球面及其截面交线构造演示
2017-09-06 08:37
本GeoGebra范例演示了球面的构造及其与平面的交线。通过使用Sphere命令创建球体,并结合PointIn、IntersectConic和Intersect等命令,动态展示球面与截面相交产生的几何对象。该模型有助于直观理解立体几何中球体截面的性质及空间解析几何的相关概念。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.380.0" id="8E70BA1A-A43C-4B13-8BD2-88B3BA3AA721" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1440" height="900" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.30486111111111114" orientation="1" />
</panes>
<views>
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3,3" size="300" window="100,100,600,400" />
<view id="1" visible="false" inframe="false" stylebar="false" location="1,3" size="500" 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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="288" window="100,100,700,550" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="439" window="100,100,250,400" />
<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="true" 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" />
<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="false" location="1" size="993" window="100,100,600,400" />
</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="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1231" height="712"/>
<coordSystem xZero="215" yZero="315" scale="50" yscale="50"/>
<evSettings axes="true" 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="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<spreadsheetView>
<size width="0" height="0"/>
<prefCellSize width="70" height="0"/>
<spreadsheetColumn id="0" width="0"/>
<spreadsheetColumn id="1" width="0"/>
<spreadsheetColumn id="2" width="0"/>
<spreadsheetColumn id="3" width="0"/>
<spreadsheetColumn id="4" width="0"/>
<spreadsheetColumn id="5" width="0"/>
<spreadsheetColumn id="6" width="0"/>
<spreadsheetColumn id="7" width="0"/>
<spreadsheetColumn id="8" width="0"/>
<selection hScroll="0" vScroll="0" column="-1" row="-1"/>
<layout showFormulaBar="false" showGrid="true" showHScrollBar="true" showVScrollBar="true" showColumnHeader="true" showRowHeader ="true" allowSpecialEditor="false" allowToolTips="true" equalsRequired="false"/>
</spreadsheetView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0" yZero="0" zZero="-1.4999999999999996" scale="32.91761080778032" xAngle="3" zAngle="-710.5923189559019"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="1"/>
</euclidianView3D>
<construction title="球面" author="" date="">
<expression label ="B" exp="(4.18, 5.82, 0.5)" type="point"/>
<element type="point3d" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="4.18" y="5.82" z="0.5" w="1"/>
<pointSize val="4"/>
</element>
<command name="Sphere">
<input a0="B" a1="3"/>
<output a0="b"/>
</command>
<element type="quadric" label="b">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="215" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="42.594800000000006" A4="0" A5="0" A6="0" A7="-4.18" A8="-5.82" A9="-0.5"/>
</element>
<command name="PointIn">
<input a0="b"/>
<output a0="D"/>
</command>
<element type="point3d" 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="0" playing="false"/>
<isShape val="false"/>
<coords x="2.540937089110086" y="7.472397704967536" z="2.392895823536811" w="1"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="10.4" y="7.607889330988799" z="2" w="1"/>
<pointSize val="4"/>
</element>
<command name="Sphere">
<input a0="A" a1="5"/>
<output a0="a"/>
</command>
<element type="quadric" label="a">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="145.0399800725732" A4="0" A5="0" A6="0" A7="-10.4" A8="-7.607889330988799" A9="-2"/>
</element>
<command name="IntersectConic">
<input a0="b" a1="a"/>
<output a0="c"/>
</command>
<element type="conic3d" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="12" type="10" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.516164939604896" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<element type="point3d" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="4.576812507943055" y="5.891654496181534" z="3" w="1"/>
<pointSize val="4"/>
</element>
<command name="Sphere">
<input a0="C" a1="4"/>
<output a0="d"/>
</command>
<element type="quadric" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="48.65880543524008" A4="0" A5="0" A6="0" A7="-4.576812507943055" A8="-5.891654496181534" A9="-3"/>
</element>
<command name="Intersect">
<input a0="c" a1="d"/>
<output a0="e" a1="e_2" a2="" a3=""/>
</command>
<element type="point3d" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="6.89894490915371" y="4.661882827079241" z="-0.01585191166957034" w="1"/>
<pointSize val="6"/>
</element>
<element type="point3d" label="e_2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="5.845291596735843" y="8.274052049590622" z="0.047857947387048294" w="1"/>
<pointSize val="6"/>
</element>
</construction>
</geogebra>