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We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most L on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichmüller geodesic flow. [ABSTRACT FROM AUTHOR]

Most printed material is produced by printing halftone dot patterns. One of the key issues that determine the attainable print quality is the structure of the paper surface, but the relation is non-deterministic in nature. We examine the halftone print quality and study the statistical dependence between the defects in printed dots and the topography measurement of the unprinted paper. The work concerns SC paper samples printed by an IGT gravure test printer. We have small-scale 2D measurements of the unprinted paper surface topography and the reflectance of the print result. The measurements before and after printing are aligned with subpixel resolution, and individual printed dots are detected. First, the quality of the printed dots is studied using Self Organizing Map and clustering and the properties of the corresponding areas in the unprinted topography are examined. The printed dots are divided into high and low print quality. Features from the unprinted paper surface topography are then used to classify the corresponding paper areas using Support Vector Machine classification. The results show that the topography of the paper can explain some of the print defects. However, there are many other factors that affect the print quality, and the topography alone is not adequate to predict the print quality. [ABSTRACT FROM AUTHOR]

Photogrammetry has gained the interest of professionals and researchers for activities related to construction projects' progress monitoring via attaining precise 3D point models. However, the precision of the generated models is directly linked with the precise scaling of the point cloud to ground truth dimensions (GTDs). Available scaling-up procedures for the close-range photogrammetry technique are complex, time consuming, and require human intervention, which adds the risk of error in the scaled-up model dimensions. Such a scenario creates hesitation among industry professionals toward implementing point cloud technologies. This paper devises an automated scaling-up methodology to overcome the said concerns by considering the construction progress monitoring theme. The intact process of automated scaling up of point cloud model to GTDs is controlled by two main parameters, that is, Python-based modules and designed ArUco-supported controlled markers. Remarkable outcomes are achieved with less than 1% scaled-up error compared with GTDs, which will improve the confidence of industry professionals toward point cloud technologies. Photogrammetry applications have been adopted in several domains and the optimum usage of attained models can be executed with 3D replicas having precise details of surface features and geometry. Therefore, to attain 3D point cloud models with ground truth dimensions (GTDs), or actual dimensions of the targeted object the practitioners mostly follow the markers/ground control points (GCPs) technique (minimum three GCPs/markers), manual scaling, or georeferencing data. However, the accuracy of traditional GCPs/markers' technique and manual rescaling is dependent on the experience of the site staff/operator, and error chances may increase with the increasing number of GCPs/markers, whereas the georeferencing data-based technique is more technical and complex. Therefore, this paper developed an automated system for scaling up 3D point cloud models to GTDs with minimal human involvement. The system works with the help of specialized designed markers known as ArUco-supported controlled markers (ASCM). Only one ASCM marker is placed beside the targeted object for imaging; the devised system detects the marker in the images and rescales the developed point cloud model following the designed strategy. The system has high accuracy and can easily be implemented for scaling up close-range photogrammetry models in any domain. [ABSTRACT FROM AUTHOR]

Photogrammetry has gained the interest of professionals and researchers for activities related to construction projects' progress monitoring via attaining precise 3D point models. However, the precision of the generated models is directly linked with the precise scaling of the point cloud to ground truth dimensions (GTDs). Available scaling-up procedures for the close-range photogrammetry technique are complex, time consuming, and require human intervention, which adds the risk of error in the scaled-up model dimensions. Such a scenario creates hesitation among industry professionals toward implementing point cloud technologies. This paper devises an automated scaling-up methodology to overcome the said concerns by considering the construction progress monitoring theme. The intact process of automated scaling up of point cloud model to GTDs is controlled by two main parameters, that is, Python-based modules and designed ArUco-supported controlled markers. Remarkable outcomes are achieved with less than 1% scaled-up error compared with GTDs, which will improve the confidence of industry professionals toward point cloud technologies. Photogrammetry applications have been adopted in several domains and the optimum usage of attained models can be executed with 3D replicas having precise details of surface features and geometry. Therefore, to attain 3D point cloud models with ground truth dimensions (GTDs), or actual dimensions of the targeted object the practitioners mostly follow the markers/ground control points (GCPs) technique (minimum three GCPs/markers), manual scaling, or georeferencing data. However, the accuracy of traditional GCPs/markers' technique and manual rescaling is dependent on the experience of the site staff/operator, and error chances may increase with the increasing number of GCPs/markers, whereas the georeferencing data-based technique is more technical and complex. Therefore, this paper developed an automated system for scaling up 3D point cloud models to GTDs with minimal human involvement. The system works with the help of specialized designed markers known as ArUco-supported controlled markers (ASCM). Only one ASCM marker is placed beside the targeted object for imaging; the devised system detects the marker in the images and rescales the developed point cloud model following the designed strategy. The system has high accuracy and can easily be implemented for scaling up close-range photogrammetry models in any domain. [ABSTRACT FROM AUTHOR]

Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns are known to emerge. In this paper, we study the effect of geometry on the dynamical response of soft surfaces moving relative to each other. Using a simple experimental scheme, we measure friction between a highly bendable thin polymer sheet and a hydrogel substrate. At this soft and low-friction interface, we find a strong dependence of friction on the relative geometry of the two surfaces--a flat sheet experiences significantly larger friction on a spherical substrate than on flat or cylindrical substrate. We show that the stress developed in the sheet due to its geometrically incompatible confinement is responsible for the enhanced friction. This mechanism also leads to a transition in the nature of friction as the sheet radius is increased beyond a critical value. Our finding reveals a hitherto unnoticed mechanism based on an interplay between geometry and elasticity that may influence friction significantly in soft, biological, and nanoscale systems. In particular, it provokes us to reexamine our understanding of phenomena such as the curvature dependence of biological cell mobility. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group R T . At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C 2 -smooth surface in the roto-translation group away from characteristic points and signed geodesic curvature associated with two kinds of canonical connections for C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss-Bonnet theorem in the R T . [ABSTRACT FROM AUTHOR]

