Search

This paper introduces a novel method for solving the resection problem in two and three dimensions based on conformal geometric algebra (CGA). Advantage is taken because of the characteristics of CGA, which enables the representation of points, lines, planes, and volumes in a unified mathematical framework and offers a more intuitive and geometric understanding of the problem, in contrast to existing purely algebraic methods. Several numerical examples are presented to demonstrate the efficacy of the proposed method and to compare its validity with established techniques in the field. Numerical simulations indicate that our vector geometric algebra implementation is faster than the best-known algorithms to date, suggesting that the proposed GA-based methods can provide a more efficient and comprehensible solution to the two- and three-dimensional resection problem, paving the way for further applications and advances in geodesy research. Furthermore, the method's emphasis on graphical and geometric representation makes it particularly suitable for educational purposes, allowing the reader to grasp the concepts and principles of resection more effectively. The proposed method has potential applications in a wide range of other fields, including surveying, robotics, computer vision, or navigation. [ABSTRACT FROM AUTHOR]

The relationship between brain lesions and stroke outcomes is crucial for advancing patient prognosis and developing effective therapies. Stroke is a leading cause of disability worldwide, and it is important to understand the neurological basis of its varied symptomatology. Lesion-symptom mapping (LSM) methods provide a means to identify brain areas that are strongly associated with specific symptoms. However, inner variations in LSM methods can yield different results. To address this, our study aimed to characterize the lesion-symptom mapping variability using three different LSM methods. Specifically, we sought to determine a lesion symptom core across LSM approaches enhancing the robustness of the analysis and removing potential spatial bias. A cohort consisting of 35 patients with either right- or left-sided middle cerebral artery strokes were enrolled and evaluated using the NIHSS at 24 h post-stroke. Anatomical T1w MRI scans were also obtained 24 h post-stroke. Lesion masks were segmented manually and three distinctive LSM methods were implemented: ROI correlation-based, univariate, and multivariate approaches. The results of the LSM analyses showed substantial spatial differences in the extension of each of the three lesion maps. However, upon overlaying all three lesion-symptom maps, a consistent lesion core emerged, corresponding to the territory associated with elevated NIHSS scores. This finding not only enhances the spatial accuracy of the lesion map but also underscores its clinical relevance. This study underscores the significance of exploring complementary LSM approaches to investigate the association between brain lesions and stroke outcomes. By utilizing multiple methods, we can increase the robustness of our results, effectively addressing and neutralizing potential spatial bias introduced by each individual method. Such an approach holds promise for enhancing our understanding of stroke pathophysiology and optimizing patient care strategies. [ABSTRACT FROM AUTHOR]

AbstractSpatial heterogeneity is of great importance in social, economic, and environmental science studies. The spatially varying coefficient model is a popular and effective spatial regression technique to address spatial heterogeneity. However, accounting for heterogeneity comes at the cost of reducing model parsimony. To balance flexibility and parsimony, this article develops a class of generalized partially linear spatially varying coefficient models which allow the inclusion of both constant and spatially varying effects of covariates. Another significant challenge in many applications comes from the enormous size of the spatial datasets collected from modern technologies. To tackle this challenge, we design a novel distributed heterogeneity learning (DHL) method based on bivariate spline smoothing over a triangulation of the domain. The proposed DHL algorithm has a simple, scalable, and communication-efficient implementation scheme that can almost achieve linear speedup. In addition, this article provides rigorous theoretical support for the DHL framework. We prove that the DHL constant coefficient estimators are asymptotic normal and the DHL spline estimators reach the same convergence rate as the global spline estimators obtained using the entire dataset. The proposed DHL method is evaluated through extensive simulation studies and analyses of U.S. loan application data. [ABSTRACT FROM AUTHOR]

