Geometric Visualization Research Articles

Geometrical Shape Analysis for Investment Casting Turbine Blade Based on Optical Measurement

Turbine blade is one of the key components of the aero engine. It needs to be inspected comprehensively and carefully during its production stage. The methods for investment turbine blade geometrical shape analysis based on optical scanning measurement were presented, including optical measurement data collection, blade model reliable alignment and geometrical shape deviation fast calculation and visualization. Real measurement data from a structure light measurement device for a turbine blade was used to validate the discussed methods.

ERMES: A nodal-based finite element code for electromagnetic simulations in frequency domain

In this work we present a new finite element code in frequency domain called ERMES. The novelty of this computational tool rests on the formulation behind it. ERMES is the C++ implementation of a simplified version of the weighted regularized Maxwell equation method. This finite element formulation has the advantage of producing well-conditioned matrices and the capacity of solving problems in the low (quasi-static) and high frequency regimens. As a consequence of this versatility, ERMES has been applied successfully to microwave engineering, antenna design, electromagnetic compatibility and eddy currents problems. This paper describes the main features of ERMES and explains how to use this numerical tool for computing electromagnetic fields in frequency domain. Program summaryProgram title: ERMESCatalogue identifier: AEPV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 223528No. of bytes in distributed program, including test data, etc.: 35954099Distribution format: tar.gzProgramming language: C++.Computer: Any computer with Microsoft Windows (32-bits or 64-bits) installed.Operating system: Microsoft Windows 32-bits or 64-bits.RAM: Problem dependent. See [1] for examples of computational performance.Classification: 10.External routines:GiD [5] is used for geometrical modeling, data input, meshing and visualization of results.Nature of problem:Time-harmonic Maxwell equations.Solution method:Finite element formulation based on the weighted regularized Maxwell equation method [2, 1, 3, 4].Additional comments:!!!!! The distribution file for this program is approximately 35 Mbytes and therefore is not delivered directly when the download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!!!Running time:Problem dependent (see [1]).

Visualizing nD Point Clouds as Topological Landscape Profiles to Guide Local Data Analysis

Analyzing high-dimensional point clouds is a classical challenge in visual analytics. Traditional techniques, such as projections or axis-based techniques, suffer from projection artifacts, occlusion, and visual complexity. We propose to split data analysis into two parts to address these shortcomings. First, a structural overview phase abstracts data by its density distribution. This phase performs topological analysis to support accurate and nonoverlapping presentation of the high-dimensional cluster structure as a topological landscape profile. Utilizing a landscape metaphor, it presents clusters and their nesting as hills whose height, width, and shape reflect cluster coherence, size, and stability, respectively. A second local analysis phase utilizes this global structural knowledge to select individual clusters or point sets for further, localized data analysis. Focusing on structural entities significantly reduces visual clutter in established geometric visualizations and permits a clearer, more thorough data analysis. This analysis complements the global topological perspective and enables the user to study subspaces or geometric properties, such as shape.

Geometric visualization of self-propulsion in a complex medium.

Combining geometric mechanics theory, laboratory robotic experiment, and numerical simulation, we study the locomotion in granular media of the simplest noninertial swimmer, the Purcell three-link swimmer. Using granular resistive force laws as inputs, the theory relates translation and rotation of the body to shape changes (movements of the links). This allows analysis, visualization, and prediction of effective movements that are verified by experiment. The geometric approach also facilitates comparison between swimming in granular media and in viscous fluids.

Pavel Florenskij mellom geometriske utopier og ikonkosmologi

Pavel Florensky Between Geometrical Utopies and Icon Cosmology On the occasion of the 130th anniversary of the birth of Pavel Florensky, the aim of this article is to analyse the connection between Florensky's mathematical approach to the physical space in the book Imaginations in Geometry and his influence on new the- ories of the space of the icon. The 19th and early 20th centuries witnessed a revolution in mathematics through the development of non-Euclidean geometry and the fourth dimension, which Florensky interpreted as rehabilitation of the philosophy of the Middle Ages. In Imaginations in Geometry he conceptualized a «Ptolemeic-Dantic view of the world» where by means of the Special Theory of Relativity he made an exact approach to the physical characteristics of objects in the border between Heaven and Earth. Although Florensky did not introduce any «divine geometry» when it came to the icon, the concurrent art theorist Nikolay Tarabukin was influenced by Imagina- tions in Geometry. Tarabukin interpreted the so-called «inverse perspective» as a non- Euclidean geometrical visualization of the metaphysical worldview of the Middle Ages that got lost in Europe in the Renaissance, and in Russia under Peter the Great, but is reborn in the 20th century, inspired by the experiments in mathematics.

