Find bezier control-points for curve passing through N points

jwin68 picture jwin68 · Oct 10, 2011 · Viewed 16.8k times · Source

Considering the following nice solution for finding cubic Bézier control points for a curve passing through 4 points:

How to find control points for a BezierSegment given Start, End, and 2 Intersection Pts in C# - AKA Cubic Bezier 4-point Interpolation

I wonder, if there is a straightforward extension to this for making the Bézier curve pass through N points, for N > 2 and maybe N ≤ 20?

Answer

user392870 picture user392870 · Aug 26, 2013

This is a really old question, but I'm leaving this here for people who have the same question in the future.

@divanov has mentioned that there's no Bezier curve passing through N arbitrary points for N >4.

I think the OP was asking how to compute the control points to join multiple bezier curves to produce a single curve that looks smooth.

This pdf will show you how to compute the control points: http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf

which I found on this writeup http://corner.squareup.com/2012/07/smoother-signatures.html from Square about how they render a smooth curve that passes through all the sampled points of a mouse drawn signature.