AbstractObjectiveMethodsResultsDiscussion\nIMPLICATIONS FOR REHABILITATIONWeb-based platforms for delivering physical activity (PA) to people with developmental disabilities have a great potential to improve the lives of many. However, their design, including the content design, lacks sufficient investigation. This study aims to evaluate three online platforms for delivering PA to people with developmental disabilities in terms of content quality and identify relevant barriers and facilitators of PA delivery.The study used a methodological triangulation approach which involved quantitative evaluations by experts using an evaluation rubric, on-site observations and in-depth interviews with recruited participants. The participants consisted of 15 pairs of individuals, each consisting of a person with developmental disabilities and their primary caregiver. They were instructed to watch and follow five PA video content from each of the three platforms. The on-site observations and interviews were conducted in a large computer-equipped meeting room setting.The quantitative and qualitative analysis identified a set of barriers and facilitators of PA delivery related to content quality. Key barriers identified include a lack of content diversity, insufficient understanding of developmental disabilities among content creators, inappropriate language usage, and resistance to engaging in physical activities in home settings. Significant facilitators were pinpointed, such as incorporating engaging elements for individuals with developmental disabilities, utilising easy-read language, and ensuring sufficient repetition for effective learning. The results from the triangulation showed that the multiple methods were complementary and converged on the same outcome.The study findings could contribute to the development of adequately adapted PA content to distribute knowledge to populations with developmental disabilities.Content delivered via online platforms has the potential to convey knowledge about physical activity to a significant number of individuals with developmental disabilities without the limitations of time and space.The absence of prescribed content guidelines to effectively impart physical activity to individuals with developmental disabilities impedes the process of online knowledge translation.There is a requirement for varied physical activity content encompassing various individuals with developmental disabilities, considering their diverse learning contexts.It is essential that content development is evaluated with input from experts in developmental disabilities in order to provide quality physical activity information for people with developmental disabilities.Content delivered via online platforms has the potential to convey knowledge about physical activity to a significant number of individuals with developmental disabilities without the limitations of time and space.The absence of prescribed content guidelines to effectively impart physical activity to individuals with developmental disabilities impedes the process of online knowledge translation.There is a requirement for varied physical activity content encompassing various individuals with developmental disabilities, considering their diverse learning contexts.It is essential that content development is evaluated with input from experts in developmental disabilities in order to provide quality physical activity information for people with developmental disabilities. [ABSTRACT FROM AUTHOR]

Discrete Laplacians are the basis for various tasks in geometry processing. While the most desirable properties of the discretization invariably lead to the so‐called cotangent Laplacian for triangle meshes, applying the same principles to polygon Laplacians leaves degrees of freedom in their construction. From linear finite elements it is well‐known how the shape of triangles affects both the error and the operator's condition. We notice that shape quality can be encapsulated as the trace of the Laplacian and suggest that trace minimization is a helpful tool to improve numerical behavior. We apply this observation to the polygon Laplacian constructed from a virtual triangulation [BHKB20] to derive optimal parameters per polygon. Moreover, we devise a smoothing approach for the vertices of a polygon mesh to minimize the trace. We analyze the properties of the optimized discrete operators and show their superiority over generic parameter selection in theory and through various experiments. [ABSTRACT FROM AUTHOR]

In this paper, we present a laser triangulation sensor to measure the distance between the sensor and an object without contact using a diffraction slit rather than a traditional lens. We show that by replacing the lens with a slit, we can exploit the resulting diffraction pattern to have finer and yet simpler image analysis, yielding better estimation of the distance to the object. To test our hypothesis, we build a precision position table and a laser triangulation sensor, generate large data sets to test different estimation algorithms on various materials, and compare data acquisition using a traditional lens versus using a slit. We show that position estimation when using a slit is both more precise and more accurate than comparable methods using a lens. [ABSTRACT FROM AUTHOR]

The variety of equipment implementing laser triangulation technology for 3D scanning makes it difficult to analyse their performance, comparability, and traceability. In this study, three laser triangulation sensors arranged in different configurations are analysed using high precision spheres made of different materials and surface finishes. Three types of reference parameters were used: diameter, form error, and standard deviation of the point cloud. The experimentation was based on studying the quality of the point clouds generated by the three sensors, which enabled us to find and quantify an edge effect in the horizon of the scanned surface. A procedure to reach the optimal filtering conditions was proposed, and a chart of recommended usage of each sphere (material and finish) was created for the different types of sensors. This filter enables removal of both spurious points and those few points that spoil the form error, greatly improving the quality of the measurement. [ABSTRACT FROM AUTHOR]

Golodness of a simplicial complex is defined algebraically in terms of the Stanley–Reisner ring, and it has been a long-standing problem to find its combinatorial characterization. Tightness of a simplicial complex is a combinatorial analogue of a tight embedding of a manifold into Euclidean space, and has been studied in connection to minimal manifold triangulations. In this paper, by using an idea from toric topology, we prove that tight complexes are Golod, and as a corollary, we obtain that a triangulation of a closed connected orientable manifold is Golod if and only if it is tight, which is a combinatorial characterization of Golodness for manifold triangulations. [ABSTRACT FROM AUTHOR]

