圆锥截痕:直圆锥面与平面的交线演示
2020-11-01 13:42
本GeoGebra范例动态演示直圆锥面与平面相交产生的圆锥曲线。通过调整平面的高度、倾斜角、绕Z轴旋转及平移,用户可直观观察圆、椭圆、抛物线和双曲线的形成。模型包含交互按钮与滑块,支持限定特定曲线并展示贯轴等几何特征,是学习立体几何与解析几何中圆锥曲线概念的优质可视化工具。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.609.0" app="classic" platform="w" id="ce7bbef4-8190-4720-99fb-16b39686d801" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1085" height="745" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.5529953917050692" orientation="1" />
<pane location="1" divider="0.5436241610738255" orientation="0" />
</panes>
<views>
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="true" 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 , 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="2" visible="false" inframe="false" stylebar="false" location="3,3" size="300" tab="ALGEBRA" window="1363,153,302,539" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1,2" size="330" window="50,50,500,500" />
<view id="1024" toolbar="0 | 1 501 67 , 5 19 | 2 15 45 , 18 , 7 37 | 4 3 8 9 , 13 44 | 16 51 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 | 30 29 32 31 33 | 17 | 40 41 42 , 27 28 35 , 6" visible="true" inframe="false" stylebar="false" location="1,0" size="405" window="0,0,600,400" plane="e" />
<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="4097" visible="false" inframe="false" stylebar="true" location="1" size="395" window="625,256,989,668" />
<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="false" location="3" size="600" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 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="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="597" height="437"/>
<coordSystem xZero="241.34135031226526" yZero="343.2771729256668" scale="51.45125111523292" yscale="51.45125111523289"/>
<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>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="475" height="330"/>
<coordSystem xZero="160.15000000000003" yZero="190.3" scale="54.99999999999994" yscale="55"/>
<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>
<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" yZero="0" zZero="-0.28205219267454734" scale="38.976531367746176" xAngle="15.50135956693702" zAngle="-33.690067525979785"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<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="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="2"/>
<projection type="0"/>
</euclidianView3D>
<euclidianView>
<viewId plane="e"/>
<size width="475" height="405"/>
<coordSystem xZero="215.37130606219202" yZero="243.95914767342967" scale="21.048909620211706" yscale="21.04890962021175"/>
<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"/>
<transformForPlane mirror="false" rotate="0"/>
</euclidianView>
<construction title="" author="" date="">
<element type="numeric" label="高度">
<value val="0"/>
<show object="true" label="true" ev="3"/>
<condition showObject="限定雙曲線 ≠ 1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-3" y="-11"/>
<labelMode val="1"/>
<slider min="-4.4" max="6.6" absoluteScreenLocation="true" width="150" x="313" y="164" fixed="true" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="14" type="0" typeHidden="1"/>
<animation step="0.2" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="傾斜">
<value val="0.91"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<condition showObject="限定拋物線 ≠ 1 ∧ 限定雙曲線 ≠ 1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-7" y="0"/>
<labelMode val="1"/>
<slider min="-0.4" max="2" absoluteScreenLocation="true" width="200" x="63" y="121" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="繞Z軸">
<value val="0"/>
<symbolic val="true" />
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-3.141592653589793" max="3.141592653589793" absoluteScreenLocation="true" width="200" x="12" y="89" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="π / 90" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="平移">
<value val="2.5"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<condition showObject="限定拋物線 ≠ 1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-3.9" max="4.1" absoluteScreenLocation="true" width="200" x="63" y="71" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="Point">
<input a0="zAxis"/>
<output a0="A"/>
</command>
<element type="point3d" label="A">
<show object="false" label="true" ev="20"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="0" z="5" w="1"/>
<pointSize val="5"/>
</element>
<command name="Circle">
<input a0="A" a1="3.85" a2="zAxis"/>
<output a0="c"/>
</command>
<element type="conic3d" label="c">
<show object="false" label="false" ev="20"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-14.822500000000002" A3="0" A4="0" A5="0"/>
