Morphogenesis of surfaces with planar lines of curvature and application to architectural design

This article presents a methodology to generate surfaces with planar lines of curvature from two or three curves and tailored for architectural design. Meshing with planar quadrilateral facets and optimal offset properties for the structural layout are guaranteed. The methodology relies on the invariance of circular meshes by spherical inversion and discrete Combescure transformations, and uses parametrisation of surfaces with cyclidic patches. The shapes resulting from our methodology are called super-canal surfaces by the authors, as they are an extension of canal surfaces. An interesting connection to shell theory is recalled, as the shapes proposed in this paper are at equilibrium under uniform normal loading. Some applications of these shapes to architecture are shown.