A new impartial game on a connected graph was introduced, called a feedback game , which is a variant of generalized geography. In this paper, we study the feedback game on 3-chromatic Eulerian triangulations of surfaces. We prove that the winner of the game on every 3-chromatic Eulerian triangulation of a surface all of whose vertices have degree 0 modulo 4 is always fixed. Moreover, we also study the case of 3-chromatic Eulerian triangulations of surfaces which have at least two vertices whose degrees are 2 modulo 4. In addition, as a concrete class of such graphs, we consider the octahedral path, which is obtained from an octahedron by adding octahedra in the same face, and completely determine the winner of the game on those graphs. [ABSTRACT FROM AUTHOR]

In the United States, regions (such as states or counties) are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can have a profound effect on who is elected, and drawing the districts to give an advantage to a certain group is known as gerrymandering. It can be surprisingly difficult to detect when gerrymandering is occurring, but one algorithmic method is to compare a current districting plan to a large number of randomly sampled plans to see whether it is an outlier. Recombination Markov chains are often used to do this random sampling: randomly choose two districts, consider their union, and split this union up in a new way. This approach works well in practice and has been widely used, including in litigation, but the theory behind it remains underdeveloped. For example, it is not known if recombination Markov chains are irreducible, that is, if recombination moves suffice to move from any districting plan to any other. Irreducibility of recombination Markov chains can be formulated as a graph problem: for a planar graph G , is the space of all partitions of G into k connected subgraphs (k districts) connected by recombination moves? While the answer is yes when districts can be as small as one vertex, this is not realistic in real-world settings where districts must have approximately balanced populations. Here we fix district sizes to be k 1 ± 1 vertices, k 2 ± 1 vertices, ... for fixed k 1 , k 2 , ... , a more realistic setting. We prove for arbitrarily large triangular regions in the triangular lattice, when there are three simply connected districts, recombination Markov chains are irreducible. This is the first proof of irreducibility under tight district size constraints for recombination Markov chains beyond small or trivial examples. The triangular lattice is the most natural setting in which to first consider such a question, as graphs representing states/regions are frequently triangulated. The proof uses a sweep-line argument, and there is hope it will generalize to more districts, triangulations satisfying mild additional conditions, and other redistricting Markov chains. [ABSTRACT FROM AUTHOR]

The Ehrhart polynomial ehrP(n) of a lattice polytope P counts the number of integer points in the n-th dilate of P. The f*-vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of ehrP(n) with respect to the binomial coefficient basis { n − 1 0 , n − 1 1 , ... , n − 1 d } , where d = dim P. Similarly to h/h*-vectors, the f*-vector of P coincides with the f-vector of its unimodular triangulations (if they exist). We present several inequalities that hold among the coefficients of f*-vectors of lattice polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes; e.g., the first half of the f*-coefficients increases and the last quarter decreases. Even though f*-vectors of polytopes are not always unimodal, there are several families of polytopes that carry the unimodality property. We also show that for any polytope with a given Ehrhart h*-vector, there is a polytope with the same h*-vector whose f*-vector is unimodal. [ABSTRACT FROM AUTHOR]

We construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented two-dimensional manifolds. Our construction relies on the Regge finite elements, which are piecewise polynomial symmetric (0, 2)-tensor fields possessing single-valued tangential-tangential components along element interfaces. When used to discretize the Riemannian metric tensor, these piecewise polynomial tensor fields do not possess enough regularity to define connections and curvature in the classical sense, but we show how to make sense of these quantities in a distributional sense. We then show that these distributional quantities converge in certain dual Sobolev norms to their smooth counterparts under refinement of the triangulation. We also discuss projections of the distributional curvature and distributional connection onto piecewise polynomial finite element spaces. We show that the relevant projection operators commute with certain linearized differential operators, yielding a commutative diagram of differential complexes. [ABSTRACT FROM AUTHOR]

In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now known as the Schnyder wood , to give a fundamental grid-embedding algorithm for planar maps. In the framework of mating of trees, a uniformly sampled Schnyder-wood-decorated triangulation can produce a triple of random walks. We show that these three walks converge in the scaling limit to three Brownian motions produced in the mating-of-trees framework by Liouville quantum gravity (LQG) with parameter 1, decorated with a triple of SLE_{16}'s curves. These three SLE_{16}'s curves are coupled such that the angle difference between them is 2\pi /3 in imaginary geometry. Our convergence result provides a description of the continuum limit of Schnyder's embedding algorithm via LQG and SLE. [ABSTRACT FROM AUTHOR]

