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Procedural function-based modelling of volumetric microstructures

Originality - This paper presents new results of our on-going research related to an emerging and increasingly important area of design and fabrication of heterogeneous objects with a complex internal structure. The conventional approach to representation of microstructures with polygonal meshes or voxels has its well-known problems concerned the model faults such as cracks and self-intersections, which complicate the task of digital manufacturing. A relatively low level of parameterization of the model makes the flexibility of design process problematic. In this work we show how an original approach to modelling microstructures presented by us in an earlier paper can be applied to resolving most of the above mentioned problems. We provide for the first time a detailed description of design process of modelling cellular structures taking into accounts the novel types of lattice models and their non-linear transformations.

Rigour - We have addressed modelling both regular lattices and irregular porous media microstructures using original mathematically sound techniques allowing for design of arbitrarily parameterized model. The proposed models are extremely compact (all examples in this paper can be implemented in 30-40 lines of C language), while providing precise and spatially coherent microstructures.

Significance - Small size repetitive geometric patterns called microstructures are becoming more and more important in both artistic and mechanical design. The cellular-functional framework presented in the paper overcomes the major technical obstacles intrinsic to the conventional representational approach. The level of the model parameterization can be very high including parameter-dependent changes in object’s topology. We have also described the original method of estimating parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Multiple examples of rendering and digital fabrication of microstructure models are presented.