 Projection onto a box-constrained hyperplane

For $C=\{x:0\le x\le 1,a^{T}x=b\}$, the projection of $y$ has coordinates $x_i=\min (1,\max (0,y_i-\nu a_i))$, where the scalar multiplier $\nu$ is chosen so that $a^{T}x=b$. Thus the projection reduces to a continuous one-dimensional root-finding problem.