This article explores the concept of racial triangulation theory, specifically in relation to Asian Americans. The author shares their personal experiences during the 1992 Los Angeles riots and how this theory helped them understand the dynamics between different racial groups. The theory acknowledges the discrimination faced by Asian Americans while recognizing their relative advantages in education and class. However, the author cautions against a limited application of the theory that fails to recognize the unique forms of discrimination faced by Black Americans and can unintentionally reinforce anti-Black attitudes. They stress the importance of a more comprehensive and nuanced understanding of racial dynamics. The article also discusses the need to contextualize the experiences of Asian Americans within the broader racial landscape, particularly in relation to the experiences of Black people. It highlights survey findings that demonstrate the differential racialization experienced by different racial groups, such as the perpetual foreigner stereotype faced by Asian Americans and the higher levels of police brutality experienced by Black and other non-White groups. The author warns against solely focusing on anti-Asian hate crimes and calls for a more comprehensive understanding of systemic racism and discrimination. The article concludes by discussing the significance of intergroup solidarity and the potential consequences of not applying a robust interpretation of racial triangulation theory in contemporary Asian American politics. [Extracted from the article]

The measurement of shape parameters of coarse aggregate is the premise to ensure the quality of concrete engineering. In the measurement of particle shape based on laser triangulation method, the selection of polynomial fitting parameters between different test scene displacement and image offset is often different. For coarse aggregate height measurement, an optimal laser triangulation method is proposed, and the best polynomial fitting times of aggregate measurement is obtained through data extraction and error analysis. Firstly, the laser streak information is collected from the aggregate surface based on the industrial camera, and the laser streak is processed by Gaussian filtering and color space transformation, and then the center line of the laser streak is obtained by the center method to obtain the corresponding aggregate height information. Finally, based on the comparison between the experimental measurements and the height values calculated by different polynomial fits, the laser triangulation solution method is optimized by different error factors analysis. The experimental results show that in the process of aggregate height measurement, the cubic term fitting solution is optimal with an average relative error of only 0.693%. [ABSTRACT FROM AUTHOR]

We show that the order complex of the poset of nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the original poset. Besides studying the properties of this transformation, we show that the dual of the type B permutohedron is combinatorially equivalent to the suspension of the order complex of the poset of nonempty intervals of a Boolean algebra (with the minimum and maximum elements removed). [ABSTRACT FROM AUTHOR]

Process Analytical Technology (P A T) plays a crucial role in the design of today's manufacturing lines as continuous manufacturing becomes more important. Until now P A T tools to measure the ribbon solid fraction (S F r i b b o n ) in-line are not commonly used in roll compaction. The aim of this study was therefore to establish a new approach as P A T for in-line ribbon solid fraction determination. Different placebo formulations with different binders and one formulation containing active pharmaceutical ingredient were investigated using in-line laser triangulation measurement to detect the ribbon thickness after compaction. With this the ribbon elastic recovery was determined in-line (E R i n − l i n e ) while the ribbons are attached to the roll surface. It was found that the ratio (E R r a t i o ) between the total elastic recovery and E R i n − l i n e is formulation specific and not influenced by any process parameters. This enables E R r a t i o as prediction tool for S F r i b b o n , if the solid fraction at gap (S F g a p ) width is known. S F g a p was determined with ribbon mass flow measurement or based on the Midoux model, a simplified Johanson model, gaining two prediction models for S F r i b b o n . Both models showed good agreement of the predicted S F r i b b o n and the measured one. [Display omitted] • Novel in-line laser triangulation measurement of ribbon elastic recovery in roll compaction. • In-line prediction of ribbon solid fraction as Process Analytical Technology (PAT). • Ribbon mass flow and Midoux number based model were established. • Prediction model based on Midoux number showed superior results and applicability. [ABSTRACT FROM AUTHOR]

Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the genus tends to infinity. Mirzakhani raised this question in her 2010 ICM address. We show that in the large genus case, triangulated surfaces are well distributed in moduli space in a fairly strong sense. We do this by proving upper and lower bounds for the number of triangulated surfaces lying in a Teichmüller ball in moduli space. In particular, we show that the number of triangulated surfaces lying in a Teichmüller unit ball is at most exponential in the number of triangles, independent of the genus. [ABSTRACT FROM AUTHOR]

