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scripts default iconFast Alpha Hulls (parfor enabled) (Scripts) Publisher's description

Usage: [triHull, vbOutside, vbInside] = AlphaHull(mfPoints, fAlphaRadius , triDelaunay)

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 maВ­trix, where each row deВ­fines a point in 3-space. AlphaHull will find the hull of the set of points in 'mfPoints'.

'fAlphaRadius' is a scalar disВ­tance which deВ­fines the paВ­raВ­meВ­ter alpha of the alpha hull. This disВ­tance is inВ­terВ­preted as the raВ­dius of a sphere that will "roll around" the surВ­face, with the boundВ­ary of the sphere touchВ­ing one to three of the points in 'mfPoints'. The triВ­anВ­gles of the DeВ­lauВ­nay tetraВ­heВ­dralВ­iВ­saВ­tion where the spere can fit withВ­out inВ­terВ­sectВ­ing any other points will form part of the alpha hull.

The opВ­tional paВ­raВ­meВ­ter 'triDelaunay' can be used to proВ­vide the DeВ­lauВ­nary tetraВ­heВ­dralВ­iВ­saВ­tion of the set of points, if it is known in adВ­vance.

'triHull' will be a triВ­anВ­guВ­laВ­tion conВ­tainВ­ing triВ­anВ­gles that fall eiВ­ther on the alpha hull surВ­face, or on the inВ­side surВ­face of an alpha void (a hole) within the point set. The boolean vecВ­tors 'vbOutside' and 'vbInside' deВ­fine which rows of 'triHull' deВ­fine "outВ­side" and "inВ­side" hulls. The surВ­faces reВ­turned by AlphaHull will be conВ­vex to the space paВ­raВ­meВ­ter alpha.

'triHull' will be a Tx3 maВ­trix, where each row ['p1' 'p2' 'p3'] deВ­fines a triВ­anВ­gle on an alpha surВ­face. The inВ­dices 'pn' refer to rows in 'mfPoints', and so deВ­fine triВ­anВ­gles inВ­cludВ­ing three of the origВ­iВ­nal points.

* Caveats and room for improvement *
The method for laВ­belling "inВ­side" and "outВ­side" triВ­anВ­gles is not ideal. It works by deВ­cidВ­ing whether the norВ­mal of a triВ­anВ­gle, in the diВ­recВ­tion away from the rest of the point cloud, points in the diВ­recВ­tion of the point set cenВ­troid. A betВ­ter techВ­nique might be to itВ­erВ­ate along the surВ­face, laВ­belling triВ­anВ­gles conВ­sisВ­tently as you go. If you imВ­prove on this, I'd love to hear about it.

System Requirements:

MATLAB 7.7 (R2008b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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