On Saturday 03 July 2010 10:03:32 Taco Hoekwater wrote: > On 07/02/2010 07:01 PM, Marco wrote: > > Hi, > > > > two arbitrary paths are given. A small path and a larger path, both > > cycled. How to find out if the smaller path lies completely »inside« the > > larger path? > > That is hard. The main problem is the word 'arbitrary'. An arbitrary > path does not even have to enclose anything: > > path p; p = origin--(100,100)--cycle; > > > If this is too complicated, it might help if I can find out if a given > > point lies inside a given cycled path. > > Even this is fairly tricky. Some important questions are: > > * do your arbitrary paths selfintersect? > * are your arbitrary paths convex or concave? > * is a point *on* the path in or out? > * do you want to use nonzero or even-odd filling rules? > > Best wishes, > Taco
OK, this is off-topic (and not very useful as an answer)... but is something to think about: ``posito tendendum esse a puncto ad punctum, licet nihil ultra iter determinat, via eligetur maxime facilis seu brevissima;'' Leibniz: De rerum originatione radicali, 1697 ``suppose that we are to go from one point to another, without being directed to follow a particular path, the path chosen will be the easiest or the shortest one;'' So, in a Cartesian space, if the energy cost of a kink is low, than > path p; p := origin--(100,100)--cycle; should be a straight line running back on itself. Indeed, this is what metapost produces. Now try p := origin..(100,100)..cycle; Alan ___________________________________________________________________________________ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://tex.aanhet.net archive : http://foundry.supelec.fr/projects/contextrev/ wiki : http://contextgarden.net ___________________________________________________________________________________
