三次元図形による不可能図形 （ヒント集）

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Transcript 三次元図形による不可能図形 （ヒント集） 

三次元図形による不可能図形
（ヒント集）
（COM実験第6回のメモ）
2004.09.22
2004.09.23 改訂
[email protected]
Cuboid
今回は不要
<<Graphics`Polyhedra`
Show[
Graphics3D[
Cuboid[{0, 0, 0}]
],
ViewPoint -> {100, -100, 100},
PlotRange -> All, Boxed -> False]
ViewPointの値
Show[
Graphics3D[
Cuboid[{0, 0, 0}]
],
ViewPoint -> {100, -100, 100},
PlotRange -> All, Boxed -> False]
ViewPoint -> {4, -4, 4}
ViewPoint -> {100, -100, 100}
ViewPoint -> {1, -1, 1}
ViewPoint -> {2, -2, 2}
立方体の配置
z
Show[
Graphics3D[
Cuboid[{0, 0, 0}]
(0,0,2)
y
ViewPoint -> {100, -100, 100},
PlotRange -> All, Boxed -> False]
(0,2,0)
(0,0,0)
(x,y,z)
],
(2,0,0)
x
Cuboidの連結
Show[Graphics3D[
{
Cuboid[{0,0,0}],
Cuboid[{0,0,1}],
Cuboid[{0,0,2}]
}
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
Tableによる繰り返し
Show[
Graphics3D[
Table[
Cuboid[{0,0,k}],
{k,0,2}
]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
Tableによる繰り返し
Show[
Graphics3D[
Table[
Cuboid[{0,k,0}],
{k,0,2}
]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
Tableによる繰り返し
Show[
Graphics3D[
Table[
Cuboid[{k,0,0}],
{k,0,2}
]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
斜めに配置
Show[Graphics3D[
{
Cuboid[{0,0,0}],
Cuboid[{1,1,1}],
Cuboid[{2,2,2}]
}
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
Tableによる繰り返し
Show[
Graphics3D[
Table[
Cuboid[{k,k,k}],
{k,0,2}
]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
長い Cuboid
Show[
Graphics3D[{
Cuboid[{0, 2, 0}],
Cuboid[{1, 2, 0}],
Cuboid[{2, 2, 0}],
Cuboid[{0, 0, 0}, {3, 1, 1}],
}],
ViewPoint -> {100, -100, 100},
PlotRange -> All, Boxed -> False]
不可能図形
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,3}],
Table[Cuboid[{0,0,k}],{k,1,6}],
Table[Cuboid[{k,0,6}],{k,1,3}],
Table[Cuboid[{0,3,k}],{k,1,2}]]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
同じ不可能図形
Show[Graphics3D[{
Cuboid[{0, 0, 0}, {1, 4, 1}],
Cuboid[{0, 0, 1}, {1, 1, 6}],
Cuboid[{0, 0, 6}, {4, 1, 7}],
Cuboid[{0, 3, 1}, {1, 4, 3}]
}, ViewPoint -> {100, -100, 100},
PlotRange -> All, Boxed -> False]]
でも実は．．．
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,3}],
Table[Cuboid[{0,0,k}],{k,1,6}],
Table[Cuboid[{k,0,6}],{k,1,3}],
Table[Cuboid[{0,3,k}],{k,1,2}]]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
ViewPoint{100,100,100}
ViewPoint{100,-100,100}
ViewPoint{100,100,-100}
別の不可能図形
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
Table[Cuboid[{6,0,k}],{k,1,4}],
{Cuboid[{7,0,5},{7,1,6}],
Polygon[{{6,0,5},{7,0,5},{7,0,6}}]}
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]]
実は．．．
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
Table[Cuboid[{6,0,k}],{k,1,4}],
{Cuboid[{7,0,5},{7,1,6}],
Polygon[{{6,0,5},{7,0,5},{7,0,6}}]}
],
ViewPoint{100,100,100}
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]]
ViewPoint{100,-100,100}
ViewPoint{100,100,-100}
切れてしまう
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
Table[Cuboid[{6,0,k}],{k,1,4}]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]]
多角形
Show[
Graphics3D[
Polygon[{{0,0,0},{1,0,0},{0,0,1}}]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
Show[
Graphics3D[
Polygon[{{0,0,0},{1,0,0},{1,0,1}}]
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]
間隙を埋める
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
Table[Cuboid[{6,0,k}],{k,1,4}],
{Polygon[{{6,0,5},{7,0,5},{7,0,6}}]}
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]]
間隙を埋める
Show[
Graphics3D[
Join[
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
Table[Cuboid[{6,0,k}],{k,1,4}],
{Cuboid[{7,0,5},{7,1,6}],
Polygon[{{6,0,5},{7,0,5},{7,0,6}}]}
],
ViewPoint{100,-100,100},
PlotRangeAll,BoxedFalse]]
間隙を埋める（その２）
g0=Show[Graphics3D[
{
Polygon[{{6,1,5},{7,1,5},{7,1,6}}],
Polygon[{{6,0,5},{7,0,5},{7,0,6}}],
Polygon[{{6,0,5},{6,1,5},{7,1,5},{7,0,5}}],
Polygon[{{6,0,5},{6,1,5},{7,1,6},{7,0,6}}],
Polygon[{{7,0,5},{7,0,6},{7,1,6},{7,1,5}}]
},
PlotRangeAll,BoxedFalse]]
三角柱
間隙を埋める（その２）
Show[Graphics3D[Join[
Table[Cuboid[{6,0,k}],{k,1,4}],
Table[Cuboid[{0,k,0}],{k,0,6}],
Table[Cuboid[{k,0,0}],{k,1,6}],
{
Polygon[{{6,1,5},{7,1,5},{7,1,6}}],
Polygon[{{6,0,5},{7,0,5},{7,0,6}}],
Polygon[{{6,0,5},{6,1,5},{7,1,5},{7,0,5}}],
Polygon[{{6,0,5},{6,1,5},{7,1,6},{7,0,6}}],
Polygon[{{7,0,5},{7,0,6},{7,1,6},{7,1,5}}]
}],
ViewPoint{100,-100,100},
PlotRange->All,Boxed->False]]
三角柱で蓋をする
この行をとる