It is known that the flip distance between two triangulations of a convex polygon is related to the smallest number of tetrahedra in the triangulation of some polyhedron. The latter was used to compute the diameter of the flip graph of convex polygons with a large number of vertices. However, it is yet unknown whether the flip distance and this smallest number of tetrahedra are always the same or even close. In this work, we find examples to show that the ratio between these two numbers can be arbitrarily close to 32 $\frac{3}{2}$. We also propose two conjectures in the end, one about this ratio, and the other may have some implications on when two triangulations can achieve maximal distance. [ABSTRACT FROM AUTHOR]

Background: Childhood maltreatment is common globally and impacts morbidity, mortality, and well-being. Our understanding of its impact is constrained by key substantive and methodological limitations of extant research, including understudied physical health outcomes and bias due to unmeasured confounding. We address these limitations through a large-scale outcome-wide triangulation study. Methods: We performed two outcome-wide analyses (OWAs) in the UK Biobank. First, we examined the relationship between self-reported maltreatment exposure (number of maltreatment types, via Childhood Trauma Screener) and 414 outcomes in a sub-sample of 157,316 individuals using generalized linear models ("observational OWA"). Outcomes covered a broad range of health themes including health behaviors, cardiovascular disease, digestive health, socioeconomic status, and pain. Second, we examined the relationship between a polygenic risk score for maltreatment and 298 outcomes in a non-overlapping sample of 243,006 individuals ("genetic OWA"). We triangulated results across OWAs based on differing sources of bias. Results: Overall, 23.8% of the analytic sample for the observational OWA reported at least one maltreatment type. Of 298 outcomes examined in both OWAs, 25% were significant in both OWAs and concordant in the direction of association. Most of these were considered robust in the observational OWA according to sensitivity analyses and included outcomes such as marital separation (OR from observational OWA, ORo = 1.25 (95% CI: 1.21, 1.29); OR from genetic OWA, ORg = 1.06 (1.03, 1.08)), major diet changes due to illness (ORo = 1.27 (1.24, 1.29); ORg = 1.01 (1.00, 1.03)), certain intestinal diseases (ORo = 1.14 (1.10, 1.18); ORg = 1.03 (1.01, 1.06)), hearing difficulty with background noise (ORo = 1.11 (1.11, 1.12); ORg = 1.01 (1.00, 1.01)), knee arthrosis (ORo = 1.13 (1.09, 1.18); ORg = 1.03 (1.01, 1.05)), frequent sleeplessness (ORo = 1.21 (1.20, 1.23); ORg = 1.02 (1.01, 1.03)), and low household income (ORo = 1.28 (1.26, 1.31); ORg = 1.02 (1.01, 1.03)). Approximately 62% of results were significant in the observational OWA but not the genetic OWA, including numerous cardiovascular outcomes. Only 6 outcomes were significant in the genetic OWA and null in the observational OWA; these included diastolic blood pressure and glaucoma. No outcomes were statistically significant in opposite directions in the two analyses, and 11% were not significant in either OWA. Conclusions: Our findings underscore the far-reaching negative effects of childhood maltreatment in later life and the utility of an outcome-wide triangulation design with sensitivity analyses for improving causal inference. [ABSTRACT FROM AUTHOR]

Tissue triangulation is a fundamental surgical skill in laparoscopic surgery that requires the simultaneous control of multiple surgical tools to create tension and enable tissue visualization. Robotic assistants can facilitate triangulation tasks by autonomously operating some of the tools, reducing the surgeon's cognitive workload and improving precision and safety. However, characterizing complex tissue dynamics is a significant challenge for robot-assisted tissue triangulation. This work presents Latent Regression based Model Predictive Control (LR-MPC) for tissue triangulation that guides the tissue state to lie within a target distribution in the secondary latent space. A Model Predictive Control strategy in latent space is followed for optimal robot action selection. We evaluated the proposed method in a robot-assisted triangulation task with various sizes and materials of triangular tissues. The results show that LR-MPC can achieve performance comparable to a human assistant's, demonstrating its effectiveness and robustness for autonomous tissue triangulation. [ABSTRACT FROM AUTHOR]

