Fig. 14

Grids for rules $A(2,2)$ and $A(3,2)$. Top: blue circles: the grid for rule $A(2,2)$ (i.e. level 2 in 2 spatial dimensions) using Gauss-Legendre quadrature. Red crosses: grid corresponding to $U^0\otimes U^2$ (one point horizontally, 7 vertically). Black dots: grid corresponding to $U^1\otimes U^1$ (3 points both horizontally and vertically). The three black dots on the y-axis correspond to $U^0\otimes U^1$, while the three black dots on the x-axis correspond to $U^1\otimes U^0$. Bottom: the grid for rule $A(3,2)$ (i.e. level 3 in 2 spatial dimensions). Rule $A(2,2)$ has 21 grid points, and rule $A(3,2)$ has 73.