Читать книгу Rethinking Prototyping - Группа авторов - Страница 137

The tangent planes of a curve c(u) on a surface envelope a developable surface G, called the tangent developable. For a point x on c(u), there is exactly one tangent to the curve c(u) and exactly one ruling of G that touches at x; the directions of these two lines are called conjugate, see Fig. 5. If two families of curves on a surface are such that through every point, there is one member of each family and their directions are conjugate, we speak of a conjugate network of curves. For equivalent definitions of conjugate directions see (Zadravec et al 2010), who give different examples of conjugate networks, the most important of which are principal curvature lines.

(Liu et al 2011) show that conjugate networks are a good choice for the initialization of a planarization algorithm, which can be derived from the analytical definition of conjugate directions (Do Carmo 1976). We will use conjugate directions for the choice of a ruling direction of developable strips in sec. 4.3.