<simulation>
  <header>
    <title lang="french">Cycloïde</title>
    <title lang="english">Cycloïd</title>
    <title lang="spanish">Cicloide</title>
    <author>Stéphane Mottelet, Guillaume Barbaud</author>
    <keywords lang="french">simulation,scilab,xml</keywords>
    <keywords lang="spanish">Simulación, Scilab, XML</keywords>
  </header>
  <notes lang="french">
    <p>Cliquer sur le centre du cercle et déplacer la souris pour le faire rouler.</p>
  </notes>
  <notes lang="english">
    <p>Click on the center of the circle and use the mouse to make it roll.</p>
  </notes>
  <notes lang="spanish">
    <p>Haga clic en el centro del círculo y mueva el ratón para hacerlo rodar</p>
  </notes>
  <parameters><section>
      <title lang="french">Paramètres de la courbe</title>
      <title lang="english">Parameters of the curve</title>
      <title lang="spanish">Parámetros de la curva</title>
      <scalar label="R" state="hidden"><name lang="french">R</name><name lang="spanish">R</name><value>1</value></scalar>
      <point label="center" state="hidden"><name lang="french">Centre du cercle</name><name lang="english">Center of the circle</name><name lang="spanish">Centro del círculo</name><x1 label="xc">
          <value>1</value>
        </x1><x2 label="yc">
          <value>1</value>
        </x2><constraints>
          <curve ref="seg" />
        </constraints></point>
      <scalar label="tmax" state="hidden"><name lang="french">tmax</name><name lang="spanish">tmax</name><value>xc/R</value></scalar>
    </section></parameters>
  <compute>
    <defdomain1d label="t">
      <interval steps="2+int(tmax/6.3*256)">
        <initialvalue>-0.1</initialvalue>
        <finalvalue>tmax</finalvalue>
      </interval>
    </defdomain1d>
    <defdomain1d label="theta">
      <interval steps="128">
        <initialvalue>0</initialvalue>
        <finalvalue>2*%pi</finalvalue>
      </interval>
    </defdomain1d>
  </compute>
  <graphs>
    <polyline label="seg">
      <vertex x1="0" x2="R" />
      <vertex x1="8*R" x2="R" />
    </polyline>
    <parametriccurve2d label="cercle">
      <name lang="french">Cercle</name>
      <name lang="english">Circle</name>
      <name lang="spanish">Circulo</name>
      <refdomain1d ref="theta" />
      <x1>
        <name lang="french">abscisse</name>
        <name lang="english">abscissa</name>
        <name lang="spanish">Abscisa</name>
        <value>R*tmax+R*cos(theta)</value>
      </x1>
      <x2>
        <name lang="french">ordonnee</name>
        <name lang="english">ordinate</name>
        <name lang="spanish">Ordenada</name>
        <value>R+R*sin(theta)</value>
      </x2>
    </parametriccurve2d>
    <parametriccurve2d label="cycloide">
      <name lang="french">Cycloïde</name>
      <name lang="english">Cycloïd</name>
      <name lang="spanish">Cicloide</name>
      <refdomain1d ref="t" />
      <x1 label="x">
        <name lang="french">abscisse</name>
        <name lang="english">abscissa</name>
        <name lang="spanish">Abscisa</name>
        <value>R*(t-sin(t))</value>
      </x1>
      <x2 label="y">
        <name lang="french">ordonnee</name>
        <name lang="english">ordinate</name>
        <name lang="spanish">Ordenada</name>
        <value>R*(1-cos(t))</value>
      </x2>
    </parametriccurve2d>
    <polyline label="rayon">
      <vertex x1="R*tmax" x2="R" />
      <vertex x1="R*(tmax-sin(tmax))" x2="R*(1-cos(tmax))">
        <name>M</name>
        <name lang="english">M</name>
        <name lang="spanish">M</name>
      </vertex>
    </polyline>
  </graphs>
  <display background="blue">
    <window>
      <title lang="french">Cycloïde</title>
      <title lang="english">Cycloïd</title>
      <title lang="spanish">Cicloide</title>
      <axis2d iso="yes" position="origin" xmax="8*R" xmin="0" ymax="3*R" ymin="-2*R">
        <drawcurve2d ref="cycloide" color="red" />
        <drawcurve2d ref="cercle" />
        <drawcurve2d ref="rayon" color="green" />
        <drawpoints ref="center" />
      </axis2d>
    </window>
  </display>
</simulation>