elow, where the left offset curve 
    (the red line) forms a loop when the main curve takes a sharp left turn.
  </p>

    <p class="img">
      <img src="figure/render-loop-1.svg" width="30%">
    </p>
    <p>
    The 'vwline' package eliminates those loops by calling 
    <code>polysimplify</code> from 
    the 'polyclip' package (<a href="#polyclip">Johnson and Baddeley, 2017</a>) on the
    final closed shape (after adding line ends).  In the example below,
    the left image shows offset curves that c