CODEWITHSUNDEEP
mathdistancegeometry
Alex
Alex

Reputation: 4934

Finding the distance between two circles

I'm trying to figure out how to get the distance from two circles relative to the corners of their square container boxes. I need some help with the maths here.

Finding distance between two circles

How can I work out the number of pixels for the line marked with a question mark?

Appreciate the help as always.

Upvotes: 10

Views: 38199

Answers (4)

hiddensunset4
hiddensunset4

Reputation: 6029

tldr: Calculate the distance between each circles center point, then subtract the radius' of each circle from that.

For the purpose of a demonstration, we will assume the following:

  • The 200px diameter (r1 = 100) circle is at the (x, y) coordinates of (0, 0), and
  • the 100px diameter (r2 = 50) circle is at (x, y) coordinates of (150, -150).

Given that the distance between their centers is: Distance

To find the distance between their boundaries, we subtract the radius of each circle from the distance between their centers.

This leaves us with the equation:

sqrt((x2 − x1)^2 + (y2 − y1)^2) − (r2 + r1)

Inserting your values into the above gives:

sqrt((150 − 0)^2 + (-150 − 0)^2) − (100 + 50) = 62.132034356px

Upvotes: 15

Jason S
Jason S

Reputation: 189646

The algebraically simplified version of Daniel's answer is 

  (r1 + r2) * (sqrt(2) - 1) 
= (s1 + s2) * (sqrt(2) - 1)/2

where r1,r2 are the two radii and s1,s2 are the two square sides. This is easily seen by looking at each square individually and noticing that the distance d1 from the circle/square center to the square corner is sqrt(2) * r, and the desired distance within that square is d1 - the circle radius r.

Upvotes: 2

Sufendy
Sufendy

Reputation: 1242

Do you have the middle point of each circles? If you do, first calculate the distance from the centre of circles.

distance² = center1² + center2²

Then, you will need to minus the radius of both circles. In your case, it will be 150 (100 + 50)

Upvotes: 3

user541686
user541686

Reputation: 210427

Let's see... each radius is half each side length, and subtracting the sum of the radii from the distance between the center gives you the amount that's left.

Hope that helps?

Upvotes: 2

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