Circle and Rotated Rectangle Collision Detection in Objective-C This code was ported from some code at: http://www.migapro.com/circle-and-rotated-rectangle-collision-detection/ I've changed the code to assume that it is the centre of the rectangle, not the top-left corner of the rectangle that is passed in. This makes it simpler to use from Coco…

CocosUtil.h

@interface Cocosutil : NSObject

typedef struct {
    float overlapSize;
    BOOL intersects;
} ccIntersection;

+ (ccIntersection) intersectionOfCircleWithRadius:(float)radius 
                                          atPoint:(CGPoint)circlePt
                                     andRectangle:(CGRect)rect
                                     withRotation:(float)rotation;

@end

CocosUtil.m

@implementation CocosUtil

#define CC_DEGREES_TO_RADIANS(__ANGLE__) ((__ANGLE__) * 0.01745329252f) // PI / 180

// Original code is from:
//
// http://www.migapro.com/circle-and-rotated-rectangle-collision-detection/
//
+ (ccIntersection) intersectionOfCircleWithRadius:(float)radius atPoint:(CGPoint)circlePt andRectangle:(CGRect)rect withRotation:(float)rotation {
    ccIntersection result;
    
    // Rotate circle's center point back
    float unrotatedCircleX =
        cosf(CC_DEGREES_TO_RADIANS(rotation)) * (circlePt.x - rect.origin.x) -
        sinf(CC_DEGREES_TO_RADIANS(rotation)) * (circlePt.y - rect.origin.y) + rect.origin.x;
    
    float unrotatedCircleY =
        sinf(CC_DEGREES_TO_RADIANS(rotation)) * (circlePt.x - rect.origin.x) +
        cosf(CC_DEGREES_TO_RADIANS(rotation)) * (circlePt.y - rect.origin.y) + rect.origin.y;
    
    // Closest point in the rectangle to the center of circle rotated backwards(unrotated)
    float closestX, closestY;
    
    // Find the unrotated closest x point from center of unrotated circle
    if (unrotatedCircleX  < (rect.origin.x - (rect.size.width/2.0f))) {
        closestX = rect.origin.x - (rect.size.width/2.0f);
    } else if (unrotatedCircleX  > rect.origin.x + (rect.size.width+rect.size.width/2.0f)) {
        closestX = rect.origin.x + (rect.size.width/2.0f);
    } else {
        closestX = unrotatedCircleX ;
    }
    
    // Find the unrotated closest y point from center of unrotated circle
    if (unrotatedCircleY < (rect.origin.y - (rect.size.height/2.0f))) {
        closestY = rect.origin.y - (rect.size.height/2.0f);
    } else if (unrotatedCircleY > (rect.origin.y + (rect.size.height/2.0f))) {
        closestY = rect.origin.y + (rect.size.height/2.0f);
    } else {
        closestY = unrotatedCircleY;
    }
    
    // Determine collision
    
    float distance = [CocosUtil distanceFrom:CGPointMake(unrotatedCircleX , unrotatedCircleY) to:CGPointMake(closestX, closestY)];
    
    if (distance < radius) {
        result.intersects = YES; // Collision
        result.overlapSize = radius - distance;
    } else {
        result.intersects = NO;
        result.overlapSize = 0.0f;
    }
    
    return result;
}

+ (float) distanceFrom:(CGPoint)from to:(CGPoint)to {

    float a = abs(from.x - to.x);
    float b = abs(from.y - to.y);
    
    return sqrt((a * a) + (b * b));
}

@end

If the rectangle is already rotated with the angle, I think that the calculations should take that in account and use "-rotation", because leaving it to the user to input the negative angle in the method could be a bit misleading. Thanks a lot though, it's perfect.