Swift: Is there an easy way to draw shapes and detect whether they intersect?

Question

Is there an easy way to draw shapes in Swift (preferrably with Sprite-Kit) and then detect if and where they intersect? Like here's an intersecting shape:

Answer 1

If this consists of a series of line segments, one can adapt Martin R’s answer to UIBezierPath intersect to not only detect intersections, but to also identify where the intersections are:

func intersectionBetweenSegments(_ p0: CGPoint, _ p1: CGPoint, _ p2: CGPoint, _ p3: CGPoint) -> CGPoint? {
    var denominator = (p3.y - p2.y) * (p1.x - p0.x) - (p3.x - p2.x) * (p1.y - p0.y)
    var ua = (p3.x - p2.x) * (p0.y - p2.y) - (p3.y - p2.y) * (p0.x - p2.x)
    var ub = (p1.x - p0.x) * (p0.y - p2.y) - (p1.y - p0.y) * (p0.x - p2.x)
    if (denominator < 0) {
        ua = -ua; ub = -ub; denominator = -denominator
    }
    
    guard ua >= 0 && ua <= denominator && ub >= 0 && ub <= denominator && denominator != 0 else {
        return nil
    }

    return CGPoint(x: p0.x + ua / denominator * (p1.x - p0.x), y: p0.y + ua / denominator * (p1.y - p0.y))
}

Thus, if you have an array of CGPoint values and you want to identify all of the intersections, you could do something like:

let n = points.count - 1

for i in 1 ..< n {
    for j in 0 ..< i-1 {
        if let intersection = intersectionBetweenSegments(points[i], points[i+1], points[j], points[j+1]) {
            // do whatever you want with `intersection`
        }
    }
}

For example, you can add a dot to the screen where the segments intersect:

If, however, your curve consists of cubic bezier curves, it is more complicated. You might consider, though, Checking if two cubic Bézier curves intersect.