<eqnStyle style="parametric"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="zAxis"/>
<output a0="B"/>
</command>
<element type="point3d" label="B">
<show object="false" label="true" ev="20"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="0" w="1"/>
<pointSize val="4"/>
</element>
<command name="Cone">
<input a0="c" a1="(-z(A))"/>
<output a0="a" a1="d" a2="圓錐上"/>
</command>
<element type="quadriclimited" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conic3d" label="d">
<show object="false" label="false" ev="20"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="0" A3="0" A4="0" A5="0"/>
<eqnStyle style="parametric"/>
</element>
<element type="quadricpart" label="圓錐上">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<eqnStyle style="implicit"/>
</element>
<element type="conic3d" label="c">
<show object="false" label="false" ev="20"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-14.822500000000002" A3="0" A4="0" A5="0"/>
<eqnStyle style="parametric"/>
</element>
<command name="Mirror">
<input a0="圓錐上" a1="xOyPlane"/>
<output a0="圓錐下"/>
</command>
<element type="quadricpart" label="圓錐下">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="-1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Translate">
<input a0="Translate[Rotate[Rotate[Plane[(-1, 0, 0), (1, 0, 0), (0, 1, 0)], 傾斜, xAxis], 繞Z軸, zAxis], Vector[(0, 平移, 0)]]" a1="Vector[(0, 0, 高度)]"/>
<output a0="e"/>
</command>
<element type="plane3d" label="e">
<show object="false" label="false" ev="23"/>
<objColor r="255" g="255" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="-1.579007479379901" z="1.227491498977623" w="3.9475186984497523"/>
<fading val="0"/>
<lineStyle thickness="0" type="0" typeHidden="2"/>
</element>
<command name="IntersectPath">
<input a0="e" a1="圓錐上"/>
<output a0="上截痕"/>
</command>
<element type="conic3dpart" label="上截痕">
<show object="true" label="false" ev="20"/>
<objColor r="220" g="20" b="60" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
<eigenvectors x0="0" y0="1" z0="1.0" x1="-1" y1="0" z1="1.0"/>
<matrix A0="NaN" A1="NaN" A2="NaN" A3="NaN" A4="NaN" A5="NaN"/>
<eqnStyle style="parametric"/>
</element>
<command name="Corner">
<input a0="上截痕"/>
<output a0="C" a1="D" a2="E" a3="F"/>
</command>
<element type="point3d" label="C">
<show object="false" label="true" ev="20"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="D">
<show object="false" label="true" ev="20"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="E">
<show object="false" label="true" ev="23"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="F">
<show object="false" label="true" ev="23"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<command name="IntersectPath">
<input a0="e" a1="圓錐下"/>
<output a0="下截痕"/>
</command>
<element type="conic3dpart" label="下截痕">
<show object="false" label="false" ev="20"/>
<condition showObject="高度 < 3.1 ∨ 平移 ≠ 2.5"/>
<objColor r="220" g="20" b="60" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
<eigenvectors x0="0" y0="1" z0="1.0" x1="-1" y1="0" z1="1.0"/>
<matrix A0="1" A1="0.007119696725322144" A2="7.25" A3="0" A4="-1" A5="1.534364373722029"/>
<eqnStyle style="parametric"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelOffset x="18" y="191"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="


SetViewDirection( Vector( (0,0,0),(-3,2,-1) ))"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="116" height="111" />
<caption val="還原視角"/>
</element>
<element type="point" label="H3">
<show object="false" label="true" ev="43"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.62" y="2.96" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="255" b="204" alpha="255"/>
<layer val="0"/>
<labelOffset x="140" y="191"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="
高度=2.5
平移=2.5
繞Z軸=0
傾斜=0
限定拋物線=0




"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="121" height="50" />
<caption val="(1) 圓 "/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="0"/>
<labelOffset x="270" y="190"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="高度=0
平移=2.5
繞Z軸=0
傾斜=0.5
限定拋物線=0


"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="121" height="50" />
<caption val="(2)橢 圓"/>
</element>
<element type="button" label="button3">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="175" g="238" b="238" alpha="255"/>
<layer val="0"/>
<labelOffset x="140" y="246"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="高度=0
平移=2.5
繞Z軸=0
傾斜=0.91
SetViewDirection( Vector( (0,0,0),(-3,2,-1) ))
限定拋物線=1
限定雙曲線=0


"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="121" height="50" />
<caption val="(3)拋物線"/>
</element>
<element type="button" label="button4">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="239" b="213" alpha="255"/>
<layer val="0"/>
