If one parameter is held at a constant value then the
above will represent a curve. Thus P(u,a) is a curve on the surface with the
parameter v being a constant a.
In a bicubic surface patch cubic polynomials are used to represent the edge
curves P(u,0), P(u,1), P(0,v) and P(1,v)as shown below. The surface is then
generated by sweeping all points on the boundary curve P(u,0) (say) through
cubic trajectories,defined using the parameter v, to the boundary curve P(u,1).
In this process the role of the parameters u and v can be reversed.
|
![]() |