I understand de Casteljau's algorithm and I am familiar although not fully experienced with B-Splines. I am trying to understand the geometric interpretation of B-splines through the algorithm (just like how de Casteljau's algorithm shows the geometric interpretation of Bézier curves). Thank you in advance.

  • $\begingroup$ I'm not familiar with the Lane Resienfield algorithm but I think you need to be more specific as to what you don't understand. $\endgroup$
    – Simon F
    Commented Oct 16, 2017 at 13:57
  • $\begingroup$ The actual algorithm in a geometrical sense. Like, with Castlejeaus you can explain it by taking fractions of the straight lines (1/3 of the line between A and B for example), recursively. I need something similar but for lane resienfield $\endgroup$
    – Makogan
    Commented Oct 16, 2017 at 22:28

1 Answer 1


What you're looking for is called de Boor's algorithm. It lets you compute a point on a b-spline curve by doing a series of linear interpolation (LERP) calculations. So, it works very much like the de Casteljau algorithm for Bezier curves. In fact, the de Casteljau algorithm is a special case of de Boor's algorithm.

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    $\begingroup$ "Links to external resources are encouraged, but please add context around the link so your fellow users will have some idea what it is and why it’s there. Always quote the most relevant part of an important link, in case the target site is unreachable or goes permanently offline." - Computer Graphics SE Help Center $\endgroup$ Commented Nov 1, 2017 at 15:56

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