3d model failure with Cylinders
- To: mathgroup at smc.vnet.net
- Subject: [mg128691] 3d model failure with Cylinders
- From: Roger Bagula <roger.bagula at gmail.com>
- Date: Sun, 18 Nov 2012 03:56:18 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
I don't get a 3d model out of this for some reason: only the rim torus outputs as a 3d model. Clear[n, m, gw, g2, R] n = 7; m = 3; dt = 2 Pi/n; dtm = 2 Pi/m; r = 1.0/(1 - Sin[dt/2]/Cos[dtm/2]); R = r Cos[(dt + dtm)/2]/Cos[dtm/2]; ToMatrix[z_, r_] := (I/r) {{z, r^2 - z Conjugate[z]}, {1, -Conjugate[z]}}; alist := Table[ ToMatrix[r Exp[I t], r - 1], {t, dt/2, 2 Pi, dt}]; Tlist := Join[{IdentityMatrix[2]}, alist]; homography[{{a_, b_}, {c_, d_}}, z_] := (a z + b)/(c z + d); FindT[T0_, Tlist_] := MemberQ[Tlist, T_ /; Abs[homography[T, 0] - homography[T0, 0]] < 1.0*^-3]; i2 = 1; Do[i1 = i2 + 1; i2 = Length[Tlist]; Do[Scan[(T = Tlist[[i]].#; If[! FindT[T, Tlist], Tlist = Append[Tlist, T]]) &, alist], {i, i1, i2}], {3}]; R0 = {{Cos[2*Pi/n], Sin[2*Pi/n], 0}, {-Sin[2*Pi/n], Cos[2*Pi/n], 0}, {0, 0, 1}}; Clear[g2, g3, g4] g2 = ParametricPlot3D[{(37 + Cos[\[Alpha]])*Cos[\[Beta]], (37 + Cos[\[Alpha]])* Sin[\[Beta]] , Sin[\[Alpha]] }/ 10 + {0, 0, (6.5/2)*R}, {\[Alpha], 0, 2*\[Pi]}, {\[Beta], 0, 2*\[Pi]}, Boxed -> False, Axes -> False, PlotRange -> All, ColorFunction -> "Pastel", MeshFunctions -> {#1 &}]; g3 = Graphics3D[{ColorData["LightTemperatureMap"][0.75], Table[Map[ Cylinder[ Table[z = homography[#, R Exp[I t]]; MatrixPower[R0, l].{Re[z], Im[z], Abs[z]}, {t, 0, 2 Pi, dt}], 1/(10 + Abs[z])] &, Tlist], {l, 0, 7}]}, Boxed -> False] g4 = Graphics3D[{ColorData["LightTemperatureMap"][0.75], Table[Map[ Cylinder[ Table[z = homography[#, R Exp[I t]]; MatrixPower[R0, l].{Re[z], Im[z], 6.5*R - Abs[z]}, {t, 0, 2 Pi, dt}], 1/(10 + Abs[z])] &, Tlist], {l, 0, 7}]}, Boxed -> False] gw = Show[{g2, g3, g4}, Boxed -> False, ImageSize -> 1000, ViewPoint -> {5, 5, 5}] Export["hyperbolic8_cage.3ds", gw] Export["hyperbolic8_cage.obj", gw] Export["hyperbolic8_cage.stl", gw] I expected a cage type 3d model. I've also had large triangle output in cylinders as 3d models that have to be removed.