How to equidistant resample a line (or curve)?

I have a line l_1 given with a point series p_1,...,p_n. I now want a new line l_2 having k points: q_1,...,q_k. But for all i \in {1,...,k-1}: abs( q_i - q_i+1 ) = const, meaning the segments of l_2 are equidistant or uniform.

• k >= 2
• and p_1 and p_n should be in l_2.
• abs( p_i - p_i+1 ) not const

One solution is to approximate a line with a spline, and then subsample this again, to have uniform length segments then. Can I do any better? Is there any C++ code for that?

Ah, I've missed a specific detail: those q_i should be in l_1, meaning either they are on the line segments of l_1 or they are sample points of l_1.