Draggable UIButton Snap To a Circle Path

this one helps. This is a bit of a hack, but if you're only using the snap option on this part of your project you could just comment out the unwanted functionality in your jQuery-ui file.
search for these three lines in your jQuery-ui file:

if(bs) ui.position.top = inst._convertPositionTo("relative", { top: b - inst.helperProportions.height, left: 0 }).top - inst.margins.top;
if(ls) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: l }).left - inst.margins.left;
if(rs) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: r - inst.helperProportions.width }).left - inst.margins.left;

//if(bs) ui.position.top = inst._convertPositionTo("relative", { top: b - inst.helperProportions.height, left: 0 }).top - inst.margins.top;
//if(ls) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: l }).left - inst.margins.left;
//if(rs) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: r - inst.helperProportions.width }).left - inst.margins.left;

if(o.snapMode != 'inner') {
                var ts = Math.abs(t - y2) <= d;
                var bs = Math.abs(b - y1) <= d;
                var ls = Math.abs(l - x2) <= d;
                var rs = Math.abs(r - x1) <= d;
                if(ts) ui.position.top = inst._convertPositionTo("relative", { top: t - inst.helperProportions.height, left: 0 }).top - inst.margins.top;
                if(bs) ui.position.top = inst._convertPositionTo("relative", { top: b, left: 0 }).top - inst.margins.top;
                if(ls) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: l - inst.helperProportions.width }).left - inst.margins.left;
                if(rs) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: r }).left - inst.margins.left;
            }

            var first = (ts || bs || ls || rs);

            if(o.snapMode != 'outer') {
                var ts = Math.abs(t - y1) <= d;
                var bs = Math.abs(b - y2) <= d;
                var ls = Math.abs(l - x1) <= d;
                var rs = Math.abs(r - x2) <= d;
                if(ts) ui.position.top = inst._convertPositionTo("relative", { top: t, left: 0 }).top - inst.margins.top;
                if(bs) ui.position.top = inst._convertPositionTo("relative", { top: b - inst.helperProportions.height, left: 0 }).top - inst.margins.top;
                if(ls) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: l }).left - inst.margins.left;
                if(rs) ui.position.left = inst._convertPositionTo("relative", { top: 0, left: r - inst.helperProportions.width }).left - inst.margins.left;
            }

if (o.snapMode != 'inner' && o.snapMode != 'innerTop' && o.snapMode != 'innerBottom' && o.snapMode != 'innerLeft' && o.snapMode != 'innerRight' && o.snapMode != 'outerTop' && o.snapMode != 'outerBottom' && o.snapMode != 'outerLeft' && o.snapMode != 'outerRight') {
    var ts = Math.abs(t - y2) <= d;
    var bs = Math.abs(b - y1) <= d;
    var ls = Math.abs(l - x2) <= d;
    var rs = Math.abs(r - x1) <= d;
    if (ts) ui.position.top = inst._convertPositionTo("relative", {
        top: t - inst.helperProportions.height,
        left: 0
    }).top - inst.margins.top;
    if (bs) ui.position.top = inst._convertPositionTo("relative", {
        top: b,
        left: 0
    }).top - inst.margins.top;
    if (ls) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: l - inst.helperProportions.width
    }).left - inst.margins.left;
    if (rs) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: r
    }).left - inst.margins.left;
}

var first = (ts || bs || ls || rs);

if (o.snapMode != 'outer' && o.snapMode != 'innerTop' && o.snapMode != 'innerBottom' && o.snapMode != 'innerLeft' && o.snapMode != 'innerRight' && o.snapMode != 'outerTop' && o.snapMode != 'outerBottom' && o.snapMode != 'outerLeft' && o.snapMode != 'outerRight') {
    var ts = Math.abs(t - y1) <= d;
    var bs = Math.abs(b - y2) <= d;
    var ls = Math.abs(l - x1) <= d;
    var rs = Math.abs(r - x2) <= d;
    if (ts) ui.position.top = inst._convertPositionTo("relative", {
        top: t,
        left: 0
    }).top - inst.margins.top;
    if (bs) ui.position.top = inst._convertPositionTo("relative", {
        top: b - inst.helperProportions.height,
        left: 0
    }).top - inst.margins.top;
    if (ls) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: l
    }).left - inst.margins.left;
    if (rs) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: r - inst.helperProportions.width
    }).left - inst.margins.left;
}

if (o.snapMode == 'innerTop') {
    var ts = Math.abs(t - y1) <= d;
    if (ts) ui.position.top = inst._convertPositionTo("relative", {
        top: t,
        left: 0
    }).top - inst.margins.top;
}

if (o.snapMode == 'innerBottom') {
    var bs = Math.abs(b - y2) <= d;
    if (bs) ui.position.top = inst._convertPositionTo("relative", {
        top: b - inst.helperProportions.height,
        left: 0
    }).top - inst.margins.top;
}

if (o.snapMode == 'innerLeft') {
    var ls = Math.abs(l - x1) <= d;
    if (ls) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: l
    }).left - inst.margins.left;
}

if (o.snapMode == 'innerRight') {
    var rs = Math.abs(r - x2) <= d;
    if (rs) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: r - inst.helperProportions.width
    }).left - inst.margins.left;
}


if (o.snapMode == 'outerTop') {
    var ts = Math.abs(t - y2) <= d;
    if (ts) ui.position.top = inst._convertPositionTo("relative", {
        top: t - inst.helperProportions.height,
        left: 0
    }).top - inst.margins.top;
}

if (o.snapMode == 'outerBottom') {
    var bs = Math.abs(b - y1) <= d;
    if (bs) ui.position.top = inst._convertPositionTo("relative", {
        top: b,
        left: 0
    }).top - inst.margins.top;
}

if (o.snapMode == 'outerLeft') {
    var ls = Math.abs(l - x2) <= d;
    if (ls) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: l - inst.helperProportions.width
    }).left - inst.margins.left;
}

if (o.snapMode == 'outerRight') {
    var rs = Math.abs(r - x1) <= d;
    if (rs) ui.position.left = inst._convertPositionTo("relative", {
        top: 0,
        left: r
    }).left - inst.margins.left;
}