Does the use of technology make a difference in the geometric cognitive growth of pre-service mathematics teachers?

<blockquote>This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design was used. Similar course content was used for both the control and experimental groups. The students worked through a series of geometry activities and problems. The difference between the groups was that dynamic geometry software was integrated into the teaching of the experimental group. The <em>Cognitive Development and Achievement in Secondary School Geometry</em> (CDASSG) Van Hiele geometry test was used to determine all the students' level of geometric thinking before and after the course. The study found that the use of dynamic geometry software enhanced student teachers' geometric visualisation, analysis and deduction, but not their ability to informally justify their reasoning and to understand the formal aspects of deduction.</blockquote>

Mechanistic models for the intramolecular hydroxycarbene–formaldehyde conversion and their intermolecular interactions: Theory and chemistry of radicals, mono‐, and dications of hydroxycarbene and related configurations

AbstractWe have studied with theoretical and mechanistic models the intramolecular 1,2‐hydrogen shift in trans‐hydroxycarbene‐formaldehyde and trans‐methylhydroxycarbene‐acetaldehyde/vinyl alcohol, and the corresponding intermolecular complexation between hydroxycarbene (cis and trans) with formaldehyde. The purpose of our work is making an analysis of the proposed intramolecular hydrogen shifts mainly based on thermodynamic principles and the product selectivity on monochromatic irradiation of trans‐hydroxycarbene in carbon monoxide and molecular hydrogen, and formaldehyde. A geometric visualization of the various intermolecular complexes between hydroxycarbene and formaldehyde, based on ab initio results, is demonstrated and discussed with a concept abstracted from the van't Hoff dynamics for a regular tetrahedron in which the interstitial carbon changes its position from tetrahedral into a trigonal‐bipyramidal configuration. This concept has been also used for interactions via proton transfer, concretized as hydrogen‐bonded complexation in hydroxycarbene‐formaldehyde. With the introduced definitions for various van't Hoff ratio numbers, it was possible to judge the ab initio results of the intermolecular complexes between the hydroxycarbenes and formaldehyde. To make an eye‐opener, we discuss the role of the carbene lone pair in hydroxycarbene extended to the formation of mono‐ and dications demonstrating intermediates or transition states with an exclusive mechanistic behavior. Especially, substituted diaryl methylene dications are of interest for nucleophilic substitution reactions, which occur via an in‐plane tetracoordinate carbon intermediate, showing coherence with the orbital organization of methylene dications. A reaction of this type differs fundamentally from the classical S reaction. © 2012 Wiley Periodicals, Inc.

Polyomino Dissections

SummaryOne of Gardner's passions was to introduce puzzles into the classroom. From this point of view, polyomino dissections are an excellent topic. They require little background, provide training in geometric visualization, and mostly they are fun. In this article, we put together a large collection of such puzzles, introduce a new approach in solving them, and discuss the practical considerations in presenting these puzzles to children.

Centroidal Voronoi tessellation in universal covering space of manifold surfaces

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework – the CVT in universal covering space. The novel spherical and hyperbolic CVT energy functions are defined, and the relationship between minimizing the energy and the CVT is proved. We also show by our experimental results that both spherical and hyperbolic CVTs have the similar property as their Euclidean counterpart where the sites are uniformly distributed with respect to given density values. As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus > 1) surfaces.

Sexual shape dimorphism in Serbian roe deer ( Capreolus capreolus L.)

The focus of studies of sexual dimorphism has been mainly on size whereas shape has remained largely ignored when assessing population differentiation. In order to extract exclusive information about shape variability, we combined multivariate statistical procedures with geometric morphometrics and visualization techniques (thin plate splines). All roe deer skulls, used in this study, originated from a single population in Serbia. Our results showed statistically significant sexual dimorphism of male and female skull shape. Different patterns of shape variability in males and females were observed, such as broader cranial base in males and elongated and more slender shape of female skull, with narrower basicranium. Shape differences appear to be regulated only broadly by social structure and sexual selection, and some other mechanisms could be proposed for further explanation of sexual dimorphism.

Open-system effects on slow light and electromagnetically induced transparency

The coherence properties of a three-level Λ-system influenced by a Markovian environment are analysed. A coherence vector formalism is used and a vector form of the Lindblad equation is derived. Together with decay channels from the upper state, open-system channels acting on the subspace of the two lower states are investigated, i.e. depolarization, dephasing and amplitude damping channels. We derive an analytic expression for the coherence vector and the concomitant optical susceptibility, and analyse how the different channels influence the optical response. This response depends non-trivially on the type of open-system interaction present, and even gain can be obtained. We also present a geometrical visualization of the coherence vector as an aid to understand the system response.

