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Problem in "block cutting"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121567] Problem in "block cutting"
  • From: Roger Bagula <roger.bagula at gmail.com>
  • Date: Tue, 20 Sep 2011 06:08:57 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

In architecture there is a curve called an hanging chain curve
that is based on Sinh and Cosh functions.
I want to cut an arch made of a cylinder of the hanging chain
from a rectangular set of cubic blocks.
I have it visualized but not actualized in Mathematica:

x0 = (Sinh[p]/1.2)/1.25;
y0 = Sin[t];
z0 = (2*Cosh[p] - 3)/1.25 - 0.075;
gc = ParametricPlot3D[{x0, z0, y0}, {t, -Pi, Pi}, {p, -1, 1},
  Boxed -> False, Axes -> True,
  TextureCoordinateFunction -> ({2 #4, #5} &),
  PlotStyle ->
   Directive[Brown, Specularity[White, 50],
    Texture[ExampleData[{"ColorTexture", "BurlOak"}]]],
  Lighting -> "Neutral"]
g1 = Show[
  Graphics3D[{Opacity[0.5], Cuboid[{0, -1, 0}], Cuboid[{-1, -1, 0}],
    Cuboid[{-1, -1, -1}], Cuboid[{0, -1, -1}]}], Boxed -> False]
Show[{gc, g1}, PlotRange -> All]

Something like the RegionFunction:

ga = SphericalPlot3D[
  1 + Sin[3 \[Theta]] Sin[3 \[Phi]]/3, {\[Theta], 0, Pi}, {\[Phi], 0,
   2 Pi}, RegionFunction -> (#6 > 0.95 &),
  PlotStyle -> FaceForm[Blue, Cyan], Boxed -> False, Axes -> False,
  Mesh -> False]

Would seem to be a way to approach the problem,
but I can't figure out how.
Roger Bagula




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