Abstract: Paper raw materials contain impurities, such as waxes, coating binders, hot melts and pressure-sensitive adhesives, that have a tendency to attach to the surfaces of machinery during paper production. Drying cylinders located at the beginning of the drying section are in an especially challenging position because sticky materials can easily transfer from the paper web to the hot cylinder surfaces at this point. Usually, one to four drying cylinders are coated with a nonstick coating material in order to decrease contamination. The nonstick properties of coating materials are at their best when the coatings are new, but their performance usually decreases as the materials age. To date, there is no practical method available for the on-site evaluation of the nonstick properties of coating materials or a method to monitor the condition of the coating during its life cycle. A new practical method for the on-site evaluation of nonstick cylinder coating materials has been developed. This method also provides the opportunity to compare the performance of different drying cylinder coating materials. The analysis is performed using an adhesive tape attached to a clean cylinder surface. The tape is immediately peeled off of the surface at a constant speed and peel angle. The temperature compensation is used to facilitate the comparison of surfaces at different temperatures. The force required to peel off the adhesive tape is monitored with a force meter. Our results show a linear relationship between the release force and the nonstick qualities of the coating. In this paper, a method for testing drying cylinder coatings and the results of mill tests are presented. [Copyright &y& Elsevier]

In our earlier research (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2023c]), we developed two methods for creating dividing surfaces, either based on periodic orbits or two-dimensional generating surfaces. These methods were specifically designed for Hamiltonian systems with three or more degrees of freedom. Our prior work extended these dividing surfaces to more complex structures such as tori or cylinders, all within the energy surface of the Hamiltonian system. In this paper, we introduce a new method for constructing dividing surfaces. This method differs from our previous work in that it is based on 3D surfaces or geometrical objects, rather than periodic orbits or 2D generating surfaces (see [Katsanikas & Wiggins, 2023a]). To explain and showcase the new method and to present the structure of these 3D surfaces, the paper provides examples involving Hamiltonian systems with three degrees of freedom. These examples cover both uncoupled and coupled cases of a quadratic normal form Hamiltonian system. Our current paper is the first in a series of two papers on this subject. This research is likely to be of interest to scholars and researchers in the field of Hamiltonian systems and dynamical systems, as it introduces innovative approaches to constructing dividing surfaces and exploring their applications. [ABSTRACT FROM AUTHOR]

The velocity and density of a jet resulting from the reflection of a shock wave on a surface with geometric defects (the micro-jetting process) can be an important component of jet fragmentation models. While several models in the literature allow for the calculation of jet velocity, the density is generally ignored. In this paper, we present a semi-analytical method for determining both the velocity and density of a jet from a triangular defect. This model is an extension to micro-jetting specificities of the model usually used for shaped charges. Based on the physics of two-dimensional shocks, it allows a good restitution of the jet velocity and density from classical molecular dynamics simulations. It also provides a good agreement with the literature data, both experimental and numerical. [ABSTRACT FROM AUTHOR]

In many design automation applications, accurate segmentation and classification of 3D surfaces and extraction of geometric insight from 3D models can be pivotal. This paper primarily introduces a machine earning-based scheme that leverages graph neural networks for handling 3D geometries, specifically for surface classification. Our model demonstrates superior performance against two state-of-the-art models, PointNet + + and PointMLP, in terms of surface classification accuracy, beating both models. Central to our contribution is the novel incorporation of conformal predictions, a method that offers robust uncertainty quantification and handling with marginal statistical guarantees. Unlike traditional approaches, conformal predictions enable our model to ensure precision, especially in challenging scenarios where mistakes can be highly costly. This robustness proves invaluable in design applications, and as a case in point, we showcase its utility in automating the computational fluid dynamics meshing process for aircraft models based on expert guidance. Our results reveal that our automatically generated mesh, guided by the proposed rules by experts enabled through the segmentation model, is not only efficient but matches the quality of expert-generated meshes, leading to accurate simulations. [ABSTRACT FROM AUTHOR]

Continuum robotics has emerged as a prominent trend within the robotics field for about two decades. Nevertheless, motion analysis of continuum robots based on dynamic modelling remains severely limited. In the realm of continuum robots, it is obvious that simplified theoretical models or first-order approximations utilizing springs and dampers are insufficient for capturing the dynamics of soft-bodied structures. This inadequacy is especially apparent in applications involving significant deformations in 3D space, continuous actuation, and interface effects. In this regard, the development of precise theoretical models is crucial. Within this particular framework, the paper presents the absolute nodal coordinates formulation (ANCF) to construct the kinematic models of continuum robots. The transformation between the structural, body, and element coordinate systems, as well as the derivation of the generalized external forces and moments using the principle of virtual work and the velocity gradient tensor, are demonstrated. Additionally, it proceeds to develop the strain measures required for the computation of the elastic forces of elements with circular cross sections, ultimately enabling the construction of the Forward Static Model (FSM) of continuum robots. A procedure based on B-spline surface geometry is proposed to figure out the robot shapes in space and generate the necessary nodal coordinates and gradients of ANCF elements. Finally, the inverse static model (ISM) of the ANCF-B-spline generated structure is presented using an iterative solution approach. The effectiveness of the proposed model is evaluated by the analysis of numerical examples. According to the numerical results, it can be inferred that the ANCF method well captures the modelling aspects of continuum robots. The results obtained from the FSM demonstrate a high level of accuracy, moreover, the driving forces based on the ISM provide, from a practical standpoint, satisfactory results. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal intersection length against a fixed regular reference surface. Expectation and variance have been addressed by Maffucci [Ann. Henri Poincaré 20(11), 3651–3691 (2019)] who found that the expected length is proportional to the square root of the eigenvalue times the area of the surface, while the asymptotic variance only depends on the geometry of the surface, the projected lattice points being equidistributed on the two-dimensional unit sphere in the high-energy limit. He also noticed that there are "special" surfaces, so-called static, for which the variance is of smaller order; however he did not prescribe the precise asymptotic law in this case. In this paper, we study second order fluctuations of the nodal intersection length. Our first main result is a Central Limit Theorem for "generic" surfaces, while for static ones, a sphere or a hemisphere e.g., our main results are a non-Central Limit Theorem and a precise asymptotic law for the variance of the nodal intersection length, conditioned on the existence of so-called well-separated sequences of Laplacian eigenvalues. It turns out that, in this regime, the nodal area investigated by Cammarota [Trans. Am. Math. Soc. 372(5), 3539–3564 (2019)] is asymptotically fully correlated with the length of the nodal intersections against any sphere. The main ingredients for our proofs are the Kac-Rice formula for moments, the chaotic decomposition for square integrable functionals of Gaussian fields, and some arithmetic estimates that may be of independent interest. [ABSTRACT FROM AUTHOR]

