I have piecewise curve defining a generator (think brush) and a piecewise curve representing the path the brush follows. I wish to generate the boundary that the generator curve creates as it is swept across the path.
This is for an engineering CAD like application. I am looking for a general algorithm or code samples in any language.
I suggest the following papers:
The actual answer we used is too complex to post in full but in summary.
Walk around the outside of the graph. ( again all tests are done using big rational )
The performance of the algorithm is not brilliant due to the BigRational calculations. However we tried many ways to do this in floating point and we always got numerical edges cases where the resulting graph was not planar. If the graph is not planar then you can't walk around the outside of it.
If your have an arbitrarily complex shape translating and rotating along an arbitrary path, figuring out the area swept (and its boundary) using an exact method is going to be a really tough problem.
You might consider instead using a rendering-based approach:
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