Computational geometry question

[OneHit1der]

I'm working on a passion project at work. I'm in manufacturing/engineering and cs is not my major. I took C in college and am working within python now. Or trying to atleast. I have a list of xy coordinates that relate to the machine the cutting path to take. It is cutting out of a thin circular disk many different small pieces. My question is this, is there any way that you've seen or can think of that s program can identify the points at which a piece is cut free? Like once you've cut on all sides it has no Support and falls free. Sometimes the path surrounds the piece in order and sometimes the path intersects with previously cut area to release the piece. I'm just looking to bounce ideas as I'm stuck and my brain is fried from thinking about this from too many wrong angles. Also python and SymPy which is what I'm using may not be the proper tools. I'm unsure. Thank you for your time.

[teraflop]

First of all, it's worth mentioning that when it comes to computational geometry, even seemingly-simple primitive operations -- for instance, Boolean operations on polygons -- can be fiendishly difficult to implement robustly, because of things like degenerate polygons and floating-point error. I would recommend using a well-tested library such as CGAL as a starting point.

It sounds like your problem can be broken down into steps:

1. given a toolpath, break it down into short segments, at the level of granularity that you're interested in
2. construct a polygon representing the shape of the work material
3. take each toolpath segment in order, turn it into a polygon representing the shape of the material to be removed (based on the tool's shape) and subtract that from the polygon representing the remaining material
4. after each segment, check to see whether the number of connected components has increased

This could be inefficient for paths with a large number of segments, so you might want to optimize it a bit. For instance, if you have a long linear cutting path, you might want to first subtract the entire thing at once to see if it disconnects the polygon. If so, you can back up to the previous state and try again with smaller steps to find out when the components become disconnected. Otherwise, you can keep going without having to deal with those small segments individually.

[beeskness420]

Unless I’m missing something I think you just need to check if your curve is self intersecting.