The paper presents a novel solution to the issue of incomplete regions in 3D meshes obtained through digitization. Traditional methods for estimating the surface of missing geometry and topology often yield unrealistic outcomes for intricate surfaces. To overcome this limitation, the paper proposes a neural network-based approach that generates points in areas where geometric information is lacking. The method employs 2D inpainting techniques on color images obtained from the original mesh parameterization and curvature values. The network used in this approach can reconstruct the curvature image, which then serves as a reference for generating a polygonal surface that closely resembles the predicted one. The paper's experiments show that the proposed method effectively fills complex holes in 3D surfaces with a high degree of naturalness and detail. This paper improves the previous work in terms of a more in-depth explanation of the different stages of the approach as well as an extended results section with exhaustive experiments. [Display omitted] • We perform 3D surface reconstructions using generative inpainting techniques. • 2D representation of a 3D surface geometry based on its curvature. • Application of a general purpose neural network for inpainting. • Our approach does not require dataset nor training time. • Results outperform state-of-the-art quality and naturalness of the reconstructions. [ABSTRACT FROM AUTHOR]

It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered to be displacement along a certain fault surface. Usually, when describing a source, the geometry of the fault surface is simplified to a flat rectangular area. The displacement vector is assumed to be constant. In this paper, we propose a model of an earthquake source in the form of a displacement with a constant vector along a stochastic uneven surface. A number of standard assumptions are made during the modeling. We take into account only the elastic properties of the medium. We consider the Earth's crust as a half-space and assume that the medium is homogeneous and isotropic. For the mathematical description of the earthquake source, we use the classical force equivalent of displacement along the fault. This is the distribution of double pairs of forces. The field of displacements under the action of body forces is found through a combination of Mindlin nuclei of strain. The paper presents numerical analytic solutions for displacement along the strike-slip fault corresponding to one of an earthquake source mechanism. We propose to introduce a random deformation of a rectangular flat fault surface. The paper shows the results of a computational experiment comparing the levels and regions of relative deformations of the Earth's crust in the case of displacement along a flat fault surface and along a stochastic uneven one. In the case of a stochastic fault surface, the regions of relative deformations become asymmetric. Such differences from the classical case can be useful for an explanation as to why in some cases the simulation results differ from the results of observations. [ABSTRACT FROM AUTHOR]

Ti6Al4V alloy is one of the typical difficult-to-machine materials and often results in rapid tool wear, leading to poor machining quality in aircraft assembling. Compared to conventional helical milling, the ultrasonic assistant helical milling (UAHM) process has indicated its superior performance; however, it is still a great challenge to improve the hole surface quality and accuracy. In addition, few studies have been conducted on the effect of different variables and cooling strategies on the hole-making performance in longitudinal-torsional ultrasonic assisted helical milling (LT-UAHM). This paper, for the first time, reports effects of machining variables on geometric precision and surface roughness in LT-UAHM of Ti6Al4V. In addition, the lubrication/cooling mechanism on the simultaneous application of LT-UAHM and MQL is theoretically analyzed. The design approach of Taguchi experiment was employed to study how major variables such as the cutting speed, tangential feed, axial feed, and the workpiece hardness influence the dimensional and geometrical tolerances and surface roughness. This paper also discussed the effect of three cooling strategies, i.e., dry condition, air coolant, and minimum quantity lubrication (MQL) in LT-UAHM. Theoretical analysis demonstrated that the MQL coolant can be nebulized into hyper-fine droplets owing to the resonant cavitation phenomenon. Combined with the penetrating action caused by the separate-cutting principles of LT-UAHM, the cooling and lubrication performance of MQL was further enhanced. As a result, LT-UAHM with MQL had the most positive effect on circularity, cylindricity, nominal diameter, and surface roughness, contributing to 34%, 32%, 39%, and 40%, respectively. The second important machining factor was the cutting speed, contributing to 31%, 29%, 36%, and 22%, respectively. The tangential feed and workpiece hardness have the negative effect on geometrical accuracy, respectively. [ABSTRACT FROM AUTHOR]

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed. [ABSTRACT FROM AUTHOR]

The present study focuses on an up-to-date topic regarding flying equipment identified within the category of drones that use, for propulsion and air movements, the power generated by electric motors. In this paper, researchers focus on implementing bladeless technology to calculate, develop, and construct flying equipment known in the literature as drones. The entire structure of the prototype, all the needed parts, is to be obtained using additive manufacturing technologies, which assumes practical realization using 3D-printing equipment. Nowadays, the 3D-printing process has been proven to be a reliable solution when it comes to manufacturing complex shape parts in quite a short time and with reduced costs. The practical study within the present research aims to obtain polymer-based, lightweight parts with complex shapes inside to be implemented in the propulsion of a drone. The complex surface geometry of the parts that this research used is influenced by the ventilation technology offered by the "Air Multiplier" technology. The entire structure of the final drone equipment, all the parts, is to be manufactured using fused filament fabrication (FFF). The main purpose of the fusion is to use the advantages offered by this technology in drones to obtain advantages such as augmented values of thrust, a more agreeable and muffled sound signature, or an increased level of safety. [ABSTRACT FROM AUTHOR]

