几何图形的旋转变换交互演示
2014-03-15 05:45
本范例演示平面几何中的旋转变换。通过交互式滑块控制旋转角度，展示多边形、圆、矩形等几何图形绕指定中心点旋转的动态过程。用户可观察旋转前后图形的对应点、对应边和对应角的关系，直观理解旋转变换保持图形形状与大小不变的等距性质。支持动态调节旋转中心与旋转角度等关键参数。
所属专题
坐标几何（中一）GeoGebra互动教材
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<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r3">
<show object="false" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="3" z="-12"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="F" a1="(k * theta)" a2="O"/>
<output a0="F'"/>
</command>
<element type="point" label="F'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="G" a1="(k * theta)" a2="O"/>
<output a0="G'"/>
</command>
<element type="point" label="G'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="E'" a1="F'" a2="O'" a3="G'"/>
<output a0="Rect'" a1="r1'" a2="r2'" a3="r3'" a4="r4'"/>
</command>
<element type="polygon" label="Rect'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="255" g="127" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment" label="r1'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r2'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r3'">
<show object="false" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r4'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="showRect">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="showPoint"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="510" y="10"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Show hints"/>
</element>
<expression label="input" exp=""P""/>
<element type="text" label="input">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint x="-7.500093585577798" y="1.9405328258610672" z="1"/>
</element>
<command name="Textfield">
<input a0="input"/>
<output a0="inputBox1"/>
</command>
<element type="textfield" label="inputBox1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="113" y="11"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript onUpdate="SetCaption[E,If[showAxis,input+" = %v",input]] SetCaption[E',If[showAxis,input+"' = %v",input+"'"]]"/>
<linkedGeo exp="input"/>
<length val="2"/>
<caption val="_"/>
</element>
<element type="boolean" label="showAxis">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="710" y="10"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="ShowAxes[1,showAxis] SetCaption[E,If[showAxis,input+" = %v",input]] SetCaption[E',If[showAxis,input+"' = %v",input+"'"]]"/>
<caption val="Show coordinates"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="865" y="65"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang] "/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="974" y="59"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[showPoint,If[lang==1,"點","Point"]] SetCaption[showPic,If[lang==1,"三角形ABC","Triangle ABC"]] SetCaption[showRect,If[lang==1,"顯示提示","Show hints"]] SetCaption[showAxis,If[lang==1,"顯示坐標","Show coordinates"]] SetCaption[showImage,If[lang==1,"顯示旋轉影像","Show image"]] "/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<expression label="text1" exp=""" + (If[lang ≟ 1, "繞O點：", "Rotate about point O:"]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="11"/>
<condition showObject="showPoint ∨ showPic"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="218" y="38"/>
</element>
</construction>
</geogebra>