Python: Checking If Coordinates Are Within Circle

Question

Possible Duplicate:
How can I make Turtle recognize a circle?

enter image description here I have a function that draws a few circles and I am going to place dots inside them. Depending if the dot falls within the circle, depends on wether the colour will change or not.

The biggest issue I am finding is how to check whether or not the dot is within the circle. Does anyone have any idea how to calculate coordinates within a circle or is their a method which can check coordinates against the circle?

is this a homework assignment? it looks very similar to this question: http://stackoverflow.com/questions/12049536/how-can-i-make-turtle-recognize-a-circle — zenpoy, Sep 04 '12 at 12:33

gefei · Answer 1 · 2012-09-04T11:15:45.173

15

For a circle with center (x,y) and radius r, a point (x1, y1) is within the circle if

(x1-x)² + (y1-y)² <= r²

edited Sep 04 '12 at 11:15

answered Sep 04 '12 at 11:03

gefei

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+1, this formulation is actually more elegant than mine and faster to compute since you can cache r². – Fred Foo Sep 04 '12 at 13:31

score 10 · Accepted Answer · answered Sep 04 '12 at 11:03

10

Compute (Euclidean) distance to the circle's center,
```
sqrt((x - center_x) ** 2 + (y - center_y) ** 2)
```
Check whether the result is less than the radius.

answered Sep 04 '12 at 11:03

Fred Foo

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We tried this but it was too low on the Y access for some reason. I have attached a picture. – MichaelH Sep 04 '12 at 11:25
@MichaelH: this is *the* method. You must have had a bug in your code, maybe a round-off error. – Fred Foo Sep 04 '12 at 11:32

score 1 · Answer 3 · answered Sep 04 '12 at 11:02

1

To check if a coordinate lies on a circle you can use the equation of the circle

a² + b² = r²

So to check if the point is inside the circle:

a² + b² <= r²

answered Sep 04 '12 at 11:02

Minion91

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Python: Checking If Coordinates Are Within Circle

3 Answers3