双曲面几何构造演示
2020-07-30 03:33
本范例展示了双曲面（Hyperboloid）的三维几何构造过程。通过GeoGebra的Sequence、Rotate、Translate等命令，利用线段和点的旋转与平移生成双曲面网格。该模型直观呈现了直纹曲面的特性，适用于立体几何与解析几何的教学与可视化研究。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.593.0" app="classic" platform="w" id="edd1abc6-ee82-4f63-9aa5-706144f04d33" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="801" height="501" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.4893882646691635" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1" size="336" window="580,246,700,550" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3" size="392" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="299" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="true" location="1" size="399" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="392" height="498"/>
<coordSystem xZero="136.36776046131405" yZero="291.3358655299182" scale="44.94210229072824" yscale="44.94210229072795"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-0.15447570703738567" yZero="-0.5835334003040196" zZero="-1.8727280604435697" scale="49.48462302973641" xAngle="11" zAngle="442.56243579032895"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="true" show="false" size="2"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="20"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="2" y="-6"/>
<labelMode val="2"/>
<slider min="1" max="50" absoluteScreenLocation="true" width="100" x="123" y="95" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="(1.6 * ℯ^((((ί * 2) * n) * π / a)))" a1="n" a2="0" a3="a"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<angleStyle val="0"/>
</element>
<command name="Point">
<input a0="zAxis"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="153" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="0" z="4.995225594265079" w="1"/>
<pointSize val="5"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="153" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="B" a1="C"/>
<output a0="u"/>
</command>
<element type="vector3d" label="u">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="4.995225594265079" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<startPoint exp="B"/>
</element>
<command name="Translate">
<input a0="list1" a1="u"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="b">
<value val="1.6964600329384885"/>
<show object="true" label="true"/>
<objColor r="0" g="153" b="0" alpha="0.10000000149011612" fillType="4" hatchAngle="45" hatchDistance="10"/>
<layer val="0"/>
<labelMode val="2"/>
<slider min="0" max="3.141592653589793" absoluteScreenLocation="true" width="100" x="121" y="148" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="π / 100" speed="1" type="0" playing="false"/>
</element>
<command name="Rotate">
<input a0="list2" a1="b" a2="zAxis"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="204" b="51" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Segment[Element[list1, k], Element[list3, k]]" a1="k" a2="2" a3="a"/>
<output a0="list4"/>
</command>
<element type="list" label="list4">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Point">
<input a0="list3"/>
<output a0="E"/>
</command>
<element type="point3d" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-0.200533173702887" y="1.5873835221031645" z="4.995225594265079" w="1"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="list1"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.6" y="0" z="1"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="text1" exp=""Num of points""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-2.4557765399435576" y="4.39089084558981" z="1"/>
</element>
<expression label="text2" exp=""Rotate angle""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-2.344522287357525" y="3.211595768177855" z="1"/>
</element>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="c"/>
</command>
<element type="segment3d" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="102" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>