This present study has the purpose of determining how surface topography of implants affects the initial stability of miniscrew implants (MSIs). Electronic databases like PubMed Central, Scopus, Web of Science, Embase, and Cochrane Library, as well as reference lists, were thoroughly searched up until September 2022. Clinical trials involving individuals who got anchorage through mini-implants, along with information on categories of mini-implants dimension, shape, thread design, and insertion site, were required as part of the eligibility criteria. Primary and secondary stability were also assessed. We carried out selection process for the study, extraction of data, quality assessment, and a meta-analysis. The qualitative synthesis included 10 papers: three randomized, four prospective, and four retrospective clinical investigations. The results of this meta-analysis demonstrate that the clinical state of MIs is controlled by their geometrical surface qualities, which are also influenced by their shape and thread design. According to the evidence this meta-analysis produced, this circumstance exists. The duration of the follow-up period and MI success rates did not correlate with one another. [ABSTRACT FROM AUTHOR]

Surface reconstruction using neural networks has proven effective in reconstructing dense 3D surfaces through image-based neural rendering. Nevertheless, current methods are challenging when dealing with the intricate details of large-scale scenes. The high-fidelity reconstruction performance of neural rendering is constrained by the view sparsity and structural complexity of such scenes. In this paper, we present Res-NeuS, a method combining ResNet-50 and neural surface rendering for dense 3D reconstruction. Specifically, we present appearance embeddings: ResNet-50 is used to extract the appearance depth features of an image to further capture more scene details. We interpolate points near the surface and optimize their weights for the accurate localization of 3D surfaces. We introduce photometric consistency and geometric constraints to optimize 3D surfaces and eliminate geometric ambiguity existing in current methods. Finally, we design a 3D geometry automatic sampling to filter out uninteresting areas and reconstruct complex surface details in a coarse-to-fine manner. Comprehensive experiments demonstrate Res-NeuS's superior capability in the reconstruction of 3D surfaces in complex, large-scale scenes, and the harmful distance of the reconstructed 3D model is 0.4 times that of general neural rendering 3D reconstruction methods and 0.6 times that of traditional 3D reconstruction methods. [ABSTRACT FROM AUTHOR]

This paper presents a study of the total cutting force used and selected parameters of the geometric structure of the surface (e.g., Sa, Sz) during the end milling process of NiTi alloy. The input parameters included are cutting speed (vc), feed per tooth (fz), and radial depth of cut (ae). A Box–Behnken experimental design was employed to conduct the research. The obtained experimental results were utilized within the framework of a response surface methodology (RSM) to develop mathematical and statistical models capable of predicting cutting force components and selected 3D surface parameters. These models provide valuable insights into the relationships between the cutting parameters and the output variables, facilitating the optimization of the NiTi alloy milling process. The findings of this study contribute to a better understanding of the behavior of NiTi alloy during the milling process and offer information for process optimization. By employing a Box–Behnken experimental design, it was possible to investigate the effects of different parameter combinations on the components of total cutting force and selected 3D surface parameters according to ISO 25178, thus aiding in the identification of optimal milling conditions to achieve desired outcomes in the machining of NiTi alloy. [ABSTRACT FROM AUTHOR]

Robot workpiece machining is interesting in industry as it offers some advantages, such as higher flexibility in comparison with the conventional approach based on CNC technology. However, in recent years, we have been facing a strong progressive shift to custom-based manufacturing and low-volume/high-mix production, which require a novel approach to automation via the employment of collaborative robotics. However, collaborative robots feature only limited motion capability to provide safety in cooperation with human workers. Thus, it is highly necessary to perform more detailed robot task planning to ensure its feasibility and optimal performance. In this paper, we deal with the problem of studying kinematic robot performance in the case of such manufacturing tasks, where the robot tool is constrained to follow the machining path embedded on the workpiece surface at a prescribed orientation. The presented approach is based on the well-known concept of manipulability, although the latter suffers from physical inconsistency due to mixing different units of linear and angular velocity in a general 6 DOF task case. Therefore, we introduce the workpiece surface constraint in the robot kinematic analysis, which enables an evaluation of its available velocity capability in a reduced dimension space. Such constrained robot kinematics transform the robot's task space to a two-dimensional surface tangent plane, and the manipulability analysis may be limited to the space of linear velocity only. Thus, the problem of physical inconsistency is avoided effectively. We show the theoretical derivation of the proposed method, which was verified by numerical experiments. [ABSTRACT FROM AUTHOR]

The paper presents probabilistic aspects of diagnostics of grinding processes with consideration of metrological aspects of evaluation of topography of machined surfaces and selected problems of assessment of machining accuracy. The processes of creating the geometric structure of the ground surface are described. It was pointed out that the distribution of features important for process diagnostics depends on the mechanism of cumulative effects of random disturbances. Usually, there is a multiplicative mechanism or an additive mechanism of the component vectors of relative displacements of the tool and workpiece. The paper describes a method for determining the classification ability of specific parameters used to evaluate stereometric features of ground surfaces. It is shown that the ability to differentiate the geometric structure of a certain set of surfaces using a selected parameter depends on the geometric mean of the differences in normalized and sorted, consecutive values of this parameter. A methodology is presented for evaluating the ability of various parameters to distinguish different geometric structures of surfaces. Further, on the basis of analyses of a number of grinding processes, a methodology was formulated for proceeding leading to a comprehensive evaluation of machining accuracy and forecasting its results. It was taken into account that in forecasting the accuracy of grinding, it is necessary to determine the deviations, arising under the conditions of multiplicative interaction of the effects of various causes of inaccuracy. Examples are given of processes in which, due to the deformation of the technological system, dependent on the position of the zone and machining force, varying temperature fields and tool wear, the distributions of dimensional deviations are not the realization of stationary processes. It was emphasized that on the basis of the characteristics of the dispersion of the deviation value in the sum set of elements, it is not possible to infer its causes. Only the determination of the "instantaneous" values of the deviation dispersion parameters allows a more complete diagnosis of the process. [ABSTRACT FROM AUTHOR]

