Choosing a random point within a circular image in a UIImageView - ios

Question

I have an app with a color wheel and I'm trying to pick a random color within the color wheel. However, I'm having problems verifying that the random point falls within the color wheel.
Here's the code as it currently is:
CGPoint randomPoint = CGPointMake(arc4random() % (int)colorWheel.bounds.size.width, arc4random() % (int)colorWheel.bounds.size.height);
UIColor *randomColor = [self colorOfPoint:randomPoint];
CGPoint pointInView = [colorWheel convertPoint:randomPoint fromView:colorWheel.window];
if (CGRectContainsPoint(colorWheel.bounds, pointInView)) {
NSLog(#"%#", randomColor);
}
else {
NSLog(#"out of bounds");
}
A couple of other methods of verifying the point that I've tried with no luck:
if (CGRectContainsPoint(colorWheel.frame, randomPoint)) {
NSLog(#"%#", randomColor);
}
if ([colorWheel pointInside:[self.view convertPoint:randomPoint toView: colorWheel] withEvent: nil]) {
NSLog(#"%#", randomColor);
}
Sometimes it'll output "out of bounds", and sometimes it'll just output that the color is white (the background around the color wheel is currently white but there's no white in the color wheel image).
The color wheel image is a circle, so I'm not sure if that's throwing off the test, although it seems like white pops up way too frequently for it to just be a transparent square outline around the image giving a white color.

Answer 1

If you want to generate a random point in a circle, you would do better to pick your point in polar coordinates and then convert it to Cartesian.
The polar coordinate space uses two dimesions, radius and angle. Radius is just the distance from the center, and angle usually starts at "due east" for 0, and goes around counter-clockwise up to 2π (that's in radians, 360˚ of course in degrees).
Presumably your wheel is divided into simple wedges, so the radius actually doesn't matter; you just need to pick a random angle.
uint32_t angle = arc4random_uniform(360);
// Radius will just be halfway from the center to the edge.
// This assumes the circle is exactly enclosed, i.e., diameter == width
CGFloat radius = colorWheel.bounds.size.width / 4;
This function will give you a Cartesian point from your polar coordinates. Wikipedia explains the simple math if you're interested.
/** Convert the polar point (radius, theta) to a Cartesian (x,y). */
CGPoint poltocar(CGFloat radius, CGFloat theta)
{
return (CGPoint){radius * cos(theta), radius * sin(theta)};
}
The function uses radians for theta, because sin() and cos() do, so change the angle to radians, and then you can convert:
CGFloat theta = (angle * M_PI) / 180.0
CGPoint randomPoint = poltocar(radius, theta);
One last step: this circle has its origin at the same place as the view, that is, in the corner, so you need to translate the point to use the center as the origin.
CGPoint addPoints(CGPoint lhs, CGPoint rhs)
{
return (CGPoint){lhs.x + rhs.x, lhs.y, rhs.y};
}
CGPoint offset = (CGPoint){colorWheel.bounds.size.width / 2,
colorWheel.bounds.size.height / 2};
randomPoint = addPoints(randomPoint, offset);
And your new randomPoint will always be within the circle.

Answer 2

I agree with #JoshCaswell's approach, but FYI, the reason the OP code is not working is that the test for inside a circle is incorrect.
The coordinate conversion is unnecessary, and the test against a rectangle is sure to be wrong. Instead, work out how far the random point is from the center and compare that with the radius.
CGFloat centerX = colorWheel.bounds.size.width / 2.0;
CGFloat centerY = colorWheel.bounds.size.height / 2.0;
CGFloat distanceX = centerX - randomPoint.x;
CGFloat distanceY = centerY - randomPoint.y;
CGFloat distance = distanceX*distanceX + distanceY*distanceY;
CGFloat radius = colorWheel.bounds.size.width / 2.0; // just a guess
CGFloat r2 = radius*radius;
// this compares the square of the distance with r^2, to save a sqrt operation
BOOL isInCircle = distance < r2;