The least concave majorant, $\widehat{F}$, of a continuous function $F$ on a closed interval, $I$, is defined by $$\widehat{F}\left(x\right)=inf\{G\left(x\right):G\ge F,\phantom{\rule{4pt}{0ex}}G\phantom{\rule{4.0pt}{0ex}}\text{concave}\},\phantom{\rule{1.0em}{0ex}}x\in I.$$
We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on $I$. Given any function $F\in {\mathcal{C}}^{4}\left(I\right)$, it can be well-approximated on $I$ by a clamped cubic spline $S$. We show that $\widehat{S}$ is then a good approximation to $\widehat{F}$. We give two examples, one to illustrate, the other to apply our algorithm.