Let $C$ be a non-empty, convex and closed subset of $\mathbb{R}^d$. Determine explicitly $\operatorname{proj}_C$ in the following cases:
$$\text{i) } C = \mathbb{R}_+^d, \quad \text{ii) } C = \left\{y \in \mathbb{R}^d : \|y\| \leqslant 1\right\}$$
$$\text{iii) } C = \left\{y \in \mathbb{R}^d : \sum_{i=1}^d y_i \leqslant 1\right\}, \quad \text{iv) } C = [-1,1]^d$$