An area-oriented analytical visibility method for displaying parametrically defined tensor-product surfaces (Q1080644)

The authors consider surfaces of the form \[ S(u,v)=(x(u,v),y(u,v),z(u,v))=\sum^{n-1}_{i=0}\sum^{m- 1}_{j=0}u^ iC_{ij}v^ j \] where \(0\leq u,v\leq 1\) and \(C_{ij}=(x_{ij},y_{ij},z_{ij})\). Visible areas of this surface are bounded either by the contour curves or the boundary curves of the surface S(u,v). The authors develop an analytical algorithm for the determination of the contour curves in the (u,v)-parameter plane. They introduce the concept of quantitative visibility status to compute the visible segments of the boundary curves and contour curves of the surface S(u,v).