Carl Vilbrandt

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.

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.

Function-based Shape Modeling Framework in Multilevel Education

We describe how an approach to the development of a shape modeling and visualization framework based on the rapidly progressing function representation can be used in education. The modeling language and software tools are being developed within an international HyperFun Project. We applied the theoretical framework and software tools on different levels of education starting from elementary schools to doctoral thesis research in various areas related to mathematics, computer graphics, programming languages, artistic design and animation. We illustrate the presented approach by the practical experience examples from different educational institutions and countries.

Algorithms for the Visualization of Functionally Defined Objects on Distributed Systems

This chapter presents two approaches for an efficient polygonal approximation on distributed computers of surfaces defined by the Function Representation model. The first algorithm uses a dynamic distribution of the geometric grid elements to allow maximum efficiency on grid of computers. The second algorithm targets parallel computers and cluster of computers and tries to minimize communications by distributing the geometric grid elements statically. Potential applications for these software algorithms are rendering in CAD system, and computer graphics animation for solids with complex surfaces.

Parallel hyperfun polygonizer

An advanced HyperFun polygonizer which produces high quality visualization from an object represented by the HyperFun geometric modeling language and a parallel HyperFun grid system which distributes the calculations of the HyperFun polygonizer over many computers through a network are presented. We show that distributing the calculation for visualization of HyperFun function represented models via a heterogeneous computer network with our parallel polygonization method can yield HyperFun polygonal models of reduced size in a shorter period of time.

Dancing Buddhas: new graphical tools for digital cultural heritage preservation

We discuss the use of a mathematically based tool, function representation (FRep), for modeling complex 3D objects such as sculpture, showing an improved dynamically modifiable viewing and presentation. FRep uniquely allows smooth metamorphosis between structurally dissimilar objects, even with different mathematical connectivity. We apply FReps modeling and metamorphosis capabilities to the multimedia presentation of a transformation of the kanji from a twelfth-century Japanese text of the Lotus sutra (one found in the Aizu region) into moving 3D Buddha-images, accompanied by synchronous sounds of chanting. We demonstrate some of the basic steps showing the concept and approach. Our approach gives an object at any point in its metamorphosis a mathematically accurate representation of the object at that stage of the process. We achieve this by using HyperFun, a high level geometric modeling language, for the FRep based modelling.