Computation and construction of vault geometry prototypes

Physical models and scaled prototypes of architecture play an important role in design. They enable architects and designers to investigate the formal, functional, and material attributes of the design. Understanding digital processes of realizing scaled prototypes is a significant problem confronting design practice. This paper reports on three approaches to the translation of Gaussian surface models into scaled physical prototype models. Based on the geometry of Eladio Dieste’s Gaussian Vaults, the paper reports on the aspects encountered in the process of digital to physical construction using scaled prototypes. The primary focus of the paper is on computing the design geometry, investigating methods for preparing the geometry for fabrication and physical construction. Three different approaches in the translation from digital to physical models are investigated: rapid prototyping, two-dimensional surface models in paper and structural component models using CNC fabrication. The three approaches identify a body of knowledge in the design and prototyping of Gaussian vaults. Finally the paper discusses the digital to fabrication translation processes with regards to the characteristics, benefits and limitations of the three approaches of prototyping the ruled surface geometry of Gaussian Vaults. The results of each of three fabrication processes allowed for a better understanding of the digital to physical translation process. The use of rapid prototyping permits the production of form models that provide a representation of the physical characteristics such as size, shape and proportion of the Gaussian Vault.

Gaussian vault geometry : integrated approach in design and fabrication of physical prototypes

This paper reports the second part of a study on the digital design and fabrication of scaled architectural prototypes. The first paper reported techniques in the realization of a double curved vault surface, the Gaussian Vault. The aims of the research here further extend this body of knowledge to a better understanding of constructible components. It addresses the problem of fabricating complex curved forms through the integration of the basic building elements, skin and structure, to achieve a scaled physical prototype. The focus of the experimentation is to investigate the process from which a digital surface form is conceived, to its preparation for fabrication and eventual construction in the fashion of a scaled model or workable prototype.

Femoral neck geometry and hip fracture risk : the Geelong Osteoporosis Study

To determine the relationship between femoral neck geometry and the risk of hip fracture in post-menopausal Caucasian women, we conducted a retrospective study comparing the femoral neck dimensions of 62 hip fracture cases to those of 608 randomly selected controls. Measurements were made from dual-energy X-ray absorptiometry scans (Lunar DPX-L), using the manufacturers ruler function, and included: hip axis length (HAL), femoral neck axis length (FNAL), femoral neck width (FNW), femoral shaft width (FSW), medial femoral shaft cortical thickness (FSCT_med), and lateral femoral shaft cortical thickness (FSCT_lat). The fracture group was older (median age 78.3 years vs 73.8 years), lighter (median weight 59.9 kg vs 64.5 kg), and, after adjustment for age, taller (mean height 158.7±0.8 cm vs 156.7±0.2 cm) than the controls. Furthermore, bone mineral density was lower in this group (0.682±0.016 g/cm² vs 0.791±0.006 g/cm²). After adjustment for age, bone mineral content (BMC) or height, hip fracture patients had greater FNW (up to 6.6%) and FSW (up to 6.3%) than did the controls. Each standard deviation increase in FNW and FSW was associated with a 1.7-fold (95% CI 1.3–2.3) and a 2.4-fold (95% CI 1.8–3.2) increase in the fracture risk, respectively. BMC-adjusted FNAL was greater in the fracture group (+2.1%) than in the controls, while the age-adjusted FSCT_med was reduced (–7.2%). There was a trend towards longer HAL (up to 2.1%) after adjustment for age or BMC, and thinner age-adjusted FSCT_lat (–1.7%) in fracture patients that did not reach statistical significance. In multivariate analysis, the risk of hip fracture was predicted by the combination of age, FNW, FSW, BMC and FSCT_med. HAL was not analyzed because of the small number of HAL measurements among fracture cases. We conclude that post-menopausal women with hip fractures have wider femoral necks and shafts, thinner femoral cortices and longer femoral neck axis lengths than do women with no fractures. Alteration in hip geometry is associated with the risk of hip fracture.

