线段反射与视觉差几何演示
2020-05-27 07:46
本范例演示了线段的几何构造与视觉差现象。通过GeoGebra中的线段和反射命令，构建了包含点及其对称点的几何图形。该模型直观展示了线段在特定几何变换下的位置关系与视觉差异，适合用于几何作图和变换的辅助教学。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.583.0" app="classic" platform="w" id="DD8D01DA-28C1-4E8C-8AF0-B50A09B5F5EB" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="922" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.3067708333333333" orientation="1" />
<pane location="1" divider="0.4552083333333333" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 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="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1,3" size="874" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="true" inframe="false" stylebar="true" location="1,1" size="441" window="100,100,700,550" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="589" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" 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="900" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="874" height="826"/>
<coordSystem xZero="184.87384646809844" yZero="449.09623986774704" scale="59.46478365034627" yscale="59.46478365034644"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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>
<spreadsheetView>
<size width="0" height="0"/>
<prefCellSize width="70" height="0"/>
<selection hScroll="0" vScroll="0" column="-1" row="-1"/>
</spreadsheetView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="未命名" author="" date="">
<element type="numeric" label="r">
<value val="1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0.1" max="1" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="l">
<value val="4.1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="200" x="29" y="144" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="t">
<value val="0.3"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.64"/>
<bgColor r="0" g="0" b="0" alpha="153"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0.1" max="0.9" absoluteScreenLocation="true" width="200" x="44" y="81" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<expression label="A" exp="(0, 0)" type="point"/>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="0" g="153" b="204" alpha="0"/>
<layer val="0"/>
<labelOffset x="-33" y="27"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="(l, 0)" type="point" />
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="0" g="153" b="204" alpha="0"/>
<layer val="0"/>
<labelOffset x="-11" y="41"/>
<labelMode val="0"/>
<coords x="4.1" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="((2 * l), 0)" type="point" />
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="0" g="153" b="204" alpha="0"/>
<layer val="0"/>
<labelOffset x="11" y="15"/>
<labelMode val="0"/>
<coords x="8.2" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="sAB"/>
</command>
<element type="segment" label="sAB">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="4.1" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C"/>
<output a0="sBC"/>
</command>
<element type="segment" label="sBC">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="4.1" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="UA" exp="A + (r * (cos((t * π)), sin((t * π))))" type="point" />
<element type="point" label="UA">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5877852522924731" y="0.8090169943749475" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="UA"/>
<output a0="sUA"/>
</command>
<element type="segment" label="sUA">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8090169943749475" y="0.5877852522924731" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="UB" exp="B + (r * ((-cos((t * π))), sin((t * π))))" type="point" />
<element type="point" label="UB">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.5122147477075263" y="0.8090169943749475" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="UC" exp="C + (r * ((-cos((t * π))), sin((t * π))))" type="point" />
<element type="point" label="UC">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.612214747707526" y="0.8090169943749475" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="UB"/>
<output a0="sUB"/>
</command>
<element type="segment" label="sUB">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8090169943749475" y="-0.5877852522924734" z="3.3169696769372843"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="UC"/>
<output a0="sUC"/>
</command>
<element type="segment" label="sUC">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8090169943749475" y="-0.5877852522924734" z="6.633939353874569"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="U" exp="{sUA, sUB, sUC}" />
<element type="list" label="U">
<show object="true" label="false"/>
<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="Mirror">
<input a0="U" a1="y = 0"/>
<output a0="D"/>
</command>
<element type="list" label="D">
<show object="true" label="false"/>
<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>
</construction>
</geogebra>