# Intersection between a circle and an aabb?

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Doublefris    316

Hey, for a little physics project I want to find the collision normal and penetration for a circle and an aabb. How would I go about doing this?

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WarAmp    750

Step 1) Find the closest point on the AABB to the center (C) of the circle: This will be your potential collision location. (P)

Step 2) If the distance between C and P (D = magnitude(C - P)) is less than the radius of the circle (R), then you have a collision!

Step 3) The penetration depth is then (R - D)

Step 4) The normal is the normalized (C - P) vector.

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Doublefris    316

It works! However it leaves a tiny bit of overlap.

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DonDickieD    2751

This only works if the sphere center is outside of the box (which should be the majority of cases though). If the sphere center is inside the box you need to compute the distance to each side of the box and keep track of the closest one. The defines the axis of minimum penetration and you can construct the contact point from there.

You also need to be careful with the location of your collision point. I would move the contact point out onto the surface of the sphere for consistent friction in a rigid body simulation.

Edited by Dirk Gregorius

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Doublefris    316

For the record, using this method( The one WarAmp gave) I still get a little bit of overlap. here is my code :

            Vector2 p;
p.X = Utils.Clamp(c.myCenter.X, b.Min.X, b.Max.X);
p.Y = Utils.Clamp(c.myCenter.Y, b.Max.Y, b.Min.Y);

Vector2 toClosest = c.myCenter - p;

float d = toClosest.LengthFast;

Depth = c.myRadius - d;
myNormal = toClosest / d;

The triangle in this picture is encapsulated by a bounding circle, and this is how far it still impregnates.

Edited by Doublefris

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DonDickieD    2751

p.X = Utils.Clamp(c.myCenter.X, b.Min.X, b.Max.X);
p.Y = Utils.Clamp(c.myCenter.Y, b.Max.Y, b.Min.Y); <=== Check this line

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Doublefris    316

Ah of course! Silly error. Thanks!

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