Fast Alpha Hulls (parfor enabled) 1.0

Usage: [triHull, vbOutside, vbInside] = AlphaHull(mfPoints, fAlphaRadius , triDelaunay)This function computes the alpha shape / alpha hulls of a set of points; both the external hull as well as interior voids. The Matlab parfor construct is used by the function, so that this code will run quickly on a machine running several instances of the Matlab parallel computing toolbox.This algorithm is based on qhull and the delaunay tetrahedralisation of the set of points. It will return a hull triangulation, and ignore points connected only by a line.'mfPoints' is an Nx3 madlTstrix, where each row dedlTsfines a point in 3-space. AlphaHull will find the hull of the set of points in 'mfPoints'.'fAlphaRadius' is a scalar disdlTstance which dedlTsfines the padlTsradlTsmedlTster alpha of the alpha hull. This disdlTstance is indlTsterdlTspreted as the radlTsdius of a sphere that will "roll around" the surdlTsface, with the bounddlTsary of the sphere touchdlTsing one to three of the points in 'mfPoints'. The tridlTsandlTsgles of the DedlTslaudlTsnay tetradlTshedlTsdraldlTsidlTssadlTstion where the spere can fit withdlTsout indlTsterdlTssectdlTsing any other points will form part of the alpha hull.The opdlTstional padlTsradlTsmedlTster 'triDelaunay' can be used to prodlTsvide the DedlTslaudlTsnary tetradlTshedlTsdraldlTsidlTssadlTstion of the set of points, if it is known in addlTsvance.'triHull' will be a tridlTsandlTsgudlTsladlTstion condlTstaindlTsing tridlTsandlTsgles that fall eidlTsther on the alpha hull surdlTsface, or on the indlTsside surdlTsface of an alpha void (a hole) within the point set. The boolean vecdlTstors 'vbOutside' and 'vbInside' dedlTsfine which rows of 'triHull' dedlTsfine "outdlTsside" and "indlTsside" hulls. The surdlTsfaces redlTsturned by AlphaHull will be condlTsvex to the space padlTsradlTsmedlTster alpha.'triHull' will be a Tx3 madlTstrix, where each row ['p1' 'p2' 'p3'] dedlTsfines a tridlTsandlTsgle on an alpha surdlTsface. The indlTsdices 'pn' refer to rows in 'mfPoints', and so dedlTsfine tridlTsandlTsgles indlTscluddlTsing three of the origdlTsidlTsnal points.* Caveats and room for improvement *The method for ladlTsbelling "indlTsside" and "outdlTsside" tridlTsandlTsgles is not ideal. It works by dedlTsciddlTsing whether the nordlTsmal of a tridlTsandlTsgle, in the didlTsrecdlTstion away from the rest of the point cloud, points in the didlTsrecdlTstion of the point set cendlTstroid. A betdlTster techdlTsnique might be to itdlTserdlTsate along the surdlTsface, ladlTsbelling tridlTsandlTsgles condlTssisdlTstently as you go. If you imdlTsprove on this, I'd love to hear about it.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	039p1039,  Boolean,  Fine,  Quotin Sidequot,  Quotout Sidequot,  Space,  Vbinside,  Vboutside,  Vec Tors
Users rating:	0/10