https://stackoverflow.com/a/58596637/1271826

QuadBezier.swift

class ViewController: UIViewController {

    var bezier: QuadBezier!

    let pathLayer: CAShapeLayer = {
        let layer = CAShapeLayer()
        layer.lineWidth = 5
        layer.strokeColor = UIColor.blue.cgColor
        layer.fillColor = UIColor.clear.cgColor
        return layer
    }()

    var animation: CAKeyframeAnimation!

    var shape: CircleView = {
        let shape = CircleView()
        shape.backgroundColor = .red
        shape.frame = CGRect(origin: .zero, size: CGSize(width: 50, height: 50))
        return shape
    }()


    override func viewDidLoad() {
        super.viewDidLoad()

        view.layer.addSublayer(pathLayer)
        view.addSubview(shape)
    }

    override func viewDidLayoutSubviews() {
        super.viewDidLayoutSubviews()

        bezier = buildCurvedPath()
        pathLayer.path = bezier.path.cgPath
        shape.center = bezier.point(at: 0.5)
    }

    func buildCurvedPath() -> QuadBezier {
        let bounds = view.bounds
        let point1 = CGPoint(x: bounds.minX, y: bounds.midY)
        let point2 = CGPoint(x: bounds.maxX, y: bounds.midY)
        let controlPoint = CGPoint(x: bounds.midX, y: bounds.midY + 100)

        let path = QuadBezier(point1: point1, point2: point2, controlPoint: controlPoint)
        return path
    }

    override func touchesBegan(_ touches: Set<UITouch>, with event: UIEvent?) {
        guard let touch = touches.first else { return }
        updatePosition(for: touch)
    }

    override func touchesMoved(_ touches: Set<UITouch>, with event: UIEvent?) {
        guard let touch = touches.first else { return }
        if let touch = event?.predictedTouches(for: touch)?.last {
            updatePosition(for: touch)
        } else {
            updatePosition(for: touch)
        }
    }

    override func touchesEnded(_ touches: Set<UITouch>, with event: UIEvent?) {
        guard let touch = touches.first else { return }
        updatePosition(for: touch)
    }

    func updatePosition(for touch: UITouch) {
        let location = touch.location(in: view)
        let t = (location.x - view.bounds.minX) / view.bounds.width
        shape.center = bezier.point(at: t)
    }
}

struct QuadBezier {
    var point1: CGPoint
    var point2: CGPoint
    var controlPoint: CGPoint

    var path: UIBezierPath {
        let path = UIBezierPath()
        path.move(to: point1)
        path.addQuadCurve(to: point2, controlPoint: controlPoint)
        return path
    }

    func point(at t: CGFloat) -> CGPoint {
        let t1 = 1 - t
        return CGPoint(
            x: t1 * t1 * point1.x + 2 * t * t1 * controlPoint.x + t * t * point2.x,
            y: t1 * t1 * point1.y + 2 * t * t1 * controlPoint.y + t * t * point2.y
        )
    }
}

@IBDesignable
public class CircleView: UIView {
    override public func layoutSubviews() {
        super.layoutSubviews()

        layer.cornerRadius = min(bounds.width, bounds.height) / 2
    }
}