Due to its excellent physical properties, γ-TiAl alloy has been widely used in thin-walled components of aerospace engines. However, issues such as low thermal conductivity, poor machinability, and high cutting temperatures often result in difficulties in ensuring the geometric accuracy and surface integrity of the parts. This paper focuses on the study of the thermal deformation behavior of γ-TiAl alloy within a range of higher temperatures and strain rates. Firstly, by conducting quasi-static tests and Hopkinson bar tests on γ-TiAl alloy, the true stress–strain curves of γ-TiAl alloy are obtained within a temperature range of 20~500 °C and a strain rate range of 3000~11,000/s. Based on the Johnson–Cook model, the true stress–strain curves are fitted and analyzed with consideration of the coupling effect of strain rate, temperature, and strain. The strain rate hardening coefficient C and thermal softening exponent m are polynomialized, improving the Johnson–Cook constitutive model of γ-TiAl alloy. The improved model shows significant improvements in the correlation coefficient and absolute errors between the predicted values and experimental values, providing a better reflection of the thermal deformation behavior of γ-TiAl alloy within a range of higher temperatures and strain rates. [ABSTRACT FROM AUTHOR]

Virtual colonoscopy plays an important role in polyp detection of colorectal cancer. Noise in the colon data acquisition process can result in topological errors during surface reconstruction. Topological denoising can be employed to remove these errors on surfaces for subsequent geometry processing, such as surface simplification and parameterization. Many methods have been proposed for this task. However, many existing methods suffer from failure in computation of all the non-trivial loops, due to high genus or complex topological structures. In this paper, we propose a novel robust topological denoising method for surfaces based on homotopy theory. The proposed method was evaluated on two datasets of colon meshes. We compared our method with the State-of-the-Art persistent-homology-based method. Our method can successfully compute the loops on all colon data for topological denoising, whereas the persistent homology method fails on some colon data. Moreover, our method detects all loops with shorter lengths than those detected by the persistent homology method. Our experimental results show that the proposed method is effective and robust in topological denoising, and that it has the potential for practical application to virtual colonoscopy. [ABSTRACT FROM AUTHOR]

The movement of a thin vortex in a thin viscous fluid by the motion of a curve propagating in Lorentz–Minkowski space E 1 3 is described by the vortex filament or smoke ring equation and can be viewed as a dynamical system on the space curves in E 1 3 . This paper investigates the harmonic evolute surfaces of time-like Hasimoto surfaces in E 1 3 . Also, we discuss the geometric properties of these surfaces, namely, we obtain the Gaussian and mean curvatures of the first and second fundamental forms. As a verification, we construct a concrete example for the meant surfaces to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, reinforced porous Pt-based alloy SPE membrane electrodes were synthesized by using ion beam sputtering, combinatorial electrochemical acid etching, and hot-pressing technology. The influences of combinatorial electrochemical acid etching on the phase structure, geometric specific surface area (SSA), electrochemical surface area (ESA), surface morphology, chemical state, exposed crystal surface, and catalytic hydrogenation performance of a Pt-based alloy catalyst and SPE membrane electrodes were investigated. The results shown that the Pt-based alloy catalyst was composed of the body-centered orthogonal Pt5Ti3 phase and simple orthogonal PtTi phase with the Ce element dispersed at grain boundaries in the form of amorphous cerium oxide. On the surface, there were mesopores ranging from 3 to 15 nm in diameter, Pt-rich grains less than 10 nm in size, and a few polyhedral grains of 20–50 nm. The crystal plane spacings of the exposed (2 2 ¯ 0), (400), and (220) high-index crystal planes of the Pt5Ti3 phase showed some interplanar space shrinkage of 5–7%. The contribution of the geometric surface area of the Pt-based alloy catalyst to the ESA was up to 352.16%. The energy consumption of catalytic cyclohexene hydrogenation was reduced by 39.33%. The current efficiencies of cyclohexene hydrogenation and the cyclohexene conversion rate were increased by 41.40% and 132.65%, respectively. The reinforced porous Pt-based alloy SPE membrane electrodes have advantages such as short process synthesis with pure products, and high-index exposed crystal planes regulation, strong catalytic activity, and low energy consumption. [ABSTRACT FROM AUTHOR]

Accurate registration of 3D scans is crucial in creating precise and detailed 3D models for various applications in cultural heritage. The dataset used in this study comprised numerous point clouds collected from different rooms in the Museum of King Jan III's Palace in Warsaw using a structured light scanner. Point clouds from three relatively small rooms at Wilanow Palace: The King's Chinese Cabinet, The King's Wardrobe, and The Queen's Antecabinet exhibit intricate geometric and decorative surfaces with diverse colour and reflective properties. As a result, creating a high-resolution full 3D model require a complex and time-consuming registration process. This process often consists of several steps: data preparation, registering point clouds, final relaxation, and evaluation of the resulting model. Registering two-point clouds is the most fundamental part of this process; therefore, an effective registration workflow capable of precisely registering two-point clouds representing various cultural heritage interiors is proposed in this paper. Fast Adaptive Multimodal Feature Registration (FAMFR) workflow is based on two different handcrafted features, utilising the colour and shape of the object to accurately register point clouds with extensive surface geometry details or geometrically deficient but with rich colour decorations. Furthermore, this work emphasises the challenges associated with high-resolution point clouds registration, providing an overview of various registration techniques ranging from feature-based classic approaches to new ones based on deep learning. A comparison shows that the algorithm explicitly created for this data achieved much better results than traditional feature-based or deep learning methods by at least 35%. [ABSTRACT FROM AUTHOR]

