L-Drawings of Directed Graphs

We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive $x$- and $y$-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally. We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristics based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristics which confirms its effectiveness.Comment: 11 pages, 7 figure

Planar L-Drawings of Directed Graphs

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

System and method of designing a load bearing layer that interfaces to a structural pass-through of an inflatable vessel

A method for determining a design of an inflatable module including a rigid member disposed in a restraint layer, wherein the restraint layer includes orthogonal straps, includes modeling a strap adjacent to the rigid member and a strap connected to the rigid member. The adjacent strap and the member strap extend in a first direction. The method further includes selecting a first length of the member strap such that the adjacent strap carries load before the member strap during pressurization of the inflatable module, modeling tensions in the member strap with the first length and the adjacent strap during pressurization of the inflatable model, and outputting the modeled tensions in the member strap with the first length and the adjacent strap. An inflatable module includes a member strap having a length such that an adjacent strap carries load before the member strap during pressurization of the inflatable module

Specific Nature of Spatial Awareness Formation of the Bachelor of Technical Higher Education Institution of Ukraine During the Basic Course

A formed spatial awareness is one of the main professionally important quality of a young professional, a graduate of Technical and Vocational Education and Training (TVET) and higher technical education institutions. The carried out analysis of graphical preparation in the process of school studying has allowed to ascertain that enrollees of basic technical specialties are prepared not at sufficient level, the spatial awareness is formed at a low level. The shortlisting of future students on the ground of the availability of elementary spatial awareness is not conducted. The formation of spatial awareness of students during the basic course in higher technical education institutions of Ukraine is rested exclusively on instructors. As a result of the literature sources and normative documentation analysis, we have developed a structural-stage model of the process of spatial awareness formation of a bachelor of higher technical education institutions which includes the initial, basic and professional stages. There were defined problems in the first stage of training at the level of basic knowledge of the spatial awareness, and was suggested to begin studying with consideration and solving of problems on the plane with the subsequent transfer of the solution to the spatial model. The transfer to the inverse process can be accomplished only after full understanding of the interrelation of the carried out geometric actions and learning the techniques and methods of solving metric and positional problems with two and three-dimensional figures. A logframe of classes conduction and measures for its realization have been developed. Carried out experimental investigations in regards to application of the specified approach in the training process have made it possible to increase the level of formation of the basic level of spatial awareness at the beginning of training

A Typology of Design Knowledge: A Theoretical Framework

This paper is a theoretical approach to structure design-specific knowledge into a framework, which can be used within the context of organizational and societal development. We conducted an extensive literature review about existing definitions of design knowledge, and knowledge in general. Based on this, we developed a typology, which consists of four different types of design knowledge and three interjacent transitions. According to our proposed framework, design knowledge can be represented in physical artifacts, as tacit gut feeling, as codified knowledge, or as scientific theories. To illustrate further we present examples for each knowledge type and transition and we suggest prototypical approaches for transferring these types of design knowledge in the context of design education. We believe this paper contributes to a better understanding of design knowledge, and our suggested framework might serve as a foundation for further design research, and for developing ITsystems to support design processes

Algorithms and Bounds for Drawing Directed Graphs

In this paper we present a new approach to visualize directed graphs and their hierarchies that completely departs from the classical four-phase framework of Sugiyama and computes readable hierarchical visualizations that contain the complete reachability information of a graph. Additionally, our approach has the advantage that only the necessary edges are drawn in the drawing, thus reducing the visual complexity of the resulting drawing. Furthermore, most problems involved in our framework require only polynomial time. Our framework offers a suite of solutions depending upon the requirements, and it consists of only two steps: (a) the cycle removal step (if the graph contains cycles) and (b) the channel decomposition and hierarchical drawing step. Our framework does not introduce any dummy vertices and it keeps the vertices of a channel vertically aligned. The time complexity of the main drawing algorithms of our framework is $O(kn)$, where $k$ is the number of channels, typically much smaller than $n$ (the number of vertices).Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Design and manufacture of 3DOF reaction wheels as actuators for attitude control of a 1U CubeSat

The main objective of this thesis is the design and additive manufacture of various assemblies of Reaction Wheels for the Attitude Control Subsystem of a 1U CubeSat. A CubeSat is a small satellite which dimensions are 10 × 10 × 10 cm and weights 1 kg. These nanosatellites make space exploration more accessible since a lower volume of materials is needed. The mathematical models to perform numerical simulations of the reaction wheels consist of the dynamics and kinematics equations used to describe the satellite, here a quaternion representation is used. Furthermore, the derivation of the distribution matrices of each reaction wheel configuration are presented, the considered configurations are: Orthogonal, NASA Standard, Pyramid and Tetrahedral. Thereafter, the control law used for the simulation model is introduced. It was chosen to apply the typical control law for spacecraft attitude, a PD controller. This is then expressed in the quaternion feedback control, including a counteract for the gyroscopic effect of the rotating body. The Reaction Wheels mechanical design and the simulation model were established. In the mechanical design, the motor selected is the Maxon 20 EC flat. From this motor, four reaction wheel concepts are created, each one of them has a version for the NASA Standard and the Pyramid configuration. These configurations are chosen because they offer redundancy and are suitable to fit in the CubeSat constraints. The fifth concept C5 is for another motor of interest due to its reduced size. Successively, the simulation model is introduced, with an explanation of each block with their inputs and outputs. Subsequently, the concepts were 3D printed and manually assembled. Thereafter, the simulation results showed that the chosen reaction wheels can efficiently control the attitude of the satellite even when one wheel of the redundant system fails. The outcomes for this thesis are that Concept 4 of the mechanical design is the most convenient since it takes advantage of the extra inertia of the external-rotor of the motor. Furthermore, in the numerical simulations the tetrahedral configuration performs the maneuver more effectively, however for a better layout distribution of the wheels, the pyramid configuration is the optimal with good performance results and the best space usability in the CubeSat