Digitally interpreting traditional folk crafts

The cultural heritage preservation requires that objects persist throughout time to continue to communicate an intended meaning. The necessity of computer-based preservation and interpretation of traditional folk crafts is validated by the decreasing number of masters, fading technologies, and crafts losing economic ground. We present a long-term applied research project on the development of a mathematical basis, software tools, and technology for application of desktop or personal fabrication using compact, cheap, and environmentally friendly fabrication devices, including '3D printers', in traditional crafts. We illustrate the properties of this new modeling and fabrication system using several case studies involving the digital capture of traditional objects and craft patterns, which we also reuse in modern designs. The test application areas for the development are traditional crafts from different cultural backgrounds, namely Japanese lacquer ware and Norwegian carvings. Our project includes modeling existing artifacts, Web presentations of the models, automation of the models fabrication, and the experimental manufacturing of new designs and forms

Trimming implicit surfaces

ABSTRACT Algorithms of trimming implicit surfaces yielding surface sheets and stripes are presented. These twodimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm. The presented applications include modeling several spiral shaped surface sheets and stripes (after M. Escher's art works) and extraction of ridges on implicit surfaces. Another promising application of the presented algorithms is modeling heterogeneous objects as implicit complexes

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

KEYWORDS Trimming Implicit Surfaces

Algorithms of trimming implicit surfaces yielding surface sheets and stripes are presented. These twodimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm. The presented applications include modeling several spiral shaped surface sheets and stripes (after M. Escher’s art works) and extraction of ridges on implicit surfaces. Another promising application of the presented algorithms is modeling heterogeneous objects as implicit complexes. 1

Ternary Blending Operations

We discuss new analytical formulations for localized and controllable blending operations in the functionbased solid modeling. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend are controlled by an additional bounding solid thus turning the operation into a ternary one. We also describe a new approach to solving the problem of shape metamorphosis between k-dimensional shapes by applying space-time bounded blending to the specially constructed (k+1)dimensional half-cylinders and making cross-sections for getting intermediate shapes under the transformation. 1 Blending in solid modeling Blending operations in solid modeling generate smooth transitions between two or several surfaces. Blending is also considered a natural property of implicit surfaces, where the basic operation is an algebraic sum (or difference) between skeleton-based scalar fields. Blending operations are typically used in computer-aided design for modeling fillets and chamfers. These operations are usually smooth versions of set-theoretic operations on solids (intersection, union, and difference), which approximate exact results of these operations by rounding sharp edges and vertices. The major requirements to blending operations [1] are tangency of the blend surface with the initial surfaces, automatic clipping of unwanted parts of the blending surface, C1 continuity of the blending function everywhere in the domain, support of added and subtracted material blends. Special attention is paid to the intuitive control of the blend shape and position: the construction of the blend and its parameters should have clear geometric interpretation

DESKTOP MANUFACTURING FROM EASILY TRANSMITTED HIGH RESOLUTION DIGITAL FILES AND ITS APPLICATION CASE STUDIES

The technical reports are published for early dissemination of research result

Modeling of conceptual multiresolution analysis by an incrementally modular abstraction hierarchy

Recent advances of Web information systems such as ecommerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific, the modeling formulation is worked out in an incrementally modular abstraction hierarchy with emphasis on the two levels of the hierarchy appropriate for conceptual modeling: the adjunction space level and the cellular structured space level. Examples are shown to demonstrate the usefulness of the presented model as well as an implementation of a flower structure case. Key words: conceptual multiresolution analysis, adjunction spaces, cellular structured spaces, incrementally modular abstraction hierarchy, Web information systems 1

Digital Preservation of Cultural Heritage through Constructive Modeling (e)

The issues of digital preservation of shapes and internal structures of historical and cultural objects are discussed. An overview of existing approaches to computer modeling of shapes is presented and corresponding problems are considered. We propose a digital preservation paradigm quite different from the currently popular "scan and mesh " approach yielding visible surface models. Our approach is based on constructive modeling that reflects the logical structure of modeled shapes. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations which fit the purposes of long term digital preservation. Examples of CSG based reconstruction of historical temples and FRep based modeling of traditional lacquer ware are given