I know a useful function [LineScaledCoordinate](https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html) through [animate-point-going-around-a-triangle](http://mathematica.stackexchange.com/questions/72415/animate-point-going-around-a-triangle), so does it have an inverse function?

```
Needs["GraphUtilities`"];
pts = {{0, 0}, {1, 0}, {0.6, 0.4}, {0.1, 0.5}};
P = LineScaledCoordinate[pts, 0.3]

```

Suppose this function is called `pathParameter`, `pathParameter[pts, P]` should return `0.3`.

Related link: [Line Scaled Segment or Arc length parametrization for Line](https://mathematica.stackexchange.com/questions/157616/line-scaled-segment-or-arc-length-parametrization-for-line)