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Geometric Design

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lightbulbAbout this topic
Geometric design is the branch of engineering and mathematics that focuses on the creation and analysis of geometric shapes and structures. It involves the application of geometric principles to optimize the layout, safety, and efficiency of physical spaces, particularly in transportation infrastructure, urban planning, and architectural design.
lightbulbAbout this topic
Geometric design is the branch of engineering and mathematics that focuses on the creation and analysis of geometric shapes and structures. It involves the application of geometric principles to optimize the layout, safety, and efficiency of physical spaces, particularly in transportation infrastructure, urban planning, and architectural design.

Key research themes

1. Why do multiple geometric constructions persist in classical architectural and mathematical practices despite the availability of simpler methods?

This theme explores the historical and practical reasons behind the persistence of diverse geometric construction methods in classical Europe, especially focusing on the division of a straight line into n equal parts (n-section). Understanding why practitioners favored a variety of techniques, often not the simplest, sheds light on the intersection of intellectual traditions, material conditions, and scale in architectural and engineering applications of geometry.

Key finding: This paper presents a comprehensive survey of about fifteen methods for n-section lines developed from antiquity through classical Europe. It finds that the most widespread geometric constructions were not the simplest ones... Read more

2. How can parametric modeling and computational shape grammars enhance flexibility and automation in architectural design generation?

This theme focuses on computational design methodologies, particularly parametric design and shape grammars, that detach shape knowledge from procedural knowledge. These techniques allow designers to specify flexible, non-deterministic design processes with logical constraints, supporting exploration and automatic generation of complex architectural and urban forms.

Key finding: The work introduces Alternative Shaper, a spatial grammar framework that separates procedural from shape knowledge, enabling flexible automatic design generation. By emphasizing symbolic representations and predicates rather... Read more
Key finding: This thesis foregrounds the role of parametric designers who leverage parametric models to explore multiple architectural design solutions. It defines parametric design as the use of variable parameters that enable automatic... Read more
Key finding: Through the parametric modeling of extensible rod and node structures, the paper demonstrates how geometric and kinematic analyses underpin architectural transformable systems. It combines digital modeling with parametric... Read more

3. What geometric constraints can be integrated into shape and topology optimization frameworks to accommodate aesthetics, fabrication, and user preferences in architectural conceptual design?

This theme delves into augmenting shape and topology optimization with geometric constraints that reflect architectural concerns beyond pure mechanical criteria. It addresses how incorporating geometric measures related to aesthetics, manufacturability, and user taste within numerical optimization frameworks can influence design outcomes and bridge the gap between mathematical optimization and creative architectural practice.

Key finding: This paper introduces three novel geometric constraints for shape and topology optimization tailored to architectural design: two addressing aesthetics (via signed distance functions and shape features) and one addressing... Read more

4. How do geometric principles and tessellation configurations manifest in architectural structural systems and influence design and construction?

This research area examines the application of tessellation—a mathematical concept of subdividing space without gaps or overlaps—in structural systems within architecture. It addresses how geometric patterns like Voronoi, hexagrids, and fractal tessellations guide form-finding, structural performance, and aesthetics, providing a rigorous link between mathematical design, parametric modeling, and physical architectural expression.

Key finding: Through analysis of eight diverse architectural buildings, this study reveals the varied use of tessellation configurations—including Voronoi, hexagrid, and fractal forms—in structural systems. It identifies how parametric... Read more

