + rr2),2)- sqrdistance;
part2 = sqrdistance - Math.pow((rr1 - rr2),2);
areaoftri = (Math.sqrt(part1*part2))/4;
System.out.println("Area of Triangle is >"+areaoftri+"> Not OK! Not Yet Tested! ");
return areaoftri;
}
/*
* This method calculate the squre of distance between
* the two points of the circle centers
*
*/
publicdouble sqrdistBetweenCenters(){
double sqrdistance = 0;
double aa = 0, bb = 0, pp = 0, qq = 0;
aa = getA();
bb = getB();
pp = getP();
qq = getQ();
sqrdistance = (Math.pow((pp-aa),2)) + (Math.pow((qq-bb),2));
return sqrdistance;// OK. Test Passed.(kiran)
}
protected String kirankumarVemula;
/* Given Point 1(x1, y1) with distance d1*/
privatedouble a;
privatedouble b;
privatedouble r1;
/* Given Point 2 (x2, y2) with distance d2*/
privatedouble p;
privatedouble q;
privatedouble r2;
/* Calculated Point 1 */
privatedouble X1;
privatedouble Y1;
/* Calculated Point 2 */
privatedouble X2;
privatedouble Y2;
}
