title: How to translate a point into another plane space using Unity?
body: <p>I am currently slicing a three-dimensional mesh using Unity but I have encountered an issue that is causing artefacts on the final result. To slice a mesh that has already previously been sliced, I need to keep track of the previous triangulated surfaces so that they can be added to their new mesh. To do this, I am simply iterating over the facet's points and determining which point is above the plane and which is below and from there I construct two different facets. However, if the plane lies between two points, then it creates a gap in the triangulated facet.</p>
  
  <p><a href="https://i.stack.imgur.com/g1GjD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/g1GjD.png" alt="enter image description here"></a></p>
  
  <p>This can be seen in the above image where the blue lines represent <em>below</em> the plane, and red <em>above</em>.</p>
  
  <p>I know a solution to this but I am unsure how to do it.</p>
  
  <p>I already have the plane's position, which is directly where I want a new point inserted (which is directly between the two points where the gap is visible and this should add an extra triangle to close the gap) however this plane position is not on the triangulated plane.</p>
  
  <p>How would I translate this point into the facet's plane?</p>