How to check if circles overlap

问题

I'm trying to write a program that checks if a circle contains another circle, if a certain point is inside a circle, or the one I'm having trouble with, if a circle overlaps with another circle.

import javafx.scene.shape.Circle;
public class Problem10_11 {
    public static void main(String[] args) {
        //Create circle with certain parameters.
        Circle2D c1 = new Circle2D(2, 2, 5.5);

        //Create output which will be tested by all our methods.
        System.out.println("The area for circle 1 is " +c1.getArea()+ 
                " and its perimeter is " + c1.getPerimeter());
        System.out.println("Is (3,3) contained within circle 1? " 
                + c1.contains(3, 3));
        System.out.println("Does circle 1 contain circle 2? " 
                + c1.contains(new Circle2D(4,5,10.5)));
        System.out.println("Does circle 1 overlap with circle 3? " 
                + c1.overlaps(new Circle2D(3, 5, 2.3)));
    }
}
class Circle2D {
    double x; //first parameter
    double y; //second parameter
    double radius; //third parameter

    Circle2D() {
    }
    public Circle2D(double x, double y, double radius) {
        this.x = x;
        this.y = y;
        this.radius = radius;
    }
    public void setX(double x) {
        this.x = x;  //set x
    }
    public double getX() {
        return x; //grab x
    }
    public void setY(double y) {
        this.y = y; //set y
    }
    public double getY() {
        return y; //grab y
    }
    public void setRadius(double radius) {
        this.radius = radius; //set radius
    }
    public double getRadius() {
        return radius; //grab radius
    }
    public double getArea() {
            double area = Math.PI*radius*radius; //formula for area
                return area;
    }
    public double getPerimeter() {
            double perimeter = 2*Math.PI*radius; //formula for perimeter
                return perimeter;
    }
    public boolean contains(double x, double y) {
        //Use distance formula to check if a specific point is within our circle. 
            double distance = Math.sqrt(Math.pow(this.x - x, 2) + (Math.pow(this.y - y, 2)));
            if (distance  <= radius * 2)
                return true;
            else {
                return false;
            }
    }
    public boolean contains(Circle2D circle) {
        //Use distance formula to check if a circle is contained within another circle.
        double distance = Math.sqrt(Math.pow(circle.getX() - x, 2) + (Math.pow(circle.getY() - y, 2)));
        if (distance <= (this.radius - circle.radius)) {
            return true;
        } else {
            return false;
        }
    }
    public boolean overlaps(Circle2D circle) {
        //Use distance formula to check if a circle overlaps with another circle.
            double distance = Math.sqrt(Math.pow(circle.getX() - x, 2) + (Math.pow(circle.getY() - y, 2)));



    }
}

So my overlap method is all the way at the bottom but I don't really have anything inside because I'm not sure exactly what to do. I tried this :

if (distance <= radius) return true;
        else return false;

but that didnt work. So I'm not sure what else to try. FYI, I'm trying to check if c1 overlaps with a circle with parameters (3, 5, 2.3). I appreciate any suggestions/advice.

回答1:

You can refer to Relative position of two circles.

public boolean overlaps(Circle2D circle) {
        //Use distance formula to check if a circle overlaps with another circle.
        double distance = Math.sqrt(Math.pow(circle.getX() - x, 2) + (Math.pow(circle.getY() - y, 2)));
        return distance <= (this.radius + circle.radius) and distance >= Math.abs(this.radius - circle.radius)
}

回答2:

if the distance between the centres of the circles is less than the sum of the radius of the two circles then they are overlapping.

double minDistance = Math.max(circle.getRadius(),this.radius) - Math.min(circle.getRadius(),this.radius);
    if (distance <= (this.radius + circle.getRadius()) && distance>= minDistance) return true;
            else return false;

回答3:

1.- you have to to place both circles in space, give them some cordinates
2.- you have to get the vectors from 2 circles.
3.- you have to normailze those vectors and get the correct distance in units, im gonna use pixels.
4.- finally you have to check if the distance between those 2 vectors are less that the radious of both circles, if so, then they are overlaped.
here you have a link that is better explained: https://gamedevelopment.tutsplus.com/tutorials/when-worlds-collide-simulating-circle-circle-collisions--gamedev-769, actually this is something very common we use in game development when we want to check circle collisions ( for 2D games )

来源：https://stackoverflow.com/questions/49433930/how-to-check-if-circles-overlap