title: Algorithm to cut a catmull-rom spline?
body: <p>I have a catmull-rom spline with 6 CVs and want to cut it at an arbitrary point along the spline. </p>
  
  <p>How do I calculate the end points of the two new splines so that they keep the shape as they had before they were cut in two? </p>
  
  <p>So, imagine this being the spline with 6 points:</p>
  
  <pre><code>p0      p2      p4
   \     / \     / \
    \   /   \C  /   \
     \ /     \ /     \
      p1      p3      p5
  </code></pre>
  
  <p>if I want to cut this spline at point C, I will then have two new splines with I guess 5 CVs each?</p>
  
  <pre><code>Spline #1: p0, p1, p2, X, C
  Spline #2: C, X, p3, p4, p5
  </code></pre>
  
  <p>Where X is a CV that I need to add in order to maintain the shape of the spline. But how do I calculate the position that X needs to be at?</p>
  
  <p>Or is my logic wrong altogether and there is a whole different solution to the problem?</p>
  
  <p>Thank you!</p>