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Re: Problem in "block cutting"
*To*: mathgroup at smc.vnet.net
*Subject*: [mg121590] Re: Problem in "block cutting"
*From*: Heike Gramberg <heike.gramberg at gmail.com>
*Date*: Wed, 21 Sep 2011 05:34:02 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201109201008.GAA00710@smc.vnet.net>
Since Cosh[p]^2-Sinh[p]^2==1 for all p, x0 and z0 satisfy the equation
(((z0 + 0.075) 1.25 + 3)/2)^2 - (x0 1.25 1.2)^2 ==1
Therefore you could do something like
Module[{x, y, z},
Show[RegionPlot3D[(((y + 0.075) 1.25 + 3)/2)^2 - (x 1.25 1.2)^2 <= 1,
##, Boxed -> False, Axes -> True,
TextureCoordinateFunction -> ({2 #1 + #2, #2 + #3} &),
Mesh -> None,
PlotStyle ->
Directive[Brown, Specularity[White, 50],
Texture[ExampleData[{"ColorTexture", "BurlOak"}]]],
Lighting -> "Neutral",
AxesLabel -> {"x", "y", "z"}] & @@@ {{{x, 0, 1}, {y, -1, 0}, {z,
0, 1}},
{{x, 0, 1}, {y, -1, 0}, {z, -1, 0}},
{{x, -1, 0}, {y, -1, 0}, {z, 0, 1}},
{{x, -1, 0}, {y, -1, 0}, {z, -1, 0}}}, PlotRange -> All,
Axes -> False, BoxRatios -> {2, 1, 2}]]
Heike.
On 20 Sep 2011, at 12:08, Roger Bagula wrote:
> 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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