Special Shapes

There are no pre-defined special shapes in the ASDF. All trajectories use the same underlying type of spline – see ASDF Splines.

Square

Trajectories in the ASDF are smooth curves by default, and a little extra effort is required to create movements with sharp corners. There are two simple settings to get straight line segments: tension="1" or continuity="-1". Both options are shown in square.asd:

<asdf version="0.4">
  <par>
    <clip file="audio/marimba.ogg">
      <channel id="one" />
      <channel id="two" />
    </clip>
    <transform apply-to="one" tension="1">
      <o pos="0 2" />
      <o pos="-2 0" />
      <o pos="0 -2" />
      <o pos="2 0" />
      <o pos="closed" />
    </transform>
    <transform apply-to="two" continuity="-1">
      <o pos="0 2" />
      <o pos="2 0" />
      <o pos="0 -2" />
      <o pos="-2 0" />
      <o pos="closed" />
    </transform>
  </par>
</asdf>

Circle

Non-rational cubic polynomial curves – which is the type of curve the ASDF uses for position trajectories – cannot exactly describe circles. But this is no problem, because circles can be approximated very closely. This can be done by providing the corner points of a square and using a tension value of about -0.66. However, there is actually a way to create exact circles: by applying a rotation spline to a translated object. The example scene circle.asd shows both approaches:

<asdf version="0.4">
  <par>
    <clip file="audio/marimba.ogg">
      <channel id="one" pos="0 2" />
      <channel id="two" />
    </clip>
    <!-- this is a perfect circle: -->
    <transform apply-to="one">
      <o rot="-10" />
      <o rot="-100" />
      <o rot="-190" />
      <o rot="-280" />
      <o rot="closed" />
    </transform>
    <!-- this is extremely close to a circle: -->
    <transform apply-to="two" tension="-0.66">
      <o pos="0 2" />
      <o pos="2 0" />
      <o pos="0 -2" />
      <o pos="-2 0" />
      <o pos="closed" />
    </transform>
  </par>
</asdf>

In this example, the center of rotation is the origin. If the center of rotation is supposed to be somewhere else, it can be moved by applying a new <transform> element with the desired pos attribute to the <transform> that does the rotation.

Helix

A helical movement can be created by combining a (repeated) circular movement (using one of the methods shown above) with a linear movement perpendicular to the plane of the circle. This is shown in helix.asd:

<asdf version="0.4">
  <par>
    <clip id="ukulele" file="audio/ukewave.ogg" pos="-2 0" />
    <transform id="circular-motion" apply-to="ukulele" repeat="10">
      <o rot="0 0 0" />
      <o rot="0 0 90" />
      <o rot="0 0 180" />
      <o rot="0 0 -90" />
      <o rot="closed" />
    </transform>
    <transform id="forward-motion" apply-to="circular-motion">
      <o pos="0 -2" />
      <o pos="0 2" />
    </transform>
  </par>
</asdf>

In this example, the <clip> is offset to the left and a rotation spline rotates this offset multiple times around the roll axis. This circular motion is then translated along the default view direction. In this case, it doesn’t matter if forward-motion is applied to circular-motion or directly to ukulele.

Sinusoidal Oscillation

Sine waves are not directly supported by the ASDF, but they can be approximated to some degree. By setting speed="0" at the desired maxima and minima, something similar to sine and cosine oscillations can be created. This is illustrated in sine-wave.asd:

<asdf version="0.4">
  <par>
    <clip file="audio/marimba.ogg">
      <channel id="one" />
      <channel id="two" pos="0 2" />
    </clip>
    <transform id="left-right-motion" apply-to="one two" repeat="2">
      <o pos="0 0" />
      <o pos="2 0" speed="0" time="25%" />
      <o pos="-2 0" speed="0" time="75%" />
      <o pos="closed" />
    </transform>
    <transform id="forward-backward-motion" apply-to="one" repeat="2">
      <o pos="0 2" speed="0" />
      <o pos="0 -2" speed="0" time="50%" />
      <o pos="closed" />
    </transform>
  </par>
</asdf>

Lissajous Figures

Once we have sinusoidal oscillations (or at least something similar), we can make Lissajous figures, as shown in lissajous.asd:

<asdf version="0.4">
  <par repeat="2">
    <clip id="ukulele" file="audio/ukewave.ogg" vol="0.3" />
    <par repeat="3">
      <transform id="left-right" apply-to="ukulele">
        <o pos="-2 0" speed="0" />
        <o pos="2 0" time="50%" speed="0" />
        <o pos="closed" />
      </transform>
      <seq repeat="3">
        <transform id="front-back" apply-to="ukulele">
          <o pos="0 0" />
          <o pos="0 2" time="25%" speed="0" />
          <o pos="0 -2" time="75%" speed="0" />
          <o pos="closed" />
        </transform>
      </seq>
    </par>
  </par>
</asdf>