= Binary linear interpolatory subdivision
{title2=$p'_{2i}=p_i,\quad p'_{2i+1}=(p_i+p_{i+1})/2$}
The centered <subdivision mask> $[1,2,1]/2$ retains old <control points> and inserts edge midpoints. Its <control polygon> is unchanged as a geometric curve by refinement. Its basic limit is the hat $\phi(t)=\max(1-|t|,0)$, with support $[-1,1]$. This <linear spline> representation reproduces constants and linear functions, and is $C^0$ but generally not $C^1$ at its <spline knots>.
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