Iterative geometric design for architecture

This work investigates on computer aided integrated architectural design and production. The aim is to provide integral solutions for the design and the production of geometrically complex free-form architecture. Investigations on computer aided geometric design and integrated manufacturing are carried out with equal importance. This research is considering an integral and interdisciplinary approach, including computer science, mathematics and architecture. Inspired by fractal geometry, the IFS formalism is studied with regards to discrete architectural geometric design. The geometric design method studied provides new shape control possibilities unifying two separate design paradigms of rough and smooth objects. Capable to design fractal geometric figures, the method also covers the generation of classical objects such as conics and NURBS-curves. Close attention has been paid to the design of iterative free-form surfaces, which are composed entirely out of planar elements. A surface method based on projected vector sums is proposed. The resulting geometric figures are expressed in a discrete form and can be easily translated into a coherent set of constructional elements. The studies for translation of the geometrical elements into constructional elements consider integrated manufacturing. Addressing and numbering of the elements by iterative geometric design are investigated and compared to lexicographically ordered addressing systems, in order to provide an adequate data structure for the design, production and assembly of the constructional elements. For the generation of the data describing constructional elements, problems related to thickening and offset meshes are discussed. Once the global geometry of the constructional part has been computed, parameters are defined for generic automated detailing. Hereby the entire description of the constructional elements is completed. These elements are mapped and packed with regards to the coordinate system of a CNC-machine and the properties and the dimensions of the raw material, providing the complete set of workshop plans needed for integrated manufacturing. For automated generation of machine instructions (G-code), machining strategies – depending on the type of machine used, tool and material properties – are elaborated. Finally, the integrated digital design methods studied within the scope of this thesis are tested and verified by the realization of different reduced scale prototypes. The studied applications range from bearing vault structures to fractal and smooth timber panel shell structures. The developed methods have shown to be efficient for the design and the realization of geometrically complex architectural objects. The required planning effort to handle and manipulate the design and the production data has been greatly reduced. Some of the proposed methods have proved to be robust and general enough to be applied on real world applications. Iterative geometric design provides high degree of design possibilities offering an efficient tool for the creation of smooth and rough free form objects. The possibility to incorporate successive folds in free-form objects allows structural applications

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

Motion patterns of subviral particles: Digital tracking, image data processing and analysis

At the Institute of Virology, Philipps-University, Marburg, Germany, currently research on the understanding of the transport mechanisms of Ebola- and Marburgvirus nucleocapsids is carried out. This research demands a profound knowledge about the various motion characteristics of the nucleocapids. The analysis of large amounts of samples by conventional manual evaluation is a laborious task and does not always lead to reproducible and comparable results. In a cooperation between the Institute of Virology, Marburg, and the Institute for Biomedical Engineering, University of Applied Sciences, Giessen, Germany, algorithms are developed and programmed that enable an automatic tracking of subviral particles in fluorescence microscopic image sequences. The algorithms form an interface between the biologic and the algorithmic domain. Furthermore, methods to automatically parameterize and classify subviral particle motions are created. Geometric and mathematical approaches, like curvature-, fractal dimension- and mean squared displacement-determination are applied. Statistical methods are used to compare the measured subviral particle motion parameters between different biological samples. In this thesis, the biological, mathematical and algorithmic basics are described and the state of the art methods of other research groups are presented and compared. The algorithms to track, parameterize, classify and statistically analyze subviral particle tracks are presented in the Methods section. All methods are evaluated with simulated data and/or compared to data validated by a virologist. The methods are applied to a set of real fluorescence microscopic image sequences of Marburgvirus infected live-cells. The Results chapter shows that subviral particle motion can be successfully analyzed using the presented tracking and analysis methods. Furthermore, differences between the subviral particle motions in the analyzed groups could be detected. However, further optimization with manually evaluated data can improve the results. The methods developed in this project enhance the knowledge about nucleocapsid transport and may be valuable for the development of effective antiviral agents to cure Ebola- and Marburgvirus diseases. The thesis concludes with a chapter Discussion and Conclusions