Hybrid Modelling of Heterogeneous Volumetric Objects
Heterogeneous multi-material volumetric modelling is an emerging and rapidly developing field. A Heterogeneous object is a volumetric object with interior structure where different physically-based attributes are defined. The attributes can be of different nature: material distributions, density, microstructures, optical properties and others. Heterogeneous objects are widely used where the presence of the interior structures is an important part of the model. Computer-aided design (CAD), additive manufacturing, physical simulations, visual effects, medical visualisation and computer art are examples of such applications. In particular, digital fabrication employing multi-material 3D printing techniques is becoming omnipresent. However, the specific methods and tools for representation, modelling, rendering, animation and fabrication of multi-material volumetric objects with attributes are only starting to emerge. The need for adequate unifying theoretical and practical framework has been obvious. Developing adequate representational schemes for heterogeneous objects is in the core of research in this area. The most widely used representations for defining heterogeneous objects are boundary representation, distance-based representations, function representation and voxels. These representations work well for modelling homogeneous (solid) objects but they all have significant drawbacks when dealing with heterogeneous objects. In particular, boundary representation, while maintaining its prevailing role in computer graphics and geometric modelling, is not inherently natural for dealing with heterogeneous objects especially in the context of additive manufacturing and 3D printing, where multi-material properties are paramount as well as in physical simulation where the exact representation rather than an approximate one can be important. In this thesis, we introduce and systematically describe a theoretical and practical framework for modelling volumetric heterogeneous objects on the basis of a novel unifying functionally-based hybrid representation called HFRep. It is based on the function representation (FRep) and several distance-based representations, namely signed distance fields (SDFs), adaptively sampled distance fields (ADFs) and interior distance fields (IDFs). It embraces advantages and circumvents disadvantages of the initial representations. A mathematically substantiated theoretical description of the HFRep with an emphasis on defining functions for HFRep objects’ geometry and attributes is provided. This mathematical framework serves as the basis for developing efficient algorithms for the generation of HFRep objects taking into account both their geometry and attributes. To make the proposed approach practical, a detailed description of efficient algorithmic procedures has been developed. This has required employing a number of novel techniques of different nature, separately and in combination. In particular, an extension of a fast iterative method (FIM) for numerical solving of the eikonal equation on hierarchical grids was developed. This allowed for efficient computation of smooth distance-based attributes. To prove the concept, the main elements of the framework have been implemented and used in several applications of different nature. It was experimentally shown that the developed methods and tools can be used for generating objects with complex interior structure, e.g. microstructures, and different attributes. A special consideration has been devoted to applications of dynamic nature. A novel concept of heterogeneous space-time blending (HSTB) method with an automatic control for metamorphosis of heterogeneous objects with textures, both in 2D and 3D, has been introduced, algorithmised and implemented. We have applied the HSTB in the context of ‘4D Cubism’ project. There are plans to use the developed methods and tools for many other applications.