Shape Theory Research Articles

From reverse engineering to shape engineering in mechanical design

Reverse engineering and shape reconstruction play an important role in design and manufacturing through the increased use of shape acquisition and processing technologies in the product development process. The application of shape theories to geometric modelling and variability characterization are paving the way to shape engineering and more generic methods for reverse engineering.This paper investigates the fundamentals of shape representation, shape processing and mining at a conceptual, geometric and computational level to address geometric reverse engineering issues in mechanical design. New developed concepts based on discrete curvatures and their applications are presented. Challenges and future researches are also highlighted.

超精密切削加工における機上計測のためのセッティング誤差の影響解析に関する研究

In order to achieve ultraprecision machining, commercial scanning devices for on-machine measurement have been developed to realize corrective machining without removing the workpiece from machine tools. However, the shapes to be machined shift to more complicated free curved surface such as a non-axisymmetric and non-spherical shape. Thus, it takes long time to scan whole surface of the workpiece. In addition, tool setting errors are remarkably larger than positioning errors of ultraprecision machine tools. Therefore, in order to generate efficient scanning paths, a method based on form shaping theory is devised to analyze both the machined surface and the measurement results influenced by the tool setting errors.

On some problem of Borsuk concerning decompositions of shapes into prime factors

In this paper we show that there exists a 3-dimensional continuum with two different decompositions into a direct product of prime factors in the shape category. This gives the positive answer to a question of K. Borsuk from his monograph “Theory of Shape” (1975).

False pop out.

A single, unique target often pops out quickly and efficiently from a field of homogenous distractors in visual search. Pop out has helped shape theories of visual attention and feature integration as well as to identify basic features in human vision. Here we report a new phenomenon, false pop out, wherein one of the homogenous distractors competes with the singleton target to pop out, perhaps by breaking an overall grouping or pattern emerging from the display. We show the effect occurs with more than 1 type of stimulus, and we discuss the implications of such a counterintuitive finding for theories of visual search.

Elliptical affine shape distributions for real normed division algebras

The statistical affine shape theory is set in this work in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical distribution; then the separated published works about real and complex shape distributions can be obtained as corollaries by a suitable selection of the field parameter and univariate integrals involving the generator elliptical function. As a particular case, the complex normal affine density is derived and applied in brain magnetic resonance scans of normal and schizophrenic patients. • Statistical affine shape theory in the context of real normed division algebras is studied. • Affine shape density is obtained. • The complex normal affine density is derived and applied in brain magnetic resonance scans of normal and schizophrenic patients.

Linkage model and manufacturing process of shaping non-circular gears

Current research of non-circular gear processing mainly focuses on gear hobbing. However, this method has many limitations including being unable to process internal gears or non-circular external gears with a concave pitch curve and is likely to undercut when processing non-circular gears of greater curvature with a smaller number of teeth. Gear shaping, in contrast, is a method that is able to overcome the limitations of gear hobbing. Relevant studies on gear shaping have focused on the theoretical bases rather than the concrete processes and tools. Through the combination of shaping theory and practice, this paper aimed to derive a linkage model for shaping non-circular gears, and to refine the feeding strategy, and develop a cutter retraction and cutter setting method. Finally, with a pair of 3-order sinusoidal-gear-ratio non-circular gears, this paper demonstrated the entire process in a CNC gear-shaping machine, thus proving the accuracy of the mathematical model and providing a valid reference for shaping non-circular gears.

An Investigative Study on Early Diagnosis of Breast Cancer Using a New Approach of Mathematical Shape Theory and Neuro-Fuzzy Classification System

Breast cancer is one of the main causes of death among women in the world. For the early detection and classification of the abnormal growth of masses in the breast either in benign or malignant stage, the authors have used the extracted shape-based features from the mammographic images. This paper presents an investigation and comparison study of the extracted shape-based features such as shape distance and shape similarity measure from the region of interest of the mammographic image with the neuro-fuzzy classification system for pattern recognition.

Rule-Based Design, in Honour of Lionel March

Design rules are directives that guide the design process towards the product. They are often specific descriptions of decisions and acts, which, taken as a whole, make up a design. Sometimes numeric, sometimes verbal, and most often visual or spatial, these descriptions have formed the core of analyses and recreations of design thinking since early history, with the most recent connotations arising in design computing. This issue of the Network Nexus Journal is dedicated to Lionel March, whose seminal contributions to computational art, architecture and design have profoundly influenced our understanding of creative thinking since the 1970s. As the preparations ensued for the tenth Nexus conference ‘‘Nexus 2014: Relationships between Architecture and Mathematics’’ (Ankara, 2014), it was decided that one of the sessions, Rule-Based Design, was to celebrate the legacy of Lionel March in the year of his 80th birthday. Four of the papers presented in that session in Ankara have found their way to this special issue. When Lionel could not attend the conference personally, Kim Williams and I pursued the idea of a celebration in other forms. I am grateful to Kim, who then invited me to guest edit this issue and gave me the chance to bring together texts by prominent scholars of computational design and architecture with much appreciation for Lionel’s presence in the field. In line with the breadth of the impact that Lionel March has had in the field, the issue offers fourteen texts on a variety of topics and approaches of research. Seven of the papers focus on design ontologies, typologies, generative specifications and generating designs that range in scale from the city to furniture. Nine of the papers, some overlapping with the above seven, either directly focus or refer to shape grammars, a computational theory of shapes and visual thinking in design. Among

