Question

Given:

• point clickWheelCenter
• point startPoint (first touch)
• point point (actual touch)

I want to determine the angle between these three point, and I want to know, in which quadrant the last touch was found.
The calculation of the angle is working well, while the quadrant is always 1 or 2, never 3 or 4.

Where am I wrong?

CGFloat DistanceBetweenTwoPoints(CGPoint point1,CGPoint point2)
{
    CGFloat dx = point2.x - point1.x;
    CGFloat dy = point2.y - point1.y;
    return sqrt(dx*dx + dy*dy );
};

NSInteger GetQuadrant(double angle)
{
    double sinAngle = sin(angle);
    double cosAngle = cos(angle);
    double tanAngle = tan(angle);
    double cotAngle = 1.0/tanAngle;

    NSLog(@"%f %f %f %f", sinAngle, cosAngle, tanAngle, cosAngle);

    if(sinAngle > 0 && cosAngle > 0 && tanAngle > 0 && cotAngle > 0) return 1;
    if(sinAngle > 0 && cosAngle < 0 && tanAngle < 0 && cotAngle < 0) return 2;
    if(sinAngle < 0 && cosAngle < 0 && tanAngle > 0 && cotAngle > 0) return 3;
    if(sinAngle < 0 && cosAngle > 0 && tanAngle < 0 && cotAngle < 0) return 4;
    return 0;
}

double AngleBetweenThreePoints(CGPoint point1,CGPoint point2, CGPoint point3)
{
    CGPoint point_a = point1;
    CGPoint point_b = point2;
    CGPoint point_c = point3;
    CGFloat a, b, c;

    a = DistanceBetweenTwoPoints(point_b, point_c);
    b = DistanceBetweenTwoPoints(point_a, point_c);
    c = DistanceBetweenTwoPoints(point_a, point_b);
    double result = acos((b*b+c*c-a*a)/(2*b*c));

    NSLog(@"%d", GetQuadrant(result));

    return result/M_PI * 180.0;
}


-(void)touchesBegan:(NSSet *)touches withEvent:(UIEvent *)event
{
    startPoint = [[touches anyObject] locationInView:self];
}

-(void)touchesMoved:(NSSet *)touches withEvent:(UIEvent *)event
{
    CGPoint point = [[touches anyObject] locationInView:self];
    double angle = AngleBetweenThreePoints(self.clickWheelCenter, startPoint, point);
    NSLog(@"%f", angle);    
}

Answer 1

This can all be done much easier.

With {x1,y1} = first point – center point, and {x2,y2} = third point – center point, the signed angle (-pi,+pi) is given by:

atan2(x2*y1 - x1*y2,x1*x2 + y1*y2)

Depending on your definition of the sign of the angle you may or may not want to add a minus in front.

You can easily derive the quadrant from sign and absolute size.

1. size <= pi/2, sign +
2. size > pi/2, sign +
3. size > pi/2, sign –
4. size <= pi/2, sign –