Читать книгу Rethinking Prototyping - Группа авторов - Страница 139

Take a general space curve c(u), connect every point on it and an arbitrary point a (the apex) through a line segment to get a surface s(u,v) = v • c(u) + (1-v) • a. In this parameterization, the u-isolines are the straight lines (rulings of the developable surface) and the v-isolines are curves similar to c(u). If you take any curve segment on a v-isoline and the corresponding, similar curve segment on another v-isoline, you have a conical panel i.e. a patch that lies on a general cone and two of the border curves lie on intersecting lines. We will model developable strips with these in section 4. The four - if you chose the apex instead of one the v-isolines, there are only three - corner points lie on the plane spanned by the bordering rulings, so planarization is obvious. Cylindrical panels are even easier, v-isolines are congruent to c(u) and u-isolines are parallel line segments, planarize as above.

Note that in both cases the u- and v-isolines form a conjugate curve network of sec. 3.1, as the cone (or cylinder) is c(u)’s tangent developable.