finding 3 rd point if 2 points and and 2 distances are given

> hi, thanks for ur reply.

> Actually i am not comfortable with coordinate

> geometry.

Then you need to brush it up.

> but the example u given is about the circle.

Yes, and in your original post you only had 2 starting points, two distances from those points and wanted to find the 3rd point (possibilibly two different 3rd points). The distances you talked about are the radii, and the starting points are the centers of your circles.

prometheuzza at 2007-7-10 3:03:49 >

thaks again.

what u said is correct. our circles' centers do not have the same y-value.

point p1 is one of the coordinate of the polygon or square. and consider for now it is not necessary for our problem. (for your understanding i mentioned).

can we solve this like finding intersection points of 2 circles ? for example,

a circle c1 with center p2(x2, y2) and radious d1, and

2nd circle c2 with centerp4(x4, y4) and radious d2, both circle intersect each other, then intersction point is p3(x3,y3).

regards,

kiran vemula.

kirankumarvemulaa at 2007-7-10 3:03:49 >

hi,

i tried to solve as u said.

mean while i tried in some other manner. please can u tellme whether this is correct way or not.

please see my 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-*/

public double getA(){

return this.a;

}

private void setA(double x1){

this.a = x1;

}

public double getB(){

return this.b;

}

private void setB(double y1){

this.b = y1;

}

public double getR1(){

return this.r1;

}

private void setR1(double d1){

this.r1 = d1;

}

/*-Given Point 2(x2, y2) distance d2-*/

public double getP(){

return this.p;

}

private void setP(double x2){

this.p = x2;

}

public double getQ(){

return this.q;

}

private void setQ(double y2){

this.q = y2;

}

public double getR2(){

return this.r2;

}

private void setR2(double d2){

this.r2 = d2;

}

/*-New Point (X1, Y1) -*/

public double getX1(){

return this.p;

}

private void setX1(double newx1){

this.X1 = newx1;

}

public double getY1(){

return this.Y1;

}

private void setY1(double newy1){

this.Y1 = newy1;

}

/*-New Point (X2, Y2) -*/

public double getX2(){

return this.X2;

}

private void setX2(double newx2){

this.X2 = newx2;

}

public double getY2(){

return this.Y2;

}

private void 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^

*

*/

public void 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;

System.out.println("*******************");

System.out.println(_y1);

System.out.println(_y2);

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)

*/

public double 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 Tested Yet");

return areaoftri;

}

/*

* This method calculate the squre of distance between

* the two points of the circle centers

*

*/

public double 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*/

private double a;

private double b;

private double r1;

/* Given Point 2 (x2, y2) with distance d2*/

private double p;

private double q;

private double r2;

/* Calculated Point 1 */

private double X1;

private double Y1;

/* Calculated Point 2 */

private double X2;

private double Y2;

}

kirankumarvemulaa at 2007-7-10 3:03:49 >

thankyou for ur reply.

i try to find out this by taking a graph sheet, drawing 2 circles by using compas, and by taking those values and substituting them in my code.:). that is working fine.

Actually my project is GIS based. no -ve points are used as GIS reference to a place, city or piece of land except for highest point like hills or top of multi store buildings.

I am just confused about whether it is correct or wrong. thats why i posted my code.

once again thanks for ur reply.

kirankumarvemulaa at 2007-7-10 3:03:49 >

you said you are getting answer like.

> (-12.99, -4.75) and (-7.59, 7.86).

yes. that is the correct answer.

i did a mistake while setting the _x1 value in method.

public double getX1(){

return this.p;

}

thats why i am getting values like

(5.0,-4.745812006454113)(-7.596622440583705,7.857880971971355)

in return statement i did a mistake.

public double getX1(){

return this.X1;

}

this will be the correct code. It will give the correct answer

same as you get. If i round the point values i am getting the same

result as you get.

once again thankyou very much for participating in this discussion.

kirankumarvemulaa at 2007-7-10 3:03:49 >