It is very challenging for robots to perform grinding and polishing tasks on surfaces with unknown geometry. Most existing methods solve this problem by modeling the relationship between the force sensing information and surface normal vectors by analyzing the forces on special end tools such as spherical tools and cylindrical tools and simplified friction model. In this paper, we propose a normal vectors learning method to simultaneously control end-effector force and direction on unknown surfaces. First, the relation that mapping the force sensing information to the surface normal vectors is learned from the demonstrated data on the known plane using locally weighted regression. Next, the learned relation is used to estimate surface normal vectors on the unknown surface. To improve the force control precision on the unknown geometry surface, the adaptive force control is developed. To improve the direction control precision due to friction, the iterative learning control is developed. The proposed method is verified by comparative simulations and experiments using the Franka robot. Results show that the end-effector can be controlled perpendicular to the surface with a certain force. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Laplacian equation with exponential Neumann boundary condition on a compact Riemann surface Σ with nonempty boundary ∂Σ. We show the existence result by using minmax methods without any assumption on the topology and the geometry of the surface. In particular, we generalize Guo–Liu's results in [Commum. Contemp. Math., 2006, 8: 737–761]. [ABSTRACT FROM AUTHOR]

The performance of a heat sink is significantly influenced by the type of cooling used: passive or active (forced), the shape of the heat sink, and the material from which it is made. This paper presents a review of the literature on the influence of geometry and surface parameters on effective heat transfer in heat sinks. The results of simulation studies for three different heat sink fin geometries and cooling types are presented. Furthermore, the influence of the surface texture of the heat sink fins on the heat transfer efficiency was determined. It was shown that the best performance in terms of geometries was that of a wave fin heat sink. When the surface texture was analyzed, it was found that an increase in the amplitude values of the texture decreases the heat dissipation efficiency in the case of active cooling, while for passive cooling, an increase in these parameters has a beneficial effect and increases the effective heat transfer to the surroundings. The cooling method was found to be the most important factor affecting heat dissipation efficiency. Forced airflow results in more efficient heat transfer from the heat sink fins to the surroundings. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the impact of beam deflection geometry on the structure, surface architecture, and friction coefficient of electron-beam-modified TC4 titanium alloys. During the experiments, the electron beam was deflected in the form of different scanning geometries, namely linear, circular, and matrix. The structure of the treated specimens was investigated in terms of their phase composition by employing X-ray diffraction experiments. The microstructure was studied by scanning electron microscopy (SEM). The surface architecture was examined by atomic force microscopy (AFM). The friction coefficient was studied by a mechanical wear test. It was found that the linear and circular deflection geometries lead to a transformation of the phase composition, from double-phase α + β to α' martensitic structure. The application of a linear manner of scanning leads to a residual amount of beta phase. The use of a matrix does not tend to structural changes on the surface of the TC4 alloy. In the case of linear geometry, the thickness of the modified zone is more than 800 μm while, in the case of EBSM using circular scanning, the thickness is about 160 μm. The electron-beam surface modification leads to a decrease in the surface roughness to about 27 nm in EBSM with linear deflection geometry and 31 nm in circular deflection geometry, compared to that of the pure TC4 substrate (about 160 nm). The electron-beam surface modification of the TC4 alloy leads to a decrease in the coefficient of friction (COF), with the lowest COF values obtained in the case of linear deflection geometry (0.32). The results obtained in this study show that beam deflection geometry has a significant effect on the surface roughness and friction coefficient of the treated surfaces. It was found that the application of a linear manner of scanning leads to the formation of a surface with the lowest roughness and friction coefficient. [ABSTRACT FROM AUTHOR]

Conformal contact is a commonly presented contact form in assemblies. Non‐proportional loading is the main characteristics of conformal contact, which leads to prominent difficulty in revealing fretting crack behavior. In this paper, a finite element prediction model for Ti‐6Al‐4V pin‐hole contact fretting fatigue crack initiation was developed, which simultaneously considered the effect of fretting wear, surface roughness, surface skewness, surface kurtosis, and residual stress. The results show that phase differences of stress component, change in direction of principal stress, and high stress gradient are the main reasons for the initiation of fretting fatigue under conformal contact condition. The model based on the Fatemi–Socie (FS) parameter successfully predicted the location, orientation, and fatigue life of crack initiation, which agrees well with the experimental results. Additionally, machining‐induced residual stress can effectively inhibit mode I crack initiation at valleys. Moreover, ignoring the surface microgeometry characteristics reduces the prediction accuracy of the crack behavior. Highlights: Surface microgeometry characteristics and residual stress were considered.Residual stress has less effect than roughness on conformal contact fretting fatigue.Consideration of surface geometry significantly improves the prediction accuracy.The predicted results are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

As one of the most important material-removing technologies, milling is used commonly for recent several decades to remove materials from a blank to get the desired surface. There are several parameters representing the geometrical qualities of a surface including topography, roughness, and waviness. Also, the surface topography directly determines contacting zone between two fitting surfaces, which may influence the friction property and the lubricity and furthermore affect the serving life of the machined surface. Therefore, the study of surface topography becomes a necessary research topic. To meet the fast-growing demand for high-performance surfaces and to figure out the challenges in this research area, the history and state-of-the-art technology/theory of this area need to be summarized. Thus, this paper tries to present a comprehensive review of the study on surface topography in the milling process. First, the construction mechanism of surface topography is analyzed. Second, the existing predicting methods are concluded. Then, influencing factors on the surface topography are discussed. Finally, the study on surface topography of complex components is investigated from geometric analysis, experimental exploration, and influence factors. Systemic analysis of research on surface topography provides a basis for future studies. [ABSTRACT FROM AUTHOR]

