Approaching an Approximation of Freeform Surfaces by Developable Strips using Apparent Contours

Francisco González-Quintial, Antonio Sánchez-Parandiet and Javier Barrallo
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 127–134 Regular Papers


The construction of free-form surfaces is limited to what is possible by graphical and constructive control. Over a few years we have seen an important development in the control of form through graphic digital technology: software and hardware that has allowed truly spectacular constructions.

An important line of research, not only in architecture but also in engineering, even sculpture, has been the adaptation of free forms by developable surfaces using different systems, many of them based on differential geometry.

Re-interpreting some methods of projective geometry that allow the use of certain CAD software, and jumping from physical to digital drawing systems, a method has been developed that allows the adaptation of free forms by developable surfaces using the apparent contours that we can draw over these free form surfaces. By using them we can construct two types of developable surfaces (cones and cylinders) that touch the surface tangentially to the contours.