Since 2014
Free-form architecture challenges designers and makers. Non-standard geometries bring many issues for the rationalisation of facades and structural layout. This research investigates two fabrication constraints relevant for glazed structures: the covering of doubly-curved shapes with planar facets, and the proper offset of support structure.
Free-form surfaces with planar facets
The covering of free-form shapes with planar panels has been an active topic of research since the 1980’s. Jörg Schlaich and Hans Schober introduced surfaces of translations in 1989. This method allows the covering of complex shapes with planar quadrangles. Triangular panels are always planar but are more complex to construct than quadrilateral meshes. In average, six beams meet along one node in triangular meshes. This number decreases to four for quadrilateral meshes, and three for hexagonal meshes.
Rather than trying to post-process arbitrary shapes, we propose simple methods to generate complex shapes covered with planar quadrilaterals. These methods often use two curves that mould curved shapes. They can be easily used and bring intuition back into free-form design.Monge’s surfaces and moulding surfaces can be covered with planar panels and can be covered with high node repetition (Mesnil et al. 2015 & 2015).
Inspiration was taken from the work of Gaspard Monge, known as the inventor of descriptive geometry, to propose an innovative technique for shape modelling. This method, called ‘Marionette technique’ by the authors, guarantees real-time modelling of shapes covered by planar facets (Mesnil et al. 2016).
Gridshells with multiple layers and torsion free nodes
Meshes are theoretical objects with zero thickness, which is not the case for civil engineering structures. This results in specific geometrical challenges. The research on this topic focuses on meshes with offsets. An offset of a mesh is a second mesh that is parallel to the first one, and which lies at a constant distance. The existence of this offset yields two benefits :
- The mesh can be built with multiple layers;
- At each node, all beams intersect on a unique axis. This considerably eases the fabrication of the nodes.
Special attention is given to circular and conical meshes. Circular meshes are meshes for which each face is inscribed in a circle. This quality implies automatically the existence of an offset at constant node distance. The research focuses on the development of design tools to generate free-form circular meshes. Conical meshes are closely related to circular meshes. They have offsets at constant face distance.
A first method has been implemented to generate discrete Monge and moulding surfaces as conical meshes (Mesnil et al. 2015). A second method has been developed to generate circular meshes based on cyclidic nets (Mesnil et al. 2015).
Coming soon
Architectural geometry is an active topic of research for architects, engineers and mathematicians. Some books or articles can be recommended on the topic of polyhedral surfaces.
Coming soon
