structural:expansion, information:extraction, stylistic:style_transfer, linguistic:voice_change
Two dimensions

In two dimensions, the domain A {\displaystyle A} may be divided into a number of two-dimensional cells A i {\displaystyle A_{i}} such that A = ⋃ i A i {\textstyle A=\bigcup _{i}A_{i}}. Each cell then can be interpreted as having an "area" denoted by Δ A i {\displaystyle \Delta A_{i}}. The two-dimensional Riemann sum is S = ∑ i = 1 n f (x i ∗, y i ∗) Δ A i, {\displaystyle S=\sum _{i=1}^{n}f(x_{i}^{*},y_{i}^{*})\,\Delta A_{i},} where (x i ∗, y i ∗) ∈ A i {\displaystyle (x_{i}^{*},y_{i}^{*})\in A_{i}}.