All papers in Geometric Design

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Estimations of average crash density as a function of traffic elements and characteristics can be used for making good decisions relating to planning, designing, operating, and maintaining roadway networks. This study describes the... more
This research investigates the utilization of human driving models in autonomous vehicles, particularly in scenarios with minimal or no interactions with other vehicles. Human driving models provide valuable insights into driver behavior... more
It is now known that roundabouts offer high levels of safety, but different researches on this type of intersection show that several factors influence the driver's behavior, causing occasionally wrong driving behaviors that can... more
More than one accident of three that involve pedestrians in urban area occurs at road intersections. The users’ inproper behaviour, the geometrical characteristics of the intersections, and the high speeds of vehicles are the main causes... more
The issue of traffic congestion at signalized intersections is a concern in transportation systems due to the growth of urban areas and increased vehicular transportation. To study the evolution of congestion and evaluate the traffic... more
This study is concerned with assessing the effect of geometric design and land use on roundabouts, which are one of the most widely used traffic calming techniques. It aims to study the speed profiles before, at, and after thirty selected... more
Various strategies exist to choose the best intersection design considering the operational performance of an intersection. There are model-based strategies which for example choose the design with the minimal average delay or rule-based... more
We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space... more
The contents of this analysis has been presented under the title "Open BIM für Infrastrukturmit OKSTRA und IFC-Alignment zur internationalen Standardisierung des Datenaustauschs" as part of 6th OKSTRA-Symposium (May 20th -21th 2015) in... more
This paper presents an investigation into the motorists' voluntary yielding behavior to bicycles and pedestrians at uncontrolled mid-block crosswalk locations. Two study sites in the state of Montana with LED rectangular rapid flashing... more
Amtrak has undertaken two tests of improved spiral geometry developed by the author. The first test was quite successful. The second test was less successful because of a problem in tamper operation that is unrelated to spiral geometry... more
A strongly polynomial algorithm is developed for finding an integer-valued feasible st-flow of given flow-amount which is decreasingly minimal on a specified subset F of edges in the sense that the largest flow-value on F is as small as... more
This paper investigates potential Stopping Sight Distance (SSD) violation for 130km/h vehicle speed, on the passing lane of left curved, divided highways overlapped with crest vertical curves. The authors previously developed a SSD... more
The adopted 2-D Stopping Sight Distance (SSD) adequacy investigation in current design practice may lead to design deficiencies due to inaccurate calculation of the available sight distance. Although this concern has been identified by... more
Traditional surveying tasks (i.e. mapping of road surfaces for constructing the as-built layout) or new promising applications (i.e. paver guidance), requiring high geometric element accuracy, could well be served by dynamic positioning... more
Proc. IV International Symposium Turkish-German Joint Geodetic Days, Berlin, 3-6 April. ... A COST-EFFECTIVE ROAD SURVEYING METHOD FOR THE ASSESSMENT OF ROAD ALIGNMENTS ... Basil Psarianos 1 , Demetre Paradisis 2 , Byron. Nakos 3 and... more
The connected vehicles are the future of transportation. Road can be much safer when vehicles are able to communicate about the traffic and road conditions to its surrounding vehicles or if they can "talk" to each other. A smooth... more
This study aimed to investigate the effects of the splitter-island on pedestrian safety at roundabouts, considering the interaction between pedestrians and vehicles. Traffic accident statistics have traditionally been used to assess... more
There are substantial methods of degree reduction in the literature. Existing methods share some common limitations, such as lack of geometric continuity, complex computations, and one-degree reduction at a time. In this paper, an... more
The sight distance at night is one of the most important driving safety factors. Sag vertical curves are one of the important elements of roads, which require a sufficient sight distance at night. The headlight sight distance is used for... more
On July 1, 2005, the State of Iowa implemented a 70 mile per hour (mph) speed limit on most rural Interstates. This document reports on a study of the safety effect of this change. Changes in speeds, traffic volume on and off the rural... more
Past roadside safety studies mostly evaluated the impact of traffic barrier geometric features using simulation tools or by conducting field crash tests. While past simulation and field crash tests could present important findings for... more
The aim of the paper is to design a grade separated intersection at Seke Road and Cripps/Dieppe Road in Harare, Zimbabwe. During the peak hours on weekdays, congestion and long queues occur at Seke Road and Cripps/Dieppe Roads... more
Jalan merupakan salah satu akses transportasi darat yang menghubungkan wilayah yang satu ke wilayah yang lain. Pada Ruas Jalan Trans Manado – Gorontalo yang berada pada desa Botumoputi merupakan jalan penghubung antar kota yang ada di... more
This paper reviews forms of spiral geometry that have been used and proposed as transition shapes in railroad tracks and compares them with respect to dynamic performance and spiral length. The dynamic performances that are compared were... more
In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA... more
The design and possible simplifications of four-leg channelized intersections are analysed in the paper. The research resulted in a new simpler approach in which all intersection elements are properly formed from the very beginning, so... more
In previous studies, a new (improved) turboroundabout design approach based on the rules of the design vehicle movement geometry was proposed, and the optimal design of elements of standard turboroundabouts for various design vehicle... more
Turbo roundabout is a specific kind of multilane roundabout with spiral circulatory roadway and physical separation of traffic lanes. This particular roundabout layout was developed in the Netherlands in the late nineties of the last... more
In the last 10 years in Croatia numerous roundabouts have been built in urban and interurban areas. As a rule, these roundabouts replaced the existing three-leg and four-leg intersection in order to increase intersection safety and... more
Safety in highways is one of the most important subjects in Transportation Engineering. Increasing rate of vehicles and the needs to design or geometrically modifying the highways, emphasized on the safe-designing of the roadways more... more
The problem of constructing a smooth C 1 continuous planar interpolated spline curve has attracted the attention of many people working in the area of CAD/CAM and its applications such as robotics. In the present paper we propose a method... more
Modern roundabouts adoption has strongly increased since change of give-way to circulating traffic. From that moment onwards, the most recognized Roundabout Design Guidelines have evolved throughout the implementation of numerous studies.... more
As many researchers have proved in recent years, it can be assumed that a consistent highway design is one which ensures successive elements coordinated in such a way as to produce harmonious and homogeneous driver performances and does... more
The Sukanagara-Bukanagara Road in Pagerwangi, Lembang District, West Bandung Regency, is an alternative route to the Lembang tourist area. This route is frequently used to avoid traffic congestion; however, accidents, such as vehicles... more
The Sturm spirals which can be introduced as those plane curves whose curvature radius is equal to the distance from the origin are embedded into oneparameter family of curves. Explicit parametrization of the ordinary Sturmian spirals... more
In general, the geometric planning of roads is done manually using drawing tools and mathematical techniques. When done manually, geometric design is complicated, time-consuming, and prone to errors. Therefore, this study will use AutoCAD... more
The purpose of this paper is to introduce some new classes of topological spaces by utilizing b-open sets and study some of their fundamental properties.
In urban agglomerations, signalized intersections are common. However, in traffic management, safety-focused strategies are often sacrificed for traffic efficiency by allowing simultaneous multiple conflicting movements. We identified... more
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and... more
This paper compares four systems of deployable scissor-like structures (also known as double layer grid-articulated joint systems). Its aim is to understand which of these require fewer elements to cover/span a given area. The results are... more
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