Читать книгу Rethinking Prototyping - Группа авторов - Страница 143

For most algorithms approximating an input surface by a developable surface (Rose et al 2007) there is no explicit choice of ruling direction, which makes no difference in computer graphics, but if the panels are to be built, the ruling directions determine two of the panels’ edges, thus having significant impact on the overall look.

As mentioned in sec. 3.2, the conjugate direction (assuming an underlying surface S) is a good choice for the ruling but need not intersect the other curve. We mimic the construction of the tangent developable surface locally by fitting a cone, whose second ruling (the first is already given by the previous iteration) should ideally intersect b in a right angle (see the choice of zi in the step 1 of the algorithm). Note that this can only be the case if b were a principal curvature line of S, see (Pottmann et al 2007).

It follows that the algorithm gives the most pleasing results if the chosen family of input curves is part of a conjugate network of curves, such as a family of principal curvature lines, as can be expected.

Fig. 8 Design study Hotel Entrance with conical glass panels, where the curve network can be divided such that the base curves are ridges and the target curves valleys. This design could also be built with planar panels, but then the panels would not yield smooth reflection lines.