Intraoperative real-time querying of white matter tracts during frameless stereotactic neuronavigation.

Brain surgery faces important challenges when trying to achieve maximum tumor resection while avoiding postoperative neurological deficits. For surgeons to have optimal intraoperative information concerning white matter (WM) anatomy, we developed a platform that allows the intraoperative real-time querying of tractography data sets during frameless stereotactic neuronavigation. Structural magnetic resonance imaging, functional magnetic resonance imaging, and diffusion tensor imaging were performed on 5 patients before they underwent lesion resection using neuronavigation. During the procedure, the tracked surgical tool tip position was transferred from the navigation system to the 3-dimensional Slicer software package, which used this position to seed the WM tracts around the tool tip location, rendering a geometric visualization of these tracts on the preoperative images previously loaded onto the navigation system. The clinical feasibility of this approach was evaluated in 5 cases of lesion resection. In addition, system performance was evaluated by measuring the latency between surgical tool tracking and visualization of the seeded WM tracts. Lesion resection was performed successfully in all 5 patients. The seeded WM tracts close to the lesion and other critical structures, as defined by the functional and structural images, were interactively visualized during the intervention to determine their spatial relationships relative to the lesion and critical cortical areas. Latency between tracking and visualization of tracts was less than a second for a fiducial radius size of 4 to 5 mm. Interactive tractography can provide an intuitive way to inspect critical WM tracts in the vicinity of the surgical region, allowing the surgeon to have increased intraoperative WM information to execute the planned surgical resection.

Large-Scale Vector Data Visualization using High Performance Computing

In computational flow visualization, integration based geometric flow visualization is often used to explore the flow field structure. A typical time-varying dataset from a Computational Fluid Dynamics (CFD) simulation can easily require hundreds of gigabytes to even terabytes of storage space, which creates challenges for the consequent data-analysis tasks. This paper presents new techniques for visualization of extremely large time-varying vector data using high performance computing. The high level require-ments that guided the formulation of the new techniques are (a) support for large dataset sizes, (b) support for temporal coherence of the vector data, (c) support for distributed memory high performance computing and (d) optimum utilization of the computing nodes with multi-cores (multi-core processors). The challenge is to design and implement techniques that meet these complex requirements and bal-ance the conflicts between them. The fundamental innova-tion in this work is developing efficient distributed visualiza-tion for large time-varying vector data. The maximum performance was reached through the parallelization of mul-tiple processes on the multiple cores of each computing node. Accuracy of the proposed techniques was confirmed compared to the benchmark results. In addition, the pro-posed techniques exhibited acceptable scalability for differ-ent data sizes with better scalability for the larger ones. Finally, the utilization of the computing nodes was satisfactory for the considered test cases.

Over Two Decades of Integration‐Based, Geometric Flow Visualization

AbstractWith ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization, which deals with large, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding algorithm upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an up‐to‐date overview of the current state‐of‐the‐art that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.

Dynamics of liquid–liquid systems based on linear thermodynamics of irreversible processes

The use of non-equilibrium models for integrated processes involving liquid–liquid systems has increased in recent years. These processes often exhibit complex dynamic behavior. These dynamical systems still pose many open questions, e.g. with regard to the sources of multiple steady states (MSS). This article analyzes the effect of mass transfer on the MSS of these systems. A generalized non-equilibrium modeling approach based on linear thermodynamics of irreversible processes (LTIP) is presented, and the dynamics of the system is studied systematically. It is shown that the non-linearity present in even the simplest non-ideal activity model acts as a source for MSS. The parameters that affect the solubility, e.g. temperature, can play a critical role on the existence of MSS in the system. A geometrical visualization of the MSS is also illustrated.

Delaunay deformable mesh for the weathering and erosion of 3D terrain

Computer-generated erosion and weathering are important to convey setting and mood in computer generated images. Heightmap based landforms are good for distant scenes, but inadequate for scenes containing concave rock formations. Voxel based terrain editing algorithms do admit concave surfaces but do not scale. We introduce weathering on triangulated surface meshes, using a memory efficient modification of the Delaunay deformable model. This structure allows the freedom of an unorganized point cloud, the geometric information and visualization of a surface mesh, and the topological freedom of volumetric approaches—all while scaling linearly with surface complexity. We implement both spheroidal weathering and hydraulic erosion algorithms on this structure and demonstrate that the resulting terrain is visually plausible at modest computational cost.

