Heterogeneous material modeling with distance fields

We propose a universal approach to the problem of computer modeling of shapes with continuously varying material properties satisfying prescribed material conditions on a finite collection of material features and global constraints. The central notion is a parameterization of space by distances from the material features – either exactly or approximately. Functions of such distances provide a systematic and intuitive means for modeling of desired material distributions as they arise in design, manufacturing, analysis and optimization of components with varying material properties. The proposed framework subsumes and generalizes a number of earlier proposals for heterogeneous material modeling. It is theoretically complete in the sense that it allows representation of all material property functions. We demonstrate that the approach can be implemented within the existing framework of solid modeling and its numerous advantages, including: precise and intuitive control using explicit, analytic, differential, and integral constraints specified on the native geometry; guaranteed smoothness and analytic properties without meshing; and applicability to material features of arbitrary dimension, shape, and topology.