正方体的截面与分割
2020-04-18 22:52
本范例演示了如何使用GeoGebra对正方体进行截面与分割。通过构造正交平面并与正方体求交，可以生成不同的截面多边形。结合平移等几何变换命令，直观展示了正方体被平面分割后的各个部分及其空间几何特征。该模型有助于深入理解立体几何中的截面问题、空间点线面位置关系以及多面体的结构。
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<keepTypeOnTransform val="true"/>
</element>
<expression label="l2" exp="{O, P, Q, L, M, N, A, B, C, D, E, F, G, H}" />
<element type="list" label="l2">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="KeepIf[Angle[OrthogonalVector[s], Vector[R, p]] ≥ π / 2 ∧ p ∈ q, p, l2]" a1="q" a2="l3"/>
<output a0="l7"/>
</command>
<element type="list" label="l7">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="KeepIf[Angle[OrthogonalVector[s], Vector[R, p]] ≤ π / 2 ∧ p ∈ q, p, l2]" a1="q" a2="l3"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Zip[Polygon[Append[Element[q, 1], Sort[Take[q, 2], Zip[Angle[Element[q, 2], Element[q, 1], p], p, Take[q, 2]]]]], q, l5]"/>
<output a0="l6"/>
</command>
<element type="list" label="l6">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="c">
<value val="0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="116" y="236" fixed="false" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.001" speed="1" type="0" playing="false"/>
</element>
<command name="Translate">
<input a0="l6" a1="Vector[(c * OrthogonalVector[s])]"/>
<output a0="l6'"/>
</command>
<element type="list" label="l6'">
<show object="true" label="false" ev="5"/>
<objColor r="0" g="100" b="0" alpha="0.800000011920929"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="RemoveUndefined">
<input a0="Zip[Polygon[Append[Element[q, 1], Sort[Take[q, 2], Zip[Angle[Element[q, 2], Element[q, 1], p], p, Take[q, 2]]]]], q, l7]"/>
<output a0="l8"/>
</command>
<element type="list" label="l8">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Translate">
<input a0="l8" a1="Vector[((-c) * OrthogonalVector[s])]"/>
<output a0="l8'"/>
</command>
<element type="list" label="l8'">
<show object="true" label="true" ev="5"/>
<objColor r="255" g="127" b="0" alpha="0.800000011920929"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
</construction>
</geogebra>