CODEWITHSUNDEEP
javamathgeometry
Ryosuke
Ryosuke

Reputation: 3892

What is the maximum and minimum distance between two points on different circles?

Suppose I have two circles with (x1,y1,r1) and (x2,y2,r2) as their coordinates and radius respectively. With this what is the maximum and minimum distance between them. What I have done till now: 

double centreDistance = Math.sqrt(Math.pow((x[i] - x[j]), 2) + Math.pow((x[i] - y[j]), 2));
if (centreDistance >= r[i] + r[j]) {
    double maxDistance = centreDistance + (r[i] + r[j]);
    double minDistance = centreDistance - (r[i] + r[j]);
} else if (centreDistance == 0) {
    double minDistance = Math.abs(r[i] - r[j]);
    double maxDistance = Math.abs(r[i] - r[j]);
} else {
    int rmax = Math.max(r[i], r[j]);
    int rmin = Math.min(r[i], r[j]);
    double minDistance = rmax - (centreDistance + rmin);
    double maxDistance = rmax + (centreDistance - rmin);
}

Here x,y,r are arrays having x,y coordinates of center of each circle and radius respectively.This gives me the wrong answer.

Upvotes: 1

Views: 1753

Answers (3)

kutschkem
kutschkem

Reputation: 8163

The else path is wrong.

This:

double maxDistance = rmax + (centreDistance-rmin);

should be:

double maxDistance = rmax + centreDistance + rmin;

You are also missing the case where the circles intersect. This is the case when

centreDistance < r1+r2 && centredistance + rmin >= rmax

In that case 

minDistance = 0 
maxDistance = rmax + centreDistance + rmin

centreDistance == 0 is also wrong, it should be maxDistance = r1 + r2 (because you should compare points on opposite side of the center. In any case, it is just a special case of the else path and can be omitted.

The real case are:

centreDistance>=r[i]+r[j]       (centres are so far apart the circles don't overlap, or touch in one point)
centreDistance < r1+r2 && centredistance + rmin >= rmax        (circles intersect)
centreDistance < r1+r2 && centredistance + rmin < rmax        (one circle inside the other)

Upvotes: 2

OmG
OmG

Reputation: 18838

The problem is rmax and rmin are integer. As you return the result of max and min it's rounded to an int value.

Upvotes: 0

Molbac
Molbac

Reputation: 81

in the case where the circle touch, you have to make some adjustments 

if (centreDistance >= r[i] + r[j]) {
        // the circle dont touch, min and max distance are the closest and most far apart parts of the circles
        // code is correct
        double maxDistance = centreDistance + (r[i] + r[j]);
        double minDistance = centreDistance - (r[i] + r[j]);
    } else if (centreDistance == 0) {
        // the circle are on top of each other
        // check if they have the same radius -> max min dist = 0
        // if not max and min distance = Math.abs(r[i] - r[j]);
        // code is correct
        double minDistance = Math.abs(r[i] - r[j]);
        double maxDistance = Math.abs(r[i] - r[j]);
    } else {
        // the circles touch 
        // max distance is the same as in case where they dont touch
        // and min distance is 0 because they touch
        // code has to be adjusted
        int rmax = Math.max(r[i], r[j]);
        int rmin = Math.min(r[i], r[j]);
        double minDistance = rmax - (centreDistance + rmin);
        double maxDistance = rmax + (centreDistance - rmin);
    }

Upvotes: 0

Related Questions