Re: Urgent

*To*: mathgroup at smc.vnet.net*Subject*: [mg27279] Re: Urgent*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Fri, 16 Feb 2001 03:58:31 -0500 (EST)*References*: <9686u0$3qi@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here are two possibilites for 2D polygons Both will give the angles in the correct quadrant. angles2c will give the angles in the range (-Pi ,2Pi] and angles2r will give them in the range (-2Pi,2Pi). To convert them to the range (-Pi ,2Pi] we could use Mod[ . , 2Pi, -Pi] but this will slow the computation down markedly. angles2c[verts_]:= Arg[RotateLeft[#]/#&[RotateLeft[#]-#&[Complex@@@verts]]] angles2r[verts_]:=(RotateLeft[#]-#)&[ArcTan@@@(RotateLeft[#]-#&[verts])] The following will work for any dimensions, but it will give answers in the range [0,Pi] and so leaves it ambiguous in 2D whether the true answer is for example Pi/2 or -Pi/2. angles[verts_] := MapThread[ArcCos[(#1 .#2)/Sqrt[(#1.#1)(#2.#2)]] &, {RotateLeft[#], #} &[{1, -1}.({ RotateLeft[#], #} &[verts])]] Here are some timings verts = Table[Random[Real, {-1, 1}], {100000}, {2}]; angles2c[verts];//Timing {10.22 Second,Null} angles2r[verts];//Timing {8.08 Second,Null} angles[verts];//Timing {62.01 Second,Null} -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "oda" <adj at ensm-douai.fr> wrote in message news:9686u0$3qi at smc.vnet.net... > Hi , all > > I'm currently use Mathematica 4.0 and I need to compute > fastly the angle between the vertices of a polygon. > The statement of the problem is : > > Let be (P) a polygon with n vertices point, I want to calulate > the angle (T) between all consecutif edge. > > (P) = {P1, P2, P3,.............,Pn} > P1 is a 2 or 3 dimension point. > angles between (PiPi+1, Pi+1Pi+2) i = 1, n-2; > > I have about (100000 points in polygon) > > Thanks in advance >