SpriteKit - Push sprite away from touch location - ios

Question

I am building a game and want one of my sprites to move directly away from the place the player taps.
[+] (tap location)
[+] (player)
In the example above, the player would move to the left and downwards.
Can anyone assist me in the physics?
I realise I’m to use trigonometry to calculate the angle and therefore the vector (for applyImpulse:) but the calculations I have don’t work for each quadrant surrounding the player.
Here is my code (in touchesBegan:)
UITouch *touch = [touches.allObjects objectAtIndex:0];
CGPoint touchPosition = [touch locationInNode:self];
CGPoint playerPosition = self.playerBubble.position;
double oppositeLength = (touchPosition.y - playerPosition.y);
double adjacentLength = (touchPosition.x - playerPosition.x);
double angle = atan(oppositeLength / adjacentLength);
The vector is computed as:
CGFloat playerMass = 0.0000013;
CGVector vector = CGVectorMake(playerMass * cosl(angle), playerMass * sinl(angle));
Here are the vector outputs for each quadrant surrounding the player:
+, +:
O: 133.000000, A: 42.500000, Angle: 72.278778, Theta: 1.261503
{3.9570166773706921e-07, 1.2383134543301224e-06}
-, +:
O: 95.247955, A: -79.580551, Angle: -50.120930, Theta: -0.874775
{8.335201515172361e-07, -9.9761925504652419e-07}
+, -:
O: -145.927795, A: 52.148361, Angle: -70.335281, Theta: -1.227582
{4.3747011829674742e-07, -1.2241813250586403e-06}
-, -:
O: -138.968933, A: -92.015755, Angle: 56.490189, Theta: 0.985940
{7.1770369806877642e-07, 1.0839286982100348e-06}
EDIT:
Here is my updated answer which gives the right vectors (it’s called on a SKSpriteNode instance):
- (void)moveWithTouchPosition:(CGPoint)touchPosition
{
double heightLength = (self.position.y - touchPosition.y);
double widthLength = (self.position.x - touchPosition.x);
double angle = 0.0f;
if (touchPosition.y > self.position.y && touchPosition.x > self.position.x) {
//
// +, +
//
angle = M_PI + atan(heightLength / widthLength);
} else if (touchPosition.y > self.position.y && touchPosition.x < self.position.x) {
//
// -, +
//
angle = M_PI + M_PI_2 + atan(widthLength / heightLength);
} else if (touchPosition.y < self.position.y && touchPosition.x > self.position.x) {
//
// +, -
//
angle = M_PI_2 + atan(widthLength / heightLength);
} else if (touchPosition.y < self.position.y && touchPosition.x < self.position.x) {
//
// -, -
//
angle = atan(heightLength / widthLength);
}
CGVector vector = CGVectorMake(self.physicsBody.mass * cosl(angle), self.physicsBody.mass * sinl(angle));
[self.physicsBody applyImpulse:vector];
}

Answer 1

To simplify your code, you could use atan2 instead of atan. Atan2 does the quadrants for you.
Another option is to translate and multiply vectors instead of using trigonometry at all, which might look something like:
CGVector vector = CGVectorMake(
(playerPosition.x - touchPosition.x) * playerMass + touchPosition.x,
(playerPosition.y - touchPosition.y) * playerMass + touchPosition.y
);

Answer 2

Thanks to #Bemmu it appears that all I really needed to do was to use the atan2(y, x) function and parse in the Opp and Adj lengths of the triangle which were the differences between the y and x values respectively.
E.g:
double heightLength = (self.position.y - touchPosition.y);
double widthLength = (self.position.x - touchPosition.x);
double angle = atan2(heightLength, widthLength);
CGFloat acceleration = 100.0f;
CGVector vector = CGVectorMake(self.physicsBody.mass * (cosl(angle) * acceleration), self.physicsBody.mass * (sinl(angle) * acceleration));
[self.physicsBody applyImpulse:vector];