The points that make up the quadrature rules in this encyclopedia are represented using barycentric coordinates. If \(\mathbf{v}_0,\dots,\mathbf{v}_{m-1}\in\mathbb{R}^d\) are the coordinates of the vertices of a integration domain and \((p_0,\dots,p_{m-1})\in\mathbb{R}^m\) is the barycentric coordinates of a quadrature point, then the coordinates of the corresponding quadrature point on the domain is given by
$$\sum_{i=0}^{m-1}p_i\mathbf{v}_i.$$
The quadrature weights in this encyclopedia are normalised for a domain of volume 1, so an integral can be approximated by
$$\int_I f(x)\,\mathrm{d}x\approx v(I)\sum_{i=0}^{n-1}w_if(\mathbf{p}_i),$$
where \(\{\mathbf{p}_0,\dots,\mathbf{p}_{n-1}\}\subset\mathbb{R}^d\) and \(\{w_0,\dots,w_{n-1}\}\subset\mathbb{R}\) are the quadrature points and weights, and \(v(I)\) is the volume of the integration domain \(I\).