曲面指令练习：柱坐标与球坐标的相互转化
2019-12-27 07:44
本GeoGebra范例演示了柱坐标系与球坐标系之间的相互转化过程。通过Surface等命令构建三维曲面，直观展示不同坐标系下参数方程的几何意义及空间曲面的生成原理，适合微积分与解析几何的学习与教学。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.549.0" app="classic" platform="d" id="9625fac1-913c-4f2d-bd0a-9b5851f1b2db" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="876" height="639" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.634703196347032" orientation="1" />
</panes>
<views>
<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="true" location="3,3" size="291" 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="4097" visible="false" inframe="true" stylebar="true" location="1,0" size="235" window="366,109,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="288" window="100,100,600,400" />
<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="346" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" 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 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="true" inframe="false" stylebar="true" location="3" size="556" window="100,100,600,400" />
</views>
<toolbar show="true" 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="288" height="443"/>
<coordSystem xZero="187.5504325291928" yZero="350.111548502479" scale="90.44591975465671" yscale="90.44591975465708"/>
<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" tickDistance="0.7853981633974483" tickExpression="π / 4"/>
<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="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-0.2755034975483679" yZero="0.01977813731700627" zZero="0.0815970098194963" scale="19.527378189123286" xAngle="23.0" zAngle="21693.858720559005"/>
<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="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="numeric" label="n">
<value val="5.0"/>
<symbolic val="true" />
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="3" max="15" absoluteScreenLocation="true" width="200.0" x="30.0" y="90.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="d">
<value val="1.0"/>
<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="200.0" x="30.0" y="130.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="6.0"/>
<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="10" absoluteScreenLocation="true" width="200.0" x="24.0" y="200.0" 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="Surface">
<input a0="(((((1 + (d * (If[abs(s) < 45°, sin(45°) / sin(90° - abs(s)), sin(45°) / sin(180° - abs(s))] - 1))) * (1 + (d * (sin(90° - (180°) / n) / sin(90° + (180°) / n - (t - ((360°) / n * floor((n * t / (360°)))))) - 1)))) * b) * cos(t)) * cos(s))" a1="(((((1 + (d * (If[abs(s) < 45°, sin(45°) / sin(90° - abs(s)), sin(45°) / sin(180° - abs(s))] - 1))) * (1 + (d * (sin(90° - (180°) / n) / sin(90° + (180°) / n - (t - ((360°) / n * floor((n * t / (360°)))))) - 1)))) * b) * sin(t)) * cos(s))" a2="(((1 + (d * (If[abs(s) < 45°, sin(45°) / sin(90° - abs(s)), sin(45°) / sin(180° - abs(s))] - 1))) * b) * sin(s))" a3="t" a4="0" a5="(2 * π)" a6="s" a7="((-π)) / 2" a8="π / 2"/>
<output a0="a"/>
</command>
<element type="surfacecartesian3d" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.5799999833106995"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
</construction>
</geogebra>