Drones are used by surveyors as an alternative to traditional methods of obtaining orthophoto maps and large-scale topographical maps, but several factors affect the accuracy of its data, one of them is software used in image processing. Because there are many types of software, choosing one of them is a real problem in survey projects using drones. Processing software is divided into commercial and open-source software. Commercial software is a black box situation, which highlights the challenge of isolating accurate sources of errors and judging the accuracy of processing products. In this research, the capabilities of the commercial software Pix4Dmapper, Agisoft Metashape, and 3DF Zephyr Aerial were compared in calculating the aerial triangulation of the image blocks taken by drones, with a comparison of the capabilities of this software in getting the most important spatial products for surveyors from these images (Digital Elevation Model and Orthophoto). The results showed that Pix4Dmapper was able to perform aerial triangulation more accurately than Agisoft Metashape and 3DF Zephyr Aerial, with great convergence between the results of Agisoft Metashape and 3DF Zephyr A. The results also showed that 3DF Zephyr Aerial had extracted the densest point cloud. Another finding is that Pix4Dmapper produced the most accurate orthophoto and took the shortest processing time, and that the Agisoft Metashape interface is more flexible and user-friendly than the rest of the tested software. [ABSTRACT FROM AUTHOR]

An interface-preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving (d-1)-dimensional manifold directly within the d-dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-surfaces. The underlying mesh is a conforming simplicial partition that fulfills the Delaunay property. The local remeshing algorithms allow for strong interface deformations. We give a proof that the given algorithms preserve the interface after interface deformation and remeshing steps. Originating from various numerical methods, data is attached cell-wise to the mesh. After each remeshing operation, the interface-preserving moving mesh retains valid data by projecting the data to the new mesh cells. An open source implementation of the moving mesh algorithm is available at Reference [1]. [ABSTRACT FROM AUTHOR]

Structured light (SL) sensing technology, based on the triangulation principle, is widely employed for depth perception in various applications such as face recognition, human‐computer interaction, machine vision, and more. In this approach, the baseline length, which refers to the distance between the projection device and the camera, is a critical parameter that affects depth measurement and system miniaturization. Recently, metasurfaces have emerged as promising devices for constructing compact optoelectronic systems due to their excellent performance in wavefront modulation of light and ultra‐thin characteristics. In this study, a metasurface‐based monocular SL depth detection scheme is proposed that incorporates a specially designed 3D holographic projection. Under this projected light field, the entire 3D space is labeled, and depth information can be obtained without considering the baseline length, which can further reduce the volume of SL systems. Additionally, a template‐matching algorithm based on correlation coefficient analysis is developed and experimentally demonstrates its feasibility by precisely positioning objects. It is believed that this work opens up a new perspective for compact, lightweight, and flexible design of SL sensing systems, and has a promising future in quantitative detection, automatic location, and industrial measurement. [ABSTRACT FROM AUTHOR]

One of the important issues being explored in Industry 4.0 is collaborative mobile robots. This collaboration requires precise navigation systems, especially indoor navigation systems where GNSS (Global Navigation Satellite System) cannot be used. To enable the precise localization of robots, different variations of navigation systems are being developed, mainly based on trilateration and triangulation methods. Triangulation systems are distinguished by the fact that they allow for the precise determination of an object's orientation, which is important for mobile robots. An important feature of positioning systems is the frequency of position updates based on measurements. For most systems, it is 10–20 Hz. In our work, we propose a high-speed 50 Hz positioning system based on the triangulation method with infrared transmitters and receivers. In addition, our system is completely static, i.e., it has no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear of components, etc.). In this paper, we describe the principle of the system as well as its design. Finally, we present tests of the built system, which show a beacon bearing accuracy of Δ φ = 0.51 ° , which corresponds to a positioning accuracy of Δ R = 6.55 cm, with a position update frequency of f u p d a t e = 50 Hz. [ABSTRACT FROM AUTHOR]

Triangulation is a classical geodetic practice to establish survey control networks by using measurements of angles and some spare distances. In this way, a series of reference points or simply called 'trigs' is spreading over the country. This paper aims to review geodetic survey work that was carried out for the East Malaysia and Brunei from 1918 to 1968 which is covering about 204,119 square kilometres'. However, this classical geodetic datum is not directly compatible with the current surveying trends based on Global Navigation Satellite System technologies. Therefore, in this review covered concepts and history of triangulation systems, datums and the status of transformation plan to modernise geodetic datum for Sarawak. [ABSTRACT FROM AUTHOR]

The Earth's crust is exposed by tectonic processes and is not static over time. Modelling of the Earth's surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth's surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties. [ABSTRACT FROM AUTHOR]