How to calculate intersection points between two circles in Matlab?

This page presents the circlesIntersectionPoint() Matlab function.

circlesIntersectionPoints.m

This function calculates the coordinates of the interection points between two circles. The function returns the intersection points I1 and I2 after checking if the circles intersect:

 [I1, I2, status] = circlesIntersectionPoints(P1, r1, P2, r2)

• status = -1: circles are too far apart and do not intersect;
• status = -2: one circle is inside the other and do not intersect;
• status = -3: circles are merged , there are an infinite number of points
• status = 1: single intersection point
• status = 2: two intersection points

Source code

The function implement the calculation presented on this page: How to calculate the intersection points of two circles?. here is the source code of the function:

function [I1, I2, status] = circlesIntersectionPoints(P1, r1, P2, r2)

I1=0;
I2=0;

%% Distance between centers
d = sqrt( (P2(1)-P1(1))*(P2(1)-P1(1)) + (P2(2)-P1(2))*(P2(2)-P1(2)) );

%% Check cases
if (d>r1+r2)
    % Circles are too far apart and do not intersect;
    status = -1;
    return
end

if (d<abs(r1-r2))
    % One circle is inside the other and do not intersect;
    status = -2;
    return
end

if (d==0 && r1==r2)
    % Circles are merged 
    status = -3;
    return
end

if (d==r1+r2)
    % Single intersection point;
    status = 1;
end

if (d<r1+r2)
    % Two intersection points.
    status = 1;
end

%% a and b
a = (r1*r1 - r2*r2 + d*d) / (2*d);
b = (r2*r2 - r1*r1 + d*d) / (2*d);

%% h
h=sqrt(r1*r1 - a*a);

%% P5
P5 = [ P1(1) + (a/d)*(P2(1)-P1(1)) , P1(2) + (a/d)*(P2(2)-P1(2)) ];

%% Intersection points
I1 = [ P5(1) - h*(P2(2)-P1(2))/d ; P5(2) + h*(P2(1)-P1(1))/d];
I2 = [ P5(1) + h*(P2(2)-P1(2))/d ; P5(2) - h*(P2(1)-P1(1))/d];
end

Usage example

Here is a simple example that calculate to intersection point between two circles

• C1 at center (3,4) and radius of 3.4
• C2 at center (-1,2) and radius of 2.6

%% Circle to circle intersection
%% More details at https://lucidar.me/en/mathematics/how-to-calculate-the-intersection-points-of-two-circles
close all;
clear all;
clc;

%% Parameters of the circles
P1=[3;4]; r1=3.4;
P2=[-1;2]; r2=2.6;

%% Draw circles
drawCircle = @(C,R,color) plot ( C(1) + R*cos([0:0.01:2*pi]) , C(2) + R*sin([0:0.01:2*pi]), color );
figure;
hold on;
grid on;
axis square equal;
drawCircle(P1, r1, 'r');
drawCircle(P2, r2, 'g');

%% Intersection points
[I1, I2] = circlesIntersectionPoints(P1, r1, P2, r2);

plot (I1(1), I1(2), 'o');
plot (I2(1), I2(2), 'o');

The above code displays the following figure:

Help

Here is the function's help:

>> help circlesIntersectionPoints
  circlesIntersectionPoints  Compute the intersection points of two circle

    [I1, I2, status] = circlesIntersectionPoints(P1, r1, P2, r2)

 Input parameters

    P1 is the center of circle 1
    r1 is the radius of circle 1
    P2 is the center of circle 2
    r2 is the radius of circle 1

 Output parameters

    I1 and I2 are the coordinates of intersection points
    status is the status of the intersection:
        * -1 : Circles are too far apart and do not intersect;
        * -2 : One circle is inside the other and do not intersect;
        * -3 : Circles are merged , there are an infinite number of points
        * 1  : Single intersection point
        * 2  : two intersection points

 Usage example:

    [i1, i2, s] = circlesIntersectionPoints([3,4], 3.4, [-1,2], 2.6)

Download

• circlesIntersectionPoints.m
• main.m (code example presented in the section Usage example)

  See also

• Load MNIST database in Matlab
• Matlab optimization, example of function optimization
• The right way to make animations with Matlab

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