The sum/difference of two parametric surfaces descripted in monmomial bases is straight forward as the following example shows:
$G_{1,1}(u_1,v_1) = 3*v_1(v_1-1)^2(u_1-1)^3 + 3u_1$
$G_{2,1}(u_2,v_2) = u^3_2v^2_2-u^3_2 $ \
and the difference of the two surfaces results in:
$H_1(u_1,v_1,u_2,v_2) = 3*v_1(v_1-1)^2(u_1-1)^3 + 3u_1 - u^3_2v^2_2 + u^3_2$
However I do not know how to sum/difference the two surfaces if they are defined in Bernstein Basis:
Tensor surface 1: $ F(u_1,v_1) = \sum_{i}^n \sum_{j}^m f_{i,j} *N_{i,p}(u_1) *N_{j,q}(v_1) $
Tensor surface 2: $ G(u_2,v_2) = \sum_{k}^n \sum_{l}^m g_{k,l} *N_{k,p}(u_2) *N_{l,q}(v_2) $
wherein $f_{i,j}$ and $g_{k,l}$ represent the coefficients.
What is the representation of the sum/difference of $H(u_1,v_1,u_2,v_2) =F(u_1,v_1) - G(u_2,v_2)$ represented in Bernstein polynom form? In particular concerning the coefficients $h_{i,j,k,l}$.