Re: Re: Problems updating Graphics3D Polygons

*To*: mathgroup at smc.vnet.net*Subject*: [mg77757] Re: [mg77705] Re: Problems updating Graphics3D Polygons*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Sat, 16 Jun 2007 03:25:53 -0400 (EDT)*References*: <12927846.1181901440802.JavaMail.root@m35> <op.tty2tklpqu6oor@monster.ma.dl.cox.net>*Reply-to*: drmajorbob at bigfoot.com

Here's a version that works for 2D and 3D (and other, if they existed) polygons: Clear[scalePts, scaleGraph] scale[pts_, m_] := Module[ {d = Dimensions[pts][[2]]}, Which[ ArrayQ[m] && Dimensions[m] == {d, d}, pts.m, VectorQ[m] && Length[m] == d, pts.DiagonalMatrix[m], NumericQ[m], pts.DiagonalMatrix[ConstantArray[1, d - 1]~Join~{m}], True, Print["error"]; pts ] ] scaleGraph[graphics_, m_] := graphics /. Polygon[pts_] :> Polygon[scale[pts, m]] g = Graphics3D[{Polygon[{{0., 0.5, 1.28}, {0., 0., 1.}, {0.5, 0., 1.28}, {0.5, 0.5, 1.64}}], Polygon[{{0.5, 0.5, 1.64}, {0.5, 0., 1.28}, {1., 0., 2.71}, {1., 0.5, 3.49}}]}]; scaleGraph[g, 1/3] scaleGraph[g, {1, 2, 1}] scaleGraph[g, RandomReal[{1/2, 3/2}, {3, 3}]] g = Graphics[Polygon[{{1, 0}, {0, Sqrt[3]}, {-1, 0}}]]; scaleGraph[g, 1/3] scaleGraph[g, {2, 3}] scaleGraph[g, RandomReal[{1/2, 3/2}, {2, 2}]] Bobby On Fri, 15 Jun 2007 11:59:34 -0500, DrMajorBob <drmajorbob at bigfoot.com> wrote: > I'm multiplying the polygon list by a 3x3 matrix. > > (I posted this before, but just in case...) > > array[dims] checks the dimensions of its argument, threeD changes a > scalar or 3-vector into a 3x3, and scaleZ multiplies the polygon list by > that matrix. The multiplication is pts.matrix; pts is n x 3 and matrix > is 3x3, so the result is n x 3 again, still suitable as the argument to > Polygon. > > (This could be modified to work for 2D plots as well, but I haven't.) > > Clear[scale, array, threeD] > array[dims_List] = ArrayQ[#] && Dimensions[#] == dims &; > threeD[m_?(array[{3, 3}])] := m > threeD[m_?(array[{3}])] := DiagonalMatrix@m > threeD[f_?NumericQ] := DiagonalMatrix@{1, 1, f} > scale[graphics_, m_] := > graphics /. Polygon[pts_] :> Polygon[pts.threeD[m]] > > gobject = > Graphics3D[{Polygon[{{0., 0.5, 1.28}, {0., 0., 1.}, {0.5, 0., > 1.28}, {0.5, 0.5, 1.64}}], > Polygon[{{0.5, 0.5, 1.64}, {0.5, 0., 1.28}, {1., 0., 2.71}, {1., > 0.5, 3.49}}]}] > > scale[gobject, 1/3] > > scale[gobject, {1, 2, 1}] > > scale[gobject, RandomReal[{1/2, 3/2}, {3, 3}]] > > Bobby > > On Fri, 15 Jun 2007 03:35:22 -0500, chuck009 <dmilioto at comcast.com> > wrote: > >> Thanks. Jean-Marc noticed in my original post that I just didn't call >> the function correctly. I like the code you used below, the >> pts.{{1,0,0},{0,1,0},{0,0,ratio}}. I see what it does just not sure of >> the construct. I'll figure it out though. Thanks! >> >>> "In[473]:ExpandZ[g_,ratio_]: >>> g/.Polygon[pts_]:>Polygon[{#[[1]],#[[2]],#[[3]]*ratio} >>> & /@pts];" >>> >>> There are a couple of "=" signs missing; not sure >>> what you're seeing at >>> your machine. >>> >>> This works at mine: >>> >>> Clear[expandZ] >>> expandZ[g_, ratio_] := >>> g /. Polygon[pts_] :> >>> Polygon[{#[[1]], #[[2]], #[[3]]*ratio} & /@ >>> & /@ pts]; >>> >>> But I prefer >>> >>> Clear[expandZ] >>> expandZ[g_, ratio_] := >>> g /. Polygon[pts_] :> >>> Polygon[pts.{{1, 0, 0}, {0, 1, 0}, {0, 0, >>> 0, 0, ratio}}]; >>> >> >> > > > -- DrMajorBob at bigfoot.com