Fabrication-Aware Freeform Design based on Shape Space Exploration

Freeform surfaces play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction of architectural freeform structures remains a challenge. In order to make a freeform design realizable, an optimization process known as rationalization has to be applied. This means its decomposition into smaller parts, thereby meeting two competing objectives: feasibility, and consistency with the designer`s intentions. Depending on what constitutes the design, there have been different approaches to this problem (with strong involvement of our research group) which have led to different kinds of specific geometric and computational questions. Mostly these questions involve replacing smooth surfaces (possibly with an additional curve network on them) by other structures like meshes with special properties. The guiding thought in all considerations is the efficient manufacturing of the surface parts and their respective necessary supporting/connecting elements. Both simple geometry and repetition of elements contribute to this goal of efficiency. In any case, a rationalized design is the output of a possibly very complicated nonlinear optimization, and it is very hard to make changes to such a highly constrained geometric model. The present project aims to develop basic methods for unifying two traditionally separate phases in freeform architecture, namely (i) shape design and (ii) rationalization in view of the actual fabrication. While motivated by architecture, such fabrication- aware design or design exploration makes sense in many other applications as well, in particular, since 3D models and designs will be available on the web (or in data bases of companies) in large numbers. Hence, design modification by keeping essential constraints (related to the actual production) is expected to be of great interest and impact. The method we plan to apply for the present task is shape space exploration. This means that we view the set of all feasible designs which fulfil the constraints (posed by manufacturing and other practical aspects) as points of a high-dimensional manifold (shape space). Then design exploration is accomplished by an efficient navigation in this manifold. In a pre-study, we have developed and verified some basic concepts to perform this navigation. The ideas are coming from computational differential geometry and nonlinear optimization. The project will develop a proper mathematical and computational framework for shape space navigation and apply it to the most fundamental structures in freeform architecture, in particular to quadrilateral meshes with planar faces. It is also planned to explore applications towards other types of nonlinearly constrained geometric models.

Freeform surfaces play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction of architectural freeform structures remains a challenge. In order to make a freeform design realizable, an optimization process known as rationalization has to be applied. This means its decomposition into smaller parts, thereby meeting two competing objectives: feasibility, and consistency with the designers intentions. Depending on what constitutes the design, there have been different approaches to this problem (with strong involvement of our research group) which have led to different kinds of specific geometric and computational questions. Mostly these questions involve replacing smooth surfaces (possibly with an additional curve network on them) by other structures like meshes with special properties. The guiding thought in all considerations is the efficient manufacturing of the surface parts and their respective necessary supporting/connecting elements. Both simple geometry and repetition of elements contribute to this goal of efficiency. In any case, a rationalized design is the output of a possibly very complicated nonlinear optimization, and it is very hard to make changes to such a highly constrained geometric model.The present project developed methodology for unifying two traditionally separate phases in freeform architecture, namely (i) shape design and (ii) rationalization in view of the actual fabrication. While motivated by architecture, such fabrication-aware design or design exploration makes sense in many other applications as well.The applied method is shape space exploration. This means that we view the set of all feasible designs which fulfil the constraints (posed by manufacturing and other practical aspects) as points of a high-dimensional manifold (shape space). Then design exploration is accomplished by an efficient navigation in this manifold. The ideas come from computational differential geometry and nonlinear optimization. We developed efficient algorithms for interactive modelling while satisfying constraints from manufacturing and in the case of architecture also from statics. Besides Architecture, we mainly studied modelling of so-called developable surfaces since they play an important role in several manufacturing technologies and their treatment in CAD systems has so far been quite limited.