Magnetically‐actuated soft robots for medical applications are required to be functional, biocompatible, as well as capable of robust motion inside human organs. In this paper, a ring‐shaped magnetic soft robot, with a flexible biopolymeric film coating, capable of motion on mucus‐coated surfaces is designed and investigated. The biopolymeric film made from chitosan–glycerol (C–G) solution endows the robot with robust locomotion capabilities on surfaces of diverse geometrical shapes and orientations. By utilizing mucoadhesive locomotion, the robot has the potential to carry out clinical procedures on enclosed mucus‐coated tissue surfaces. Material characterization shows that the mucoadhesion increases with the increase of contact times and/or preload forces. The softness of the C–G film can be adjusted by controlling the concentration of glycerol. The ring‐shaped design and magnetization profile decouple the locomotion and functions of the robot. Additionally, the C–G film‐coated robot is tested to be biocompatible for a human colorectal adenocarcinoma cell line with epithelial morphology (HT29). The C–G film reduces the negative effects (superoxide generation) of ferromagnetic particles. Three robot functions including pick‐and‐place, cargo transportation, and liquid capsule release are demonstrated on different surfaces to show the maneuverability, functionality, and potential of implementing clinical procedures through mucoadhesion. [ABSTRACT FROM AUTHOR]

In this paper, a passive hazard detection and avoidance (HDA) system is presented, relying only on images as observations. To process these images, convolutional neural networks (CNNs) are used to perform semantic segmentation and identify hazards corresponding to three different layers, namely feature detection, shadow detection, and slope estimation. The absence of active sensors such as light detection and ranging (LiDAR) makes it challenging to assess the surface geometry of a celestial body, and the training of the neural networks in this work is oriented towards coping with that drawback. The image data set for the training is generated using blender, and different body shape models (also referred to as meshes) are included, onto which stochastic feature populations and illumination conditions are imposed to produce a more diverse database. The CNNs are trained following a transfer learning approach to reduce the training effort and take advantage of previously trained networks. The results accurately predict the hazards in the images belonging to the data set, but struggle to yield successful predictions for the slope estimation, when images external to the data set are used, indicating that including the geometry of the target body in the training phase makes an impact on the quality of these predictions. The obtained predictions are composed to create safety maps, which are meant to be given as input to the guidance block of the spacecraft to evaluate the need for a manoeuvre to avoid hazardous areas. Additionally, preliminary hardware-in-the-loop (HIL) test results are included, in which the algorithms developed are confronted against images taken using real hardware. [ABSTRACT FROM AUTHOR]

Advances in architectural geometry and computation have created strategies to rationalize complex building envelopes. This paper presents techniques to identify paths on freeform surfaces by prescribing specific curvature properties. The paths can be defined by the normal curvature or the geodesic torsion. In special cases, asymptotic and principal curvature lines can be determined. Such paths are used for the design of gridshells with lamellar elements. A brief introduction to differential geometry of freeform surfaces provides the relevant foundations for the method. The relevant quantities and relations are highlighted with illustrations. The consistent description of the paths in the parameter space of the surface avoids unnecessary and complex projection operations. This allows a computationally efficient and robust implementation. The tracing is explained for the simple case of a single surface and extended to trimmed multipatches which are used for geometric modeling in common computer-aided design (CAD) programs. The topological structure of the multipatch was used to trace paths across several surfaces. To enable interactive design, the path tracing techniques were integrated into the parametric CAD package Grasshopper for Rhino. Additional components for curvature analysis were implemented to analyze and evaluate designs. To simplify the handling of curvature lines, a geometry type for embedded curves was introduced and implemented within a CAD environment. Finally, the use of these tools for the design of architecturally sophisticated gridshells is presented along with three projects of increasing complexity. [ABSTRACT FROM AUTHOR]

The field of additive manufacturing has experienced a surge in popularity over recent decades, particularly as a viable alternative to traditional metal part production. Directed energy deposition (DED) is one of the most promising additive technologies, characterized by its high deposition rate, with wire arc additive manufacturing (WAAM) being a prominent example. Despite its advantages, DED is known to produce parts with suboptimal surface quality and geometric accuracy, which has been a major obstacle to its widespread adoption. This is due, in part, to a lack of understanding of the complex geometries produced by the additive layer. To address this challenge, researchers have focused on characterizing the geometry of the additive layer, particularly the outer part of the bead. This paper specifically investigates the geometrical characteristics and symmetry of walls produced by comparing two different techniques: an oscillated strategy and overlapping beads. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation of the sound radiation behavior of a thin exponential functionally graded material plate using the classical plate theory and Rayleigh Integral with the elemental radiator approach. The material properties of the plate material, like Poisson's ratio, are assumed constant, while Young's Modulus and density are assumed to vary according to the exponential law distribution of the constituent materials in the transverse direction. The functionally graded material is modeled using a physical neutral surface instead of a geometric middle surface. The parametric effects of exponential law index, elastic modulus ratio, different constituent materials, damping loss factor on the sound radiation from exponential functionally graded plate (E-FGM) are illustrated. Sound power level in A-weighted dBA (loudness) scale has been illustrated to compare the sound power level (noise levels) radiated from power law (P-FGM), sigmoid law (S-FGM), and an exponential law (E-FGM) FGM plates. A-weighted dBA has also been illustrated for different modulus ratios and different material constituent E-FGM plates. The principal aim of this research paper is to predict the level of sound power level or noise level radiated by the vibrating E-FGM plates. The further objective is its applications in industries to envision how beneficial it will be to use the E-FGM plate compared to P-FGM and S-FGM plate. It has been found that, for the considered plate, the modulus ratio significantly influences sound power level and sound radiation efficiency. Effects of modulus ratios on the sound power level showed frequency shift over stiffness control region in the low-frequency range (first mode for all modulus ratios). The different values of damping loss factors do not significantly influence radiation efficiency for the given material constituents of the functionally graded plate. However, the selection of material constituents influences the radiation efficiency peak. [ABSTRACT FROM AUTHOR]