<labelOffset x="270" y="245"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="高度=2.4
平移=3
繞Z軸=0
傾斜=1.57
SetViewDirection( Vector( (0,0,0),(-3,2,-1) ))
限定拋物線=0
限定雙曲線=1
"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="121" height="50" />
<caption val="(4)雙曲線"/>
</element>
<command name="Segment">
<input a0="(0, 0, -8)" a1="(0, 0, 8)"/>
<output a0="貫軸"/>
</command>
<element type="segment3d" label="貫軸">
<show object="true" label="false" ev="23"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="貫軸" a1="下截痕"/>
<output a0="G" a1="H"/>
</command>
<element type="point3d" label="G">
<show object="true" label="false" ev="20"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="H">
<show object="true" label="false" ev="20"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="4"/>
</element>
<expression label="case" exp="1"/>
<element type="numeric" label="case">
<value val="1"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="2"/>
<animation speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""直圓錐面與平面的截痕""/>
<element type="text" label="text1">
<show object="true" label="false" ev="25"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2" size="18" style="1"/>
<absoluteScreenLocation x="10" y="42"/>
</element>
<command name="PointIn">
<input a0="e"/>
<output a0="e1"/>
</command>
<element type="point3d" label="e1">
<show object="false" label="false" ev="20"/>
<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="-6" y="-3.6988320698369987" z="-7.9739877708685025" w="1"/>
<pointSize val="5"/>
</element>
<command name="Segment">
<input a0="(0, -10, 0)" a1="(0, 2.5, 0)"/>
<output a0="f1"/>
</command>
<element type="segment3d" label="f1">
<show object="false" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="PointIn">
<input a0="e"/>
<output a0="e2"/>
</command>
<element type="point3d" label="e2">
<show object="false" label="false" ev="20"/>
<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="6" y="-3.6988320698369987" z="-7.9739877708685025" w="1"/>
<pointSize val="5"/>
</element>
<command name="PointIn">
<input a0="e"/>
<output a0="e3"/>
</command>
<element type="point3d" label="e3">
<show object="false" label="true" ev="20"/>
<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="6" y="6.121099921983989" z="4.6580720641707085" w="1"/>
<pointSize val="5"/>
</element>
<command name="PointIn">
<input a0="e"/>
<output a0="e4"/>
</command>
<element type="point3d" label="e4">
<show object="false" label="true" ev="20"/>
<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="-6" y="6.121099921983989" z="4.6580720641707085" w="1"/>
<pointSize val="5"/>
</element>
<command name="Polygon">
<input a0="{e1, e2, e3, e4}"/>
<output a0="q1"/>
</command>
<element type="polygon3d" label="q1">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="20"/>
<objColor r="255" g="255" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="text2" exp=""L""/>
<element type="text" label="text2">
<show object="true" label="false" ev="37"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="2"/>
<startPoint x="-0.1" y="-0.1" z="8.2" w="1"/>
</element>
<command name="Translate">
<input a0="Translate[Rotate[Rotate[f1, 傾斜, xAxis], 繞Z軸, zAxis], Vector[(0, 平移, 0)]]" a1="Vector[(0, 0, 高度)]"/>
<output a0="f2"/>
</command>
<element type="segment3d" label="f2">
<show object="true" label="false" ev="20"/>
<condition showObject="高度 ≟ 3.2 ∧ 平移 ≟ 2.5 ∧ 傾斜 ≟ 0.91"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="限定拋物線" exp="1"/>
<element type="numeric" label="限定拋物線">
<value val="1"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="1"/>
<labelMode val="2"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button5">
<show object="true" label="true" ev="3"/>
<condition showObject="限定拋物線 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="1"/>
<labelOffset x="85" y="72"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection( Vector( (0,0,0),(-3,0,0) ))"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<dimensions width="116" height="50" />
<caption val="側看截痕"/>
</element>
<expression label="限定雙曲線" exp="0"/>
<element type="numeric" label="限定雙曲線">
<value val="0"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="1"/>
<labelMode val="2"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="polyhedron" label="Pyramid">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false" ev="20"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="polyhedron" label="Prism">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false" ev="20"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="polyhedron" label="Archimedean">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false" ev="20"/>
<objColor r="211" g="47" b="47" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>