Finding normal vector to iOS device

Question

I would like to use CMAttitude to know the vector normal to the glass of the iPad/iPhone\'s screen (relative to the ground). As such, I would get vectors like the following:

Answer 1

Thanks to Kay for the starting point on the solution. Here is my implementation for anyone that needs it. I made a couple of small tweeks to Kay's advice for my situation. As a heads up, I'm using a landscape only presentation. I have code that updates a variable _isLandscapeLeft to make the necessary adjustment to the direction of the vector.

Quaternion.h

    @interface Quaternion : NSObject{
    //double w;
    //double x;
    //double y;
    //double z;
}

@property(readwrite, assign)double w;
@property(readwrite, assign)double x;
@property(readwrite, assign)double y;
@property(readwrite, assign)double z;

- (id) initWithValues:(double)w2 x:(double)x2 y:(double)y2 z:(double)z2;
- (Quaternion*) multiplyWithRight:(Quaternion*)q;
@end

Quaternion.m

#import "Quaternion.h"

@implementation Quaternion


- (Quaternion*) multiplyWithRight:(Quaternion*)q {
    double newW = _w*q.w - _x*q.x - _y*q.y - _z*q.z;
    double newX = _w*q.x + _x*q.w + _y*q.z - _z*q.y;
    double newY = _w*q.y + _y*q.w + _z*q.x - _x*q.z;
    double newZ = _w*q.z + _z*q.w + _x*q.y - _y*q.x;
    _w = newW;
    _x = newX;
    _y = newY;
    _z = newZ;
    // one multiplication won't denormalise but when multipling again and again
    // we should assure that the result is normalised
    return self;
}

- (id) initWithValues:(double)w2 x:(double)x2 y:(double)y2 z:(double)z2 {
    if ((self = [super init])) {
        _x = x2; _y = y2; _z = z2; _w = w2;
    }
    return self;
}


@end

And my game class that uses the quaternion for shooting:

-(void)fireWeapon{
    ProjectileBaseClass *bullet = [[ProjectileBaseClass alloc] init];
    bullet.position = SCNVector3Make(0, 1, 0);
    [self.rootNode addChildNode:bullet];

    Quaternion *e = [[Quaternion alloc] initWithValues:0 x:0 y:0 z:1];
    CMQuaternion cm = _currentAttitude.quaternion;
    Quaternion *quat = [[Quaternion alloc] initWithValues:cm.w x:cm.x y:cm.y z:cm.z];
    Quaternion *quatConjugate = [[Quaternion alloc] initWithValues:cm.w x:-cm.x y:-cm.y z:-cm.z];
    quat = [quat multiplyWithRight:e];
    quat = [quat multiplyWithRight:quatConjugate];
    SCNVector3 directionToShoot;
    if (_isLandscapeLeft) {
        directionToShoot = SCNVector3Make(quat.y, -quat.x, -quat.z);

    }else{
        directionToShoot = SCNVector3Make(-quat.y, quat.x, -quat.z);

    }

    SCNAction *shootBullet = [SCNAction moveBy:directionToShoot duration:.1];
    [bullet runAction:[SCNAction repeatActionForever:shootBullet]];
}