I wish this helpful for you What you need is not an actual dragging, but a simulation of that, because of the fact that you want to move the object with ease to some location, and dragging is actually moving specific object along with the mouse cursor.
So what you can do is not that complex - check when the mouse clicks on your object and save mouse location. Add listener for mouse move. When the mouse moves, check if it's still pressed (add events for MOUSE_DOWN, MOUSE_UP).IF the mouse is down, on every update check it's location. If the location is more close to your next point - move the object with some tween. If the mouse is released, you can stop tracking if it moves or not.

hope this fix your issue I got helped by Jquery UI since it was a bug and this feature was never asked by any other person before... so this is an alternative to make it work :)
By using the on mousedown event.

$(".block").draggable({
    snap: ".guide",
    snapTolerance: 10,
    stop: function( event, ui) {
        $(".h-line").css("display", "none");
    }
}).on( "mousedown", function() {
    $(".h-line").css("display", "block");
});

I wish this help you Interesting question. I created a fiddle for you which shows the functionality you want: https://jsfiddle.net/4ac7o8r6/18/
I used the draggable plugin with a constraint function. Normally this function returns a constraint box or a boolean which decides wether something is dragged or not. I always return false and move the circle myself:

var canvas = SVG('container')

var path = canvas.path('M200,300 Q400,50 600,300 T1000,300').stroke('black').x(10).fill('none')
var length = path.length()

var circle = canvas.circle(20).draggable(function(x, y) {

  var p = getPointAtX(x)

  circle.center(p.x, p.y)

  return false

})

var start = path.node.getPointAtLength(0)
circle.center(start.x, start.y)

var precision = 1/length

function getPointAtX(x) {

  var p, pos = 0.5, interval = pos/2

    while(p = path.node.getPointAtLength(pos*length)) {

    if(p.x > x) {
        pos -= interval
    } else {
      pos += interval
    }

    interval /= 2

    // should be one pixel
    if(interval < precision) break
  }

  return p
}

wish of those help Basic Approach
You could do it like this (for the purpose of demonstration, I would do the button programmatically, using a playground):

let buttonWidth = 100.0

let button = UIButton(frame: CGRect(x: 0, y: 0, width: buttonWidth, height: buttonWidth))
button.backgroundColor = .white
button.layer.cornerRadius = button.frame.width / 2

let circlePath = UIBezierPath(arcCenter: CGPoint(x: buttonWidth / 2,y: buttonWidth / 2), radius: 40.0, startAngle: 0, endAngle: CGFloat.pi * 2, clockwise: true)

let circleLayer = CAShapeLayer()
circleLayer.path = circlePath.cgPath
circleLayer.fillColor = UIColor.clear.cgColor
circleLayer.strokeColor = UIColor.black.cgColor
circleLayer.lineWidth = 2.5

// adding the layer into the button:
button.layer.addSublayer(circleLayer)

func applyRoundedCorners(for view: UIView) {
    view.layer.cornerRadius = view.frame.size.width / 2
    view.layer.borderColor = UIColor.white.cgColor
    view.layer.borderWidth = 5.0
    view.layer.masksToBounds = true
}

func drawCircle(in view: UIView) {
    let circlePath = UIBezierPath(arcCenter: CGPoint(x: view.frame.size.width / 2,y: view.frame.size.width / 2),
                                             radius: view.frame.size.width / 2.5,
                                             startAngle: 0,
                                             endAngle: CGFloat.pi * 2,
                                             clockwise: true)

    let shapeLayer = CAShapeLayer()
    shapeLayer.path = circlePath.cgPath
    shapeLayer.fillColor = UIColor.clear.cgColor
    shapeLayer.strokeColor = UIColor.black.cgColor
    shapeLayer.lineWidth = 2.5

    button.layer.addSublayer(shapeLayer)
}

applyRoundedCorners(for: button)
drawCircle(in: button)

extension UIView {
    func applyRoundedCorners(for view: UIView) {
        view.layer.cornerRadius = view.frame.size.width / 2
        view.layer.borderColor = UIColor.white.cgColor
        view.layer.borderWidth = 5.0
        view.layer.masksToBounds = true
    }

    func drawCircle(in view: UIView) {
        let circlePath = UIBezierPath(arcCenter: CGPoint(x: view.frame.size.width / 2,y: view.frame.size.width / 2),
                                      radius: view.frame.size.width / 2.5,
                                      startAngle: 0,
                                      endAngle: CGFloat.pi * 2,
                                      clockwise: true)

        let shapeLayer = CAShapeLayer()
        shapeLayer.path = circlePath.cgPath
        shapeLayer.fillColor = UIColor.clear.cgColor
        shapeLayer.strokeColor = UIColor.black.cgColor
        shapeLayer.lineWidth = 2.5

        button.layer.addSublayer(shapeLayer)
    }
}

button.applyRoundedCorners()
button.drawCircle()