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

PlantGL : a Python-based geometric library for 3D plant modelling at different scales

In this paper, we present PlantGL, an open-source graphic toolkit for the creation, simulation and analysis of 3D virtual plants. This C++ geometric library is embedded in the Python language which makes it a powerful user-interactive platform for plant modelling in various biological application domains. PlantGL makes it possible to build and manipulate geometric models of plants or plant parts, ranging from tissues and organs to plant populations. Based on a scene graph augmented with primitives dedicated to plant representation, several methods are provided to create plant architectures from either field measurements or procedural algorithms. Because they reveal particularly useful in plant design and analysis, special attention has been paid to the definition and use of branching system envelopes. Several examples from different modelling applications illustrate how PlantGL can be used to construct, analyse or manipulate geometric models at different scales

Non-Standard Sound Synthesis with Dynamic Models

Full version unavailable due to 3rd party copyright restrictions.This Thesis proposes three main objectives: (i) to provide the concept of a new generalized non-standard synthesis model that would provide the framework for incorporating other non-standard synthesis approaches; (ii) to explore dynamic sound modeling through the application of new non-standard synthesis techniques and procedures; and (iii) to experiment with dynamic sound synthesis for the creation of novel sound objects. In order to achieve these objectives, this Thesis introduces a new paradigm for non-standard synthesis that is based in the algorithmic assemblage of minute wave segments to form sound waveforms. This paradigm is called Extended Waveform Segment Synthesis (EWSS) and incorporates a hierarchy of algorithmic models for the generation of microsound structures. The concepts of EWSS are illustrated with the development and presentation of a novel non-standard synthesis system, the Dynamic Waveform Segment Synthesis (DWSS). DWSS features and combines a variety of algorithmic models for direct synthesis generation: list generation and permutation, tendency masks, trigonometric functions, stochastic functions, chaotic functions and grammars. The core mechanism of DWSS is based in an extended application of Cellular Automata. The potential of the synthetic capabilities of DWSS is explored in a series of Case Studies where a number of sound object were generated revealing (i) the capabilities of the system to generate sound morphologies belonging to other non-standard synthesis approaches and, (ii) the capabilities of the system of generating novel sound objects with dynamic morphologies. The introduction of EWSS and DWSS is preceded by an extensive and critical overview on the concepts of microsound synthesis, algorithmic composition, the two cultures of computer music, the heretical approach in composition, non- standard synthesis and sonic emergence along with the thorough examination of algorithmic models and their application in sound synthesis and electroacoustic composition. This Thesis also proposes (i) a new definition for “algorithmic composition”, (ii) the term “totalistic algorithmic composition”, and (iii) four discrete aspects of non-standard synthesis

Une modélisation géométrique itérative basée sur les automates

Nous présentons un modèle itératif inspiré du modèle CIFS (Controlled Iterative Function System) de PRUSINKIEWICZ [PH94] - encore appelé RIFS (Recurrent Iterative Function System) par BARNSLEY ou MRIFS (Mutually Recursive Iterative Function System) par CULIK [CD93] -. Le principe de ces modèles est de définir des familles de figures géométriques avec des règles de production et des systèmes d’équations. Dans cet article, nous en présentons deux généralisations, qui permettent de contrôler la géométrie et la topologie des formes produites

Fundamental remote sensing science research program. Part 1: Status report of the mathematical pattern recognition and image analysis project

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of the Earth from remotely sensed measurement of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inference about the Earth

Resolution Enhancement in Magnetic Resonance Imaging by Frequency Extrapolation

This thesis focuses on spatial resolution enhancement of magnetic resonance imaging (MRI). In particular, it addresses methods of performing such enhancement in the Fourier domain. After a brief review of Fourier theory, the thesis reviews the physics of the MRI acquisition process in order to introduce a mathematical model of the measured data. This model is later used to develop and analyze methods for resolution enhancement, or "super-resolution'', in MRI. We then examine strategies of performing super-resolution MRI (SRMRI). We begin by exploring strategies that use multiple data sets produced by spatial translations of the object being imaged, to add new information to the reconstruction process. This represents a more detailed mathematical examination of the author's Master's work at the University of Calgary. Using our model of the measured data developed earlier in the thesis, we describe how the acquisition strategy determines the efficacy of the SRMRI process that employs multiple data sets. The author then explores the self-similarity properties of MRI data in the Fourier domain as a means of performing spatial resolution enhancement. To this end, a fractal-based method over (complex-valued) Fourier Transforms of functions with compact spatial support, derived from a fractal transform in the spatial domain, is explored. It is shown that this method of "Iterated Fourier Transform Systems" (IFTS) can be tailored to perform frequency extrapolation, hence spatial resolution enhancement. The IFTS method, however, is limited in scope, as it assumes that a spatial function f(x) may be approximated by linear combinations of spatially-contracted and range-modified copies of the entire function. In order to improve the approximation, we borrow from traditional fractal image coding in the spatial domain, where subblocks of an image are approximated by other subblocks, and employ such a block-based strategy in the Fourier domain. An examination of the statistical properties of subblock approximation errors shows that, in general, Fourier data can be locally self-similar. Furthermore, we show that such a block-based self-similarity method is actually equivalent to a special case of the auto-regressive moving average (ARMA) modeling method. The thesis concludes with a chapter on possible future research directions in SRMRI

Interpolating between Hausdorff and box dimension

Hausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all sets in the cover have the same diameter, but for Hausdorff dimension there is no such restriction. This thesis focuses on a family of dimensions parameterised by θ ∈ (0,1), called the intermediate dimensions, which are defined by requiring that diam(U) ⩽ (diam(V))ᶿ for all sets U, V in the cover. We begin by generalising the intermediate dimensions to allow for greater refinement in how the relative sizes of the covering sets are restricted. These new dimensions can recover the interpolation between Hausdorff and box dimension for compact sets whose intermediate dimensions do not tend to the Hausdorff dimension as θ → 0. We also use a Moran set construction to prove a necessary and sufficient condition, in terms of Dini derivatives, for a given function to be realised as the intermediate dimensions of a set. We proceed to prove that the intermediate dimensions of limit sets of infinite conformal iterated function systems are given by the maximum of the Hausdorff dimension of the limit set and the intermediate dimensions of the set of fixed points of the contractions. This applies to sets defined using continued fraction expansions, and has applications to dimensions of projections, fractional Brownian images, and general Hölder images. Finally, we determine a formula for the intermediate dimensions of all self-affine Bedford–McMullen carpets. The functions display features not witnessed in previous examples, such as having countably many phase transitions. We deduce that two carpets have equal intermediate dimensions if and only if the multifractal spectra of the corresponding uniform Bernoulli measures coincide. This shows that if two carpets are bi-Lipschitz equivalent then the multifractal spectra are equal."This work was supported by a Leverhulme Trust Research Project Grant (RPG-2019-034)." -- Fundin