Cubic "bezier" curve of grade n
#include &lt;vector&gt; is pointless. There is no vectors in the code.
Unless I am missing something obvious, temp_space plays no role in the calculations.
pointsi and pointsj do not sound right (too much of visual noise makes it hard to tell them apart). It is one of the rear cases where I'd go for plain i and j.
t_step_t is confusing, and strictly speaking unnecessary. You may calculate it at the point of invocation as

result[t] = *besier_interp(..., t * t_step);