Output details

Multi-scale space-variant FRep cellular structures

Originality - In this paper a novel technique allowing to model multi-scale geometric objects in the very efficient way is presented. Original mathematical tools allow defining the geometric structure of the each next level of representation by using very simple formulation and therefore the proposed technique is easy to use in the volumetric modelling systems. In the paper it is shown that the proposed technique allows creating multi-scale structures that are impossible to create by using other existing methods. The resulting cellular structures are highly parameterised to create a large variety of the resulting shapes.

Significance - Recent developments in Computer Aided Design and in general Computer Science allow researchers to look deeper into the nature of physical objects and into the way of modelling geometric objects representing these physical objects. Despite the limited number of the techniques allowing the modelling of geometric objects with different levels of representation, such as macro-, micro- and nano-levels, the interest of the community in these methods is very high. The methods presented in the paper allow for the procedural definition of multi-scale microstructures, which can undergo blending, deformations, metamorphosis and other geometric operations. Another important variation in the generation of the microstructures is the definition of nested cellular structures. This means that the object can be defined at one level of the representation, then its structure is created from a set of objects, by using a highly parameterised cellular replication and the result of this operation can be replicated once again with another parameterisation to generate a further level of detail.

Rigour - The paper presents a number of possible applications of the presented technique, including generative design for digital fabrication and industrial shape design. Methods presented in the paper were implemented in commercial software and is used by industrial designers.