Procedural Function-Based Spatial Microstructures

Abstract

Abstract:We propose a new approach to modelling heterogeneous objects containing internal spatial geometric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides a compact, precise, and arbitrarily parameterized model allowing for modelling coherent microstructures, which can undergo blending, offsetting, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations. In particular, modelling of regular lattices and porous media is discussed and illustrated. Examples of microstructure models rendering and fabrication using a variety of digital fabrication machines and materials are presented.

Multi-scale space-variant FRep cellular structures

“…Defining only isosurfaces instead of solid objects (with the surface separating subspaces with different function signs corresponding to each of them) and using non-differentiable functions (min and max) prevent the application of additional operations on a model, such as controlled blending. This approach was further developed in [2], where microstructures are considered as solid objects defined by non-negative values of a real continuous function procedurally evaluated at any given point. The initial periodic structures, their extensions for set theoretic, controlled blending and other operations in function representation (FRep) have been combined using R-functions [7].…”

“…As it was shown in [2], cell replication similar to texture tiling can be applied to any geometric model or part of a model defined inside a bounding box (called unit cell) such that this unit cell is replicated in infinite Cartesian space. For FRep models, infinite cellular structure can be generated by applying a periodic function defining a space mapping to the FRep model of the unit cell geometry.…”

“…Recently the computational overhead and handling of complex models invoving microstructures was simplified by using function-based modeling [1] [2]. Precise parametrized constructive modeling based on real functions allows for the procedural definition of multi-scale microstructures, which can undergo blending, deformations, metamorphosis and other geometric operations.…”

“…In this work we further develop cellular structures presented in [2]. The main contributions of this work include outlining several methods of generating spatial variations in microstructures: parameterization with point coordinates and distance to the external shell, metamorphosis between different unit cells, transfinite interpolation between different cellular types with given space partitions and recursive multi-scale replication.…”

BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning

“…The use of scalar fields allows for procedural modeling of microstructures such as lattices and porous media in a compact, precise and arbitrarily parametrized way [21].…”