Question

Hi all you smart people out there!
I want to create a touch interface to an iOS app, that allows the user to drag an object on the screen around.
However, this object should be restricted to move along the perimeter of a circle, so that if the user is trying to drag the object outside that path, it would stick to the nearest point of that circle.
I have done some iPhone programming, but my math is poor. Please help!

Answer 1

All you have to do is set the frame of the view to follow the equation of a circle (of the form: (x-a)^2 + (y-b)^2 = r^2). Once you detect the touch point, you can restrict the view’s frame according to the x or the y coordinate of the touch point (both ways are the same).

#define circleRadius 60.0 // r in the above eqtn
#define circlesCenter_X 160.0 // a in the above eqtn
#define circlesCenter_Y 200.0 // b in the above eqtn
#define circleCenter_y(x) sqrtf(circleRadius*circleRadius - (x-circlesCenter_X)*(x-circlesCenter_X))

-(void)touchesMoved:(NSSet *)touches withEvent:(UIEvent *)event{
    UITouch *touch = [[event touchesForView:firstPieceView] anyObject];
    CGPoint previousLocation = [touch previousLocationInView:self.view];
    CGPoint location = [touch locationInView:self.view];
    CGFloat delta_x = previousLocation.x - location.x; // constrained by x in this eg.
    CGFloat newX = firstPieceView.center.x-delta_x;
    // do limit the view's x-coordinate for possible solutions
    if(newX<circlesCenter_X - circleRadius)
        newX = circlesCenter_X - circleRadius;
    if(newX>circlesCenter_X + circleRadius)
        newX = circlesCenter_X + circleRadius;
    firstPieceView.center = CGPointMake(newX, circleCenter_y(newX)*(location.y>=circlesCenter_Y?1:-1) + circlesCenter_Y);
}

EDIT- Better solution:

#define circleRadius 60.0 // r in the above eqtn
#define circlesCenter_X 160.0 // a in the above eqtn
#define circlesCenter_Y 200.0 // b in the above eqtn
#define slope(x,y) (y-circlesCenter_Y)/(x-circlesCenter_X)
#define pointOnCircle_X(m) circleRadius/(sqrtf(m*m + 1))

-(void)touchesMoved:(NSSet *)touches withEvent:(UIEvent *)event{
    UITouch *touch = [[event touchesForView:self.view] anyObject];
    CGPoint location = [touch locationInView:self.view];
    CGFloat slope;
    CGPoint pointOnCircle;
    if(location.x==circlesCenter_X){// case for infinite slope
        pointOnCircle.x = circlesCenter_X;
        if(location.x<circlesCenter_X){
            pointOnCircle.y = circlesCenter_Y - circleRadius;
        }else{
            pointOnCircle.y = circlesCenter_Y + circleRadius;
        }
    }else{
        slope = slope(location.x,location.y);
        if(location.x<circlesCenter_X){
            pointOnCircle.x = circlesCenter_X - pointOnCircle_X(slope);
        }else{
            pointOnCircle.x = circlesCenter_X + pointOnCircle_X(slope);
        }
        pointOnCircle.y = slope * (pointOnCircle.x - circlesCenter_X) + circlesCenter_Y;
    }
    firstPieceView.center = pointOnCircle;
}

This can be applied similarly for Android, Blackberry, etc too!