Closest point on “line/curve/arccurve” in sketchup

While in maya there are some easy API call to obtain the closest point on curves it is not the case in sketchup. All sketchup curves are actually made in straight segments as edges we can compute things between lines with some help from the API. Other than that, it is more or less the same as other polyline operation with python in maya, pairing up list, looping through segments, sorting, vector operation. A thing to note, all the API function in sketchup that deals with line takes them as infinite line so some procedure is used to find if point lies on the actual line bounded by its start and end points.