As Alexandru points out, no circle collision detection is supported by AndEngine so far. The best way is to implement it yourself. His solution works fine (fast), but just in case you need a bit more precision, I will post another approximation:
// There is no need to use Sprites, we will use the superclass Entity
boolean collidesWith(Entity circle){
final float x1 = this.getX();
final float y1 = this.getY();
final float x2 = circle.getX();
final float y2 = circle.getY();
final float xDifference = x2 - x1;
final float yDifference = y2 - y1;
// The ideal would be to provide a radius, but as
// we assume they are perfect circles, half the
// width will be just as good
final float radius1 = this.getWidth()/2;
final float radius2 = circle.getWidth()/2;
// Note we are using inverseSqrt but not normal sqrt,
// please look below to see a fast implementation of it.
// Using normal sqrt would not need "1.0f/", is more precise
// but less efficient
final float euclideanDistance = 1.0f/inverseSqrt(
xDifference*xDifference +
yDifference*yDifference);
return euclideanDistance < (radius1+radius2);
}
/**
* Gets an aproximation of the inverse square root with float precision.
* @param x float to be square-rooted
* @return an aproximation to sqrt(x)
*/
public static float inverseSqrt(float x) {
float xhalf = 0.5f*x;
int i = Float.floatToIntBits(x);
i = 0x5f3759df - (i>>1);
x = Float.intBitsToFloat(i);
x = x*(1.5f - xhalf*x*x);
return x;
}
Note I am not the author of the fast inverseSqrt method, it works in Java (and more precisely in Android) because of its floating point representation (see IEEE 754 floating point representation and Java float to byte representation).
For further research, see: