A \(d\)-dimensional simplex is defined by
$$
S = \{ (\omega_1, \ldots, \omega_d) \in \mathbb{R}^d_+ : \sum_{i=1}^d \omega_i = 1 \}.
$$
Here the function defines the simplex as
$$
S = \{ (\omega_1, \ldots, \omega_d) \in [a,b]^d : \sum_{i=1}^d \omega_i = 1 \}.
$$
When d = 2 and \([a,b] = [0,1]\), a grid of points of the form
\(\{ (\omega_1, \omega_2) \in [0,1] : \omega_1 + \omega_2 = 1 \}\) is generated.