Shape classification based on interpoint distance distributions

According to Kendall (1989), in shape theory, The idea is to filter out effects resulting from translations, changes of scale and rotations and to declare that shape is what is left. While this statement applies in principle to classical shape theory based on landmarks, the basic idea remains also when other approaches are used. For example, we might consider, for every shape, a suitable associated function which, to a large extent, could be used to characterize the shape. This finally leads to identify the shapes with the elements of a quotient space of sets in such a way that all the sets in the same equivalence class share the same identifying function. In this paper, we explore the use of the interpoint distance distribution (i.e.?the distribution of the distance between two independent uniform points) for this purpose. This idea has been previously proposed by other authors e.g.,?Osada et?al. (2002), Bonetti and Pagano (2005). We aim at providing some additional mathematical support for the use of interpoint distances in this context. In particular, we show the Lipschitz continuity of the transformation taking every shape to its corresponding interpoint distance distribution. Also, we obtain a partial identifiability result showing that, under some geometrical restrictions, shapes with different planar area must have different interpoint distance distributions. Finally, we address practical aspects including a real data example on shape classification in marine biology.

Optimum Shapes of Elastic Bodies: Equistrong Wings of Aircrafts and Equistrong Underground Tunnels

Since the times of Plato (424?-347 BC) and Aristotle (384-322 BC), the form has been considered as a fundamental notion of not only the physical universe, but also the spiritual world. The forms and perfect shapes are like jewels in the rock—their search and discovery make up the highest delight to human beings. This is what constituted the motive and driving force of science and scientists beginning from Pythagoras (ca. 570-ca. 500 BC), Archimedes (ca. 287-ca. 212 BC), Euclid (ca. 330-ca. 260 BC) and all that came after. In the introduction to the present article, a brief account of Plato’s theory of forms and Aristotle’s addition to this theory are given; the theory of optimum shapes of elastic bodies can be considered as a footnote to the Plato’s theory. In the framework of the theory of elasticity, the optimal shape of a body is the shape that meets the principle of equal strength or equistrength advanced by this author in 1963. According to this principle, the safety criterion like ultimate or failure stress is simultaneously satisfied in the utmost part of the body—this body or structure is called equistrong in this case. The equistrong structure has a minimum weight for a given material and safety factor, or a maximum safety factor for a given material and weight. As distinct from traditional problems, there are no existence theorems for equistrong shapes—a success in their search depends on skills of a researcher. In the present paper, a summary of common equistrong shapes and structural elements is brought out, namely: equistrong cable of bathysphere, equistrong tower or skyscraper, equistrong beam by Galileo Galilei, equistrong rotating disk, equistrong heavy chain, equistrong pressure vessels, equistrong arcs, plates and shells, equistrong underground tunnels, equistrong perforated plates, and others. A variety of the swept wings of aircrafts is found out to be equistrong; the front and rear edges of such wings are rectilinear in the plan view, and their chord in the flight direction depends on the task of an aircraft; the equistrong design exists for any task, from transport aviation to hypersonic jet fighters. Some new equistrong shapes of elastic solids with any number of infinite branches being pulled out of a body are also discovered for plane strain and plane stress.

Cultural humility: The cornerstone of positive contact with culturally different individuals and groups?

Comments on the original article by Christopher et al. (see record 2014-20055-001) regarding cultural and folk psychologies. As noted by Christopher, Wendt, Marecek, and Goodman (2014), "U.S. psychology remains not only overwhelmingly U.S.- centric but also largely unaware of how its cultural roots shape theory and research.

ChemInform Abstract: Metallic Nanocrystals Synthesized in Solution: A Brief Review of Crystal Shape Theory and Crystallographic Characterization

AbstractReview: 73 refs.

Russia’s Legal Transitions: Marxist Theory, Neoclassical Economics and the Rule of Law

We review the role of economic theory in shaping the process of legal change in Russia during the two transitions it experienced during the course of the twentieth century: the transition to a socialist economy organised along the lines of state ownership of the means of production in the 1920s, and the transition to a market economy which occurred after the fall of the Soviet Union in the 1990s. Despite differences in methodology and in policy implications, Marxist theory, dominant in the 1920s, and neoclassical economics, dominant in the 1990s, offered a similarly reductive account of law as subservient to wider economic forces. In both cases, the subordinate place accorded to law undermined the transition process. Although path dependence and history are frequently invoked to explain the limited development of the rule of law in Russia during the 1990s, policy choices driven by a deterministic conception of law and economics also played a role.