Stochastic models of road geometry and wind condition for vehicle energy management and control

Modeling and simulation is commonly used to improve vehicle performance, to optimize vehicle system design, and to reduce vehicle development time. Vehicle performances can be affected by environmental conditions and driver behavior factors, which are often uncertain and immeasurable. To incorporate the role of environmental conditions in the modeling and simulation of vehicle systems, both real and artificial data are used. Often, real data are unavailable or inadequate for extensive investigations. Hence, it is important to be able to construct artificial environmental data whose characteristics resemble those of the real data for modeling and simulation purposes. However, to produce credible vehicle simulation results, the simulated environment must be realistic and validated using accepted practices. This paper proposes a stochastic model that is capable of creating artificial environmental factors such as road geometry and wind conditions. In addition, road geometric design principles are employed to modify the created road data, making it consistent with the real-road geometry. Two sets of real-road geometry and wind condition data are employed to propose probability models. To justify the distribution goodness of fit, Pearson's chi-square and correlation statistics have been used. Finally, the stochastic models of road geometry and wind conditions (SMRWs) are developed to produce realistic road and wind data. SMRW can be used to predict vehicle performance, energy management, and control strategies over multiple driving cycles and to assist in developing fuel-efficient vehicles.

Teaching 3-D geometry - the multi representational way

Sonja Kalbitzer and Esther Loong provide an excellent range of activities that promote geometric thinking through the exploration of three-dimensional objects. They also provide some discussion on assessing the tasks and providing student feedback.

The constructional geometry of early Javanese temples

The early development of Hindu Javanese architecture can be traced through interpretation of epigraphs, archaeological excavations, and comparison of extant temples with other traditions. However, while many scholars have speculated on connections between Javanese Hindu temples and presumed antecedents in India, these have been made on the basis of visual comparison and epigraphic interpretations. No Indian temple has been conclusively shown to be a model for the earliest Javanese temples. Archaeologist and temple historian Michael Meister has shown in his analysis of the geometric composition of early Hindu temples in South Asia how a ritual sixty-four square mandala was the geometric basis of temple construction during the formative period (fifth to eighth century) of the Indian architectural tradition. Working from an understanding of temple construction sequence as well as their ritual underpinnings, Meister found that the sixtyfour square mandala's dimensions correlate closely to the constructed dimensions at the level of the vedibandha (which corresponds with the plan level of the sanctuary threshold). Furthermore, he shows how the horizontal profile of the cella depends on the number of offsets and the proportional relationships between ech offset based on the subdivision of the sixty-four square grid. The authors have investigated whether a similar compositional basis can be found for the earliest Javanese temples on the Dieng Plateau in the highlands of central Java, despite differences in architectonic and symbolic expression. The analysis of relationships between ritual geometry and actual temple layouts for these buildings has the potential to furthering our understanding of the connections between Hindu temples in Java and those in India.

Geometry of compensatory feeding and water consumption in Drosophila melanogaster

Feeding behaviour is an expression of an animal’s underlying nutritional strategy. The study of feeding decisions can hence delineate nutritional strategies. Studies of Drosophila melanogaster feeding behaviour have yielded conflicting accounts, and little is known about how nutrients affect feeding patterns in this important model species. Here, we conducted two experiments to characterize nutrient prioritization and regulation. In a choice experiment, we allowed female flies to self-regulate their intake of yeast, sucrose and water by supplying individual flies with three microcapillary tubes: one containing only yeast of varying concentrations, another with just sucrose of varying concentrations, and the last with just water. Flies tightly regulated yeast and sucrose to a constant ratio at the expense of excess water intake, indicating that flies prioritize macronutrient regulation over excess water consumption. To determine the relative importance of yeast and sucrose, in a no-choice experiment, we provided flies with two microcapillary tubes: the first with one of the 28 diets varying in yeast and sucrose content and the other with only water. Flies increased total water intake in relation to yeast consumption but not sucrose consumption. Additionally, flies increased diet intake as diet concentration decreased and as the ratio of sugar to yeast equalized. Using a geometric scaling approach, we found that the patterns of diet intake can be explained by flies prioritizing protein and carbohydrates equally and by the lack of substitutability between the nutrients. We conclude by illustrating how our results harmonize conflicting results in the literature once viewed in a two-dimensional diet landscape.

Pseudoconvex proximal splitting for L∞problems in multiview geometry

In this paper we study optimization methods for minimizing large-scale pseudoconvex L∞problems in multiview geometry. We present a novel algorithm for solving this class of problem based on proximal splitting methods. We provide a brief derivation of the proposed method along with a general convergence analysis. The resulting meta-algorithm requires very little effort in terms of implementation and instead makes use of existing advanced solvers for non-linear optimization. Preliminary experiments on a number of real image datasets indicate that the proposed method experimentally matches or outperforms current state-of-the-art solvers for this class of problems.