title: How to find endpoint coordinates with given start, length, and euler angles
body: <p>I'm working on some 3d fractals...  If I take any arbitrary point (x,y,z), start from there, and then draw a line of given length "d", in a direction defined by Euler angles... (by rotation A about the x-axis, B about the y-axis, and C about the z-axis) -- and then calculate the resulting endpoint of the line.</p>
  
  <p>This would be simple in 2 dimensions, as I could find the endpoint like:</p>
  
  <pre><code>endX = beginX + d * cos(angle)
  endY = beginY + d * sin(angle)
  </code></pre>
  
  <p>Basically, I need to fill in the blanks here:</p>
  
  <pre><code>endX = beginX + d * (??)
  endY = beginY + d * (??)
  endZ = beginZ + d * (??)
  </code></pre>
  
  <p>Where I only know angles defined by 3 rotations, 1 about each axis</p>