CO2 absorption in band wings in near IR

The CO2 absorption was measured in the 7000 and 8000 cm–1 regions. The absorption coefficients were calculated using the asymptotic line wing shape theory. Line shape parameters were found from fitting to experimental data. The calculation results agree well with the measurement data. According to the line wing theory, the absorption in the band wings is caused by the wings of strong lines of an adjacent band. Within these assumptions, experimental and calculated data on the CO2 absorption coefficient in the band wings in the 7000 and 8000 cm–1 regions can provide information on the line shape at frequency detuning from several tens to several hundreds of half-widths. The results support the hypothesis that line shape parameters in the line wings related to transitions with the same initial state are close to each other. Deviations from a Lorentzian profile are found for some CO2 bands and turn out different for the wings of different bands

Optimal Formation of Multirobot Systems Based on a Recurrent Neural Network.

The optimal formation problem of multirobot systems is solved by a recurrent neural network in this paper. The desired formation is described by the shape theory. This theory can generate a set of feasible formations that share the same relative relation among robots. An optimal formation means that finding one formation from the feasible formation set, which has the minimum distance to the initial formation of the multirobot system. Then, the formation problem is transformed into an optimization problem. In addition, the orientation, scale, and admissible range of the formation can also be considered as the constraints in the optimization problem. Furthermore, if all robots are identical, their positions in the system are exchangeable. Then, each robot does not necessarily move to one specific position in the formation. In this case, the optimal formation problem becomes a combinational optimization problem, whose optimal solution is very hard to obtain. Inspired by the penalty method, this combinational optimization problem can be approximately transformed into a convex optimization problem. Due to the involvement of the Euclidean norm in the distance, the objective function of these optimization problems are nonsmooth. To solve these nonsmooth optimization problems efficiently, a recurrent neural network approach is employed, owing to its parallel computation ability. Finally, some simulations and experiments are given to validate the effectiveness and efficiency of the proposed optimal formation approach.

Metallic nanocrystals synthesized in solution: a brief review of crystal shape theory and crystallographic characterization

This article reviews the main theoretical/computational techniques and the experimental characterization methodologies that are used in the quest to investigate the shape, size, composition, and crystallography of metallic nanoparticles. Two morphological regimes are described, one governed by equilibrium thermodynamics, and another in which the shape can be controlled kinetically: in each case, the focus is on key phenomenological effects, ignoring to a large extent the specifics of the materials. For the equilibrium crystal shape, the field has recently experienced developments beyond the basic Wulff construction. For the kinetically controlled case, we argue that models informed by experiments can lead to insights into the growth mechanisms, as well as into the resulting shapes and morphologies. Experimentally, the increasing resolution of characterization techniques can inform and validate the growth models. While ex situ characterization techniques have become de facto standards for investigations of nanoparticles, in situ techniques offer significant advances in spatial and temporal resolution and help establish a fundamental understanding of growth mechanisms.

Dependence of the ferroelectric domain shape on the electric field of the microscope tip

A theory of an equilibrium shape of the domain formed in an electric field of a scanning force microscope (SFM) tip is proposed. We do not assume a priori that the domain has a fixed form. The shape of the domain is defined by the minimum of the free energy of the ferroelectric. This energy includes the energy of the depolarization field, the energy of the domain wall, and the energy of the interaction between the domain and the electric field of the SFM tip. The contributions of the apex and conical part of the tip are examined. Moreover, in the proposed approach, any narrow tip can be considered. The surface energy is determined on the basis of the Ginzburg-Landau-Devonshire theory and takes into account the curvature of the domain wall. The variation of the free energy with respect to the domain shape leads to an integro-differential equation, which must be solved numerically. Model results are illustrated for lithium tantalate ceramics.

Theory across time: the privileging of time-less theory in international relations

How does the understanding of time and temporality in international relations (IR) shape the study of international politics? IR is centrally concerned with the study of issues such as armed conflict, but wars are events – a series of occurrences that only come into being through their relationship across time. The concept of time at work in the understanding of this event thus plays an inextricable role in the scholarship produced. IR shares an understanding of time that pervades (traditional) social science and is based on the Western notion of clock-time. This conception of time encourages a spatiotemporal model of the past that epistemologically privileges temporal understandings that value generalizable, time-invariant theory and discount temporal fluidity and context. These temporal commitments operate at a deep level, informing and shaping theory construction in important ways and de-emphasizing alternative approaches that may more accurately reflect the contingency of international events, discontinuities in political practice, and the radical shifts in international structures, which are often most in need of scholarly analysis. This article concludes that by treating temporality as a stand-alone issue, IR can better model and predict international political practices.

Russia's Legal Transitions: Marxist Theory, Neoclassical Economics and the Rule of Law

We review the role of economic theory in shaping the process of legal change in Russia during the two transitions it experienced during the course of the twentieth century: the transition to a socialist economy organised along the lines of state ownership of the means of production in the 1920s, and the transition to a market economy which occurred after the fall of the Soviet Union in the 1990s. Despite differences in methodology and in policy implications, Marxist theory, dominant in the 1920s, and neoclassical economics, dominant in the 1990s, offered a similarly reductive account of law as subservient to wider economic forces. In both cases, the subordinate place accorded to law undermined the transition process. Although path dependence and history are frequently invoked to explain the limited development of the rule of law in Russia during the 1990s, policy choices driven by a deterministic conception of law and economics also played a role.

The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.