Turlif Vilbrandt

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented.

Multi-scale space-variant FRep cellular structures

Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations.

Cultural Heritage Preservation Using Constructive Shape Modeling

Issues of digital preservation of shapes and internal structures of historical cultural objects are discussed. An overview of existing approaches to digital preservation related to shape modeling is presented and corresponding problems are considered. We propose a new digital preservation paradigm based on both constructive modeling reflecting the logical structure of the objects and open standards and procedures. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations producing compressed yet precise data structures, thus providing inter‐operability between current and future computer platforms crucial to archiving. Examples of CSG reconstruction of historical temples and FRep modeling of traditional lacquer ware are given. We examine the application of fitting of a parameterized FRep model to a cloud of data points as a step towards automation of the modeling process. Virtual venues for public access to cultural heritage objects including real time interactive simulation of cultural heritage sites over the Web are discussed and illustrated.

Procedural Function-Based Spatial Microstructures

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 compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. Examples of rendering and digital fabrication of microstructure models are presented.

Universal desktop fabrication

Advances in digital design and fabrication technologies are leading toward single fabrication systems capable of producing almost any complete functional object. We are proposing a new paradigm for manufacturing, which we call Universal Desktop Fabrication (UDF), and a framework for its development. UDF will be a coherent system of volumetric digital design software able to handle infinite complexity at any spatial resolution and compact, automated, multi-material digital fabrication hardware. This system aims to be inexpensive, simple, safe and intuitive to operate, open to user modification and experimentation, and capable of rapidly manufacturing almost any arbitrary, complete, high-quality, functional object. Through the broad accessibility and generality of digital technology, UDF will enable vastly more individuals to become innovators of technology, and will catalyze a shift from specialized mass production and global transportation of products to personal customization and point-of-use manufacturing. Likewise, the inherent accuracy and speed of digital computation will allow processes that significantly surpass the practical complexity of the current design and manufacturing systems. This transformation of manufacturing will allow for entirely new classes of human-made, peerproduced, micro-engineered objects, resulting in more dynamic and natural interactions with the world. We describe and illustrate our current results in UDF hardware and software, and describe future development directions.

Toward organ printing: Design characteristics, virtual modelling and physical prototyping vascular segments of kidney arterial tree

Organ printing is defined as the layer by layer additive biofabrication of three-dimensional (3D) tissue and organ constructs using tissue spheroids as building blocks. Ultimately, successful bioprinting of human organ constructs is dependent on a ‘built in’ vascular tree to perfuse and maintain the viability of the organ constructs. Thus, the design of the vascular tree is a critically important step in practical implementation of organ printing technology. Bioprinting a vascular tree requires detailed knowledge of the morphometrical, morphological and biomechanical characteristics of the sequentially branched segments of the natural vascular tree as well as insight on post-printing tissue compaction and remodelling. Toward accomplishing this goal, we characterised the morphometrical, morphological and biomechanical characteristics of the initial segments of the natural kidney arterial vascular tree of the porcine kidney. Computer simulation was used to model compaction of tissue engineered tubular vascular segments with different wall thicknesses virtually biofabricated from closely packed and fused uniformly sized vascular tissue spheroids. The number of concentric layers of tissue spheroids required to bioprint tubular vascular segments with desirable wall thickness and diameter was theoretically estimated. Our results demonstrate that vascular segment compaction correlates well with reported experimental data. Finally, physical prototyping of linear and branched tubular constructs using silicon droplets as physical analogues of tissue spheroids was performed. Thus, virtual and physical prototyping provide important insights into the design parameters and demonstrate the principal feasibility of bioprinting a branched vascular tree using vascular tissue spheroids.

SMI 2013: Morphological shape generation through user-controlled group metamorphosis

Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design and generation. In contrast to existing generative procedures, an approach based on a user-controlled metamorphosis between functionally based shape models is presented. A formulation of the pairwise metamorphosis is proposed with a variety of functions described for the stages of deformation, morphing and offsetting. This formulation is then extended to the metamorphosis between groups of shapes with user-defined, dynamically correlated and weighted feature elements. A practical system was implemented in the form of plugin to Maya and tested by an industrial designer on a group of representative shapes from a particular domain.

Digitally Interpreting Traditional Folk Crafts

Preserving cultural heritage requires that objects persist throughout time and continue to communicate an intended meaning. Owing to the decreasing number of masters of folk crafts, fading technologies, and crafts losing economic ground, computer-based preservation and interpretation of such crafts is necessary. To fabricate and preserve traditional crafts, a long-term applied-research project has combined mathematics and software tools with compact, cheap, and environmentally friendly desktop fabrication tools, including 3D printers. Case studies involving the digital capture of Japanese lacquerware and Norwegian carvings illustrate the projects modeling approach and fabrication system. Besides modeling existing artifacts, the project includes Web presentations of the models, automated model fabrication, and experimental manufacturing of new designs and forms.

SMI 2011: Full Paper: Feature based volumes for implicit intersections

The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures.

Ascending in Space Dimensions: Digital Crafting of M.C. Escher's Graphic Art

ABSTRACT M.C. Eschers artwork has inspired and arguably even informed computer science, as well as geometric and shape modeling. Even today, much of his work poses challenges to conventional digital shape modeling systems. The authors introduce several interesting problems presented by Eschers graphic artworks and describe their use of a novel approach, based on implicit surfaces and their extension (Function Representation), to produce 2D, 2.5D and 3D computer models. They also discuss several physical objects or sculptures based on these models, crafted using digital fabrication processes.