The article presents the results and process analysis of the face milling of aluminium alloy 2017A with the CoroMill 490 tool on an AVIA VMC 800 vertical milling centre. The study analysed the effects of the cutting speed, the feed rate, the actual number of teeth involved in the process, the minimum thickness of the cut layer (hmin), and the relative displacement in the tool-workpiece system D(ξ) on the surface roughness parameter Ra. To measure relative displacement, an original bench was used with an XL-80 laser interferometer. The analysis of relative displacement and surface roughness allowed these factors to be correlated with each other. The purpose of this article is to determine the stable operating ranges of the CoroMill 490-050Q22-08M milling head with respect to the value of the generated relative displacement w during the face-milling process and to determine its influence on surface roughness. The research methodology presented in this paper and the cutting tests carried out allowed the determination of the optimum operating parameters of the CoroMill 490-050Q22-08M tool during the face milling of aluminium alloy 2017A, which are vc 300 m/m and fz—0.14 mm/tooth. Working with the defined cutting parameters allows all the cutting inserts in the tool body to be involved in shaping the geometrical structure of the surface, while maintaining a low vibration level D(ξ) > 1 µm, a low value of the parameter hmin > 1.5 µm, and the desired value of the parameter Ra > 0.2 µm [ABSTRACT FROM AUTHOR]

In optimizing the design of retaining structures and monitoring their health, it is important to determine the actual nonlinear slip-failure surface and the associated nonlinear lateral stress distribution. This paper presents a model developed for the nonlinear geometry of active and passive slip-failure surfaces in cohesionless soils and for determining their three main associated variables; that is, lateral earth pressure distribution, coefficient of lateral earth pressure, and location of the resultant lateral force. The variational limit-equilibrium method, as applied to a normally consolidated dry granular media, and the plane-strain critical-state friction angle at failure are used to develop the model. The model outputs the governing geometry of the slip-failure surface and its associated lateral stress distribution as a unique nonlinear function of the ultimate shearing resistance at failure. Mostly existing studies are complex unilateral approaches of the lateral stress or the slip-failure geometry as separated issues. In contrast, the present paper addresses a simple coupled solution at critical state that uses a disambiguated friction angle and avoids arbitrary input assumptions such as the geometry of the slip-failure surface. [ABSTRACT FROM AUTHOR]

Taylor–Couette flow is a canonical flow to study Taylor–Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel–Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large Re. The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low Re. In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue 'Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical transactions paper (Part 2)'. [ABSTRACT FROM AUTHOR]

Rectangular waveguides are susceptible to avalanche-style breakdown via the multipactor phenomenon. The growth in secondary electron density produced via multipactor can damage and destroy RF components. A pulse-adjustable, hard-switched modulator powering an X-band magnetron was utilized to drive a modular experimental setup that enables testing different surface geometries and coatings. Power measurements, taken via diodes, and phase measurements, facilitated via a double-balanced mixer, were integrated into the overall apparatus enabling multipactor detection with high sensitivity and nanosecond temporal resolution. The utilized 150 kW peak microwave source with 2.5 μs pulse width and 100 Hz repetition frequency allows for threshold testing without the need for initial electron seeding. This paper includes the initial results of surface conditioning of the test multipactor gap via electron bombardment. [ABSTRACT FROM AUTHOR]

Due to the production process, reinforcing steel bars possess an inhomogeneous microstructure associated with different material properties over the cross-section (e.g., hardness, ductility or strength). Furthermore, the surface required for the bond has a negative effect on the fatigue behavior. The first investigations were carried out in the 1970s and detected the fillet radius r as a key influencing factor. Until now, few studies had been carried out that investigate the quantification of the surface properties on the fatigue behavior, and none of them compared these properties with the local strengths of the material. The current paper presents the first results of a reverse-engineered reinforcing steel bar based on a previously performed laser scanning process. The rebar models were used to calculate the notch stress factors for different diameters based on von Mises stresses taken from FEM simulations. The notch stress factors showed a functional relationship with the fillet radius, which was already shown in the literature. Further experimental investigations on the fatigue and tensile behavior of the structural components in the investigated Tempcore® rebars were carried out on microstructure specimens eroded by WEDM. The results of the tensile tests were used to derive a yield and tensile strength distribution in the cross-section. Depending on the microstructure, a yield strength between 415 N/mm2 (ferrite/pearlite core) and 690 N/mm2 (tempered martensite surface) was found. The acting notch stresses show a logarithmic dependency of the fillet radius, but do not reach the material strength of the surface. [ABSTRACT FROM AUTHOR]

The objective of this research paper is to relate the influence of dynamic wetting in a liquid/liquid/solid system to the breakup of emulsion droplets in capillaries. Therefore, modeling and simulation of liquid/liquid flow through a capillary constriction have been performed with varying dynamic contact angles from highly hydrophilic to highly hydrophobic. Advanced advection schemes with geometric interface reconstruction (isoAdvector) are incorporated for high interface advection accuracy. A sharp surface tension force model is used to reduce spurious currents originating from the numerical treatment and geometric reconstruction of the surface curvature at the interface. Stress singularities from the boundary condition at the three-phase contact line are removed by applying a Navier-slip boundary condition. The simulation results illustrate the strong dependency of the wettability and the contact line and interface deformation. [ABSTRACT FROM AUTHOR]

One approach to estimate space-continuous deformation from point clouds is the parameter-based epochal comparison of approximating surfaces. This procedure allows a statistical assessment of the estimated deformations. Typically, holistic geometric models approximate the scanned surfaces. Regarding this, the question arises on how discontinuities of the object's surface resulting from e.g. single bricks or concrete blocks, influence the parameters of the approximating continuous surfaces and in further consequence the derived deformation. This issue is tackled in the following paper. B-spline surfaces are used to approximate the scanned point clouds. The approximation implies solving a Gauss–Markov-Model, thus allowing