Some Numerical Methods for Temperature and Mass Transfer Simulation on the Dehydration of Herbs

Advances in herbs based products preservation and technologies are very significant in order to reduce post-harvest losses. The dynamic mathematical model of concurrent heat and moisture transfer are being established for the simulation of temperature and moisture distributions inside the herbs material during dehydration potential of herbs in a slab-shaped solid. Mathematical modeling presents the exchange of heat and mass transfer between material and drying air. Finite-difference method (FDM) based on Crank-Nicolson was used to discretise a parabolic type partial differential equations (PDE). The key purpose of this study is to illustrate the simulation of tropical herbs’ dehydration through some numerical methods such as Jacobi, Gauss-Seidel and Red-Black Gauss-Seidel. This study focuses on the implementation of sequential algorithms on the simulation. 3D geometric visualization by COMSOL Multiphysics and graphical numerical results of FDM approximation in mass and heat transfer demonstrate the results of this study. The contribution of this study is a flourishing and modified mathematical simulation in representing the concrete process of dehydration in herbs product based industry. Most thermal and moisture models are empirical rather than theoretical. Therefore, the novelty of this paper is the best sources of thermal and moisture data for the commercial tropical herbs dehydration derived from the mathematical model in order to avoid high prototype costs and to improve inaccurate conditions and process parameters with the advancement of dryer technologies. The computational platform is based on Intel®Core™2Quad processors with MATLAB software. The performance analyses of Numerical methods are presented in terms of execution time, computational complexity, number of iterations, errors, accuracy and convergence rate.

Development of a Geometric Spatial Visualization Tool

This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns) after experiencing a carefully designed integrated lunar unit. Previous research with students using this lunar unit showed students making significant gains on lunar‐related concepts (both scientific and mathematical) on a Lunar Phases Concept Inventory (LPCI) (Lindell & Olsen, 2002). Following the administration of single domain assessments, clinical interviews were conducted to ascertain students' problem solving strategies. Results allowed us to select four suitable multiple‐choice items per domain.

Time‐Adaptive Lines for the Interactive Visualization of Unsteady Flow Data Sets

Abstract The quest for the ideal flow visualization reveals two major challenges: interactivity and accuracy. Interactivity stands for explorative capabilities and real‐time control. Accuracy is a prerequisite for every professional visualization in order to provide a reliable base for analysis of a data set. Geometric flow visualization has a long tradition and comes in very different flavors. Among these, stream, path and streak lines are known to be very useful for both 2D and 3D flows. Despite their importance in practice, appropriate algorithms suited for contemporary hardware are rare. In particular, the adaptive construction of the different line types is not sufficiently studied. This study provides a profound representation and discussion of stream, path and streak lines. Two algorithms are proposed for efficiently and accurately generating these lines using modern graphics hardware. Each includes a scheme for adaptive time‐stepping. The adaptivity for stream and path lines is achieved through a new processing idea we call ‘selective transform feedback’. The adaptivity for streak lines combines adaptive time‐stepping and a geometric refinement of the curve itself. Our visualization is applied, among others, to a data set representing a simulated typhoon. The storage as a set of 3D textures requires special attention. Both algorithms explicitly support this storage, as well as the use of precomputed adaptivity information.

Gender Differences in Lunar‐related Scientific and Mathematical Understandings

This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle‐level students interacted with the Moon through observations, sketching, journalling, two‐dimensional and three‐dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic Explorations in Astronomical Learning (REAL) curriculum. Students’ conceptual understandings were measured through analysis of pre‐test and post‐test results on a Lunar Phases Concept Inventory (LPCI) and a Geometric Spatial Assessment (GSA). The LPCI was used to assess conceptual learning of eight science and four mathematics domains. The GSA was used to assess learning of the same four mathematical domains; however, the GSA test items were not posed within a lunar context. Results showed both male and female groups to make significant gains in understanding on the overall LPCI test scores as well as significant gains on five of the eight science domains and on three of the four mathematics domains. The males scored significantly higher than the females on the science domain, phase—Sun/Earth/Moon positions, and on the mathematics domain geometric spatial visualisation. GSA results found both male and female groups achieving a significant increase in their test scores on the overall GSA. Females made significant gains on the GSA mathematics domains, periodic patterns and cardinal directions, while males made significant gains on only the periodic patterns domain. Findings suggest that both scientific and mathematical understandings can be significantly improved for both sexes through the use of spatially focused, inquiry‐oriented curriculum such as REAL.