Determine if tap is within circular area

Question

In my app I am currently able to work out whether the user's tap is within a rectangular area simply by checking all of the following conditions are true:

• Finger X > rectangle X
• Finger Y > rectangle Y
• Finger X < rectangle X + rectangle Width
• Finger Y < rectangle Y + rectangle Height

However, I now have to determine if the user taps within a circular area. Currently I have a circular shape on screen and have resorted to just checking it's bounding rectangle, which works but obviously isn't great.

Any help would be appreciated.

Answer 1

The distance between two points in two dimensions is defined as

 dist = sqrt((x2-x1)^2 + (y2-y1)^2)

To check if your tap point is inside a circle, take the centre of your circle as (x1,y1), and the 'tap location' as (x2,y2), and check if

sqrt((x2-x1)^2 + (y2-y1)^2) < R

With R being the radius of your circle.

Edit:

As John mentioned, from a computational point of view it is more interesting to compare vs R^2, to avoid the sqrt for every tap. So the condition becomes:

(x2-x1)^2 + (y2-y1)^2 < R^2