@IBAction func axisChange(sender: UISwitch) {
    UIView.animateWithDuration(1.0) {
        self.updateConstraintsForAxis()
    }
}

The updateConstraintForAxis function just sets the axis of the stack view containing the two image views:

private func updateConstraintsForAxis() {
    if (axisSwitch.on) {
        stackView.axis = .Horizontal
    } else {
        stackView.axis = .Vertical
    }
}

The animated gif below gives you an idea of how this appears:

http://i.stack.imgur.com/n0ZX0.gif