I want to create s coons patch surface from four boundary curves s1(u), s2(u) q1(v), q2(v)
I know that equations are the following (added screenshots from a presentation):
There are a few parts of the equations that are not fully understand and i did not find any good explanation:
In s1(u,v) what is the meaning of p1v(u) and p2v(u)? same goes for q1u(v) and q2u(v) in s2(u,v).
In the A matrix, what is the meaning of A00(u,v)..A11(u,v). What would be the value of these parameters if p1,p2 are only functions of u (and not v) and q1,q2 are only function of v.
I would appreciate any help on this issue.
The boundary curves are $P_1(u), P_2(u), Q_1(\nu), Q_2(\nu)$ and are complemented by four transverse derivative functions $P_1^\nu(u), P_2^\nu(u), Q_1^u(\nu), Q_2^u(\nu)$. (Verifying compatibility conditions at the corners.)
The $^u$ and $^\nu$ exponents denote the derivative with respect to these variables.
The $A_{ij}$ elements are values of the boundary curves and their partial derivatives (first order and mixed) at the four corners.
Even though the boundary curves are functions of a single parameter, one can think of them as being embedded in a surface for which the tangent plane is known on the whole boundary.