Uniform Motion Point Tool on Polyline
2020-05-10 04:25
This GeoGebra example demonstrates a construction tool for a point moving at a constant speed along a polyline. By utilizing commands such as PolyLine, Sequence, Append, and conditional statements, it achieves the animation effect of a point moving uniformly along a multi-segment path. This tool can be used to illustrate path motion, piecewise functions, or combined uniform linear motions, helping
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<gui>
<window width="1355" height="572" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2767527675276753" orientation="1" />
</panes>
<views>
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<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1354" height="571"/>
<coordSystem xZero="118.36545238533193" yZero="275.86037424850775" scale="62.1021921667866" yscale="62.10217284718856"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<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" positiveAxis="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" positiveAxis="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="2" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label="l1" exp="{(0, 0), (1, 0), (3, 1), (5, 3)}"/>
<element type="list" label="l1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="PolyLine">
<input a0="l1"/>
<output a0="f"/>
</command>
<element type="polyline" label="f">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Sequence">
<input a0="abs(l1(k + 1) - l1(k))" a1="k" a2="1" a3="Length[l1] - 1"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="v">
<value val="1.2"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-8" y="-3"/>
<labelMode val="1"/>
<slider min="-5" max="5" width="2" x="0.40517590449518026" y="-2.091170720275782" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="Append">
<input a0="0" a1="Sequence[Sum[l2, k] / v, k, 1, Length[l2]]"/>
<output a0="l3"/>
</command>
<element type="list" label="l3">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="t">
<value val="2.148"/>
<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="f / v" absoluteScreenLocation="true" width="200" x="251" y="475" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="0.4" type="0" playing="true"/>
</element>
<command name="CountIf">
<input a0="t ≥ p" a1="p" a2="l3"/>
<output a0="a"/>
</command>
<element type="numeric" label="a">
<value val="2"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="If">
<input a0="a < Length[l1]" a1="l1(a) + ((v * (t - l3(a))) * UnitVector[l1(a + 1) - l1(a)])" a2="l1(a)"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-9" y="-7"/>
<labelMode val="0"/>
<coords x="2.411048336521467" y="0.7055241682607336" z="1"/>
<pointSize val="6"/>
<pointStyle val="0"/>
<caption val="$\Large{动点} $"/>
</element>
<expression label="text1" exp=""制作：肖建伟\\
公众号：\ \ GeoGebra物理数学可视化\\
QQ群：\ \ 583765627""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<condition showObject="b"/>
<objColor r="255" g="255" b="0" alpha="0"/>
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<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
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<checkbox fixed="true"/>
<caption val="帮助"/>
</element>
</construction>
</geogebra>