 the values of $\underline{R}_{{\mathcal{C}},j}$, $\bar{{r}}_{{\mathcal{C}},j}  ({\boldsymbol{\theta}},{\boldsymbol{\theta}}')$, $\underline{{r}}_{{\mathcal{C}},j}  ({\boldsymbol{\theta}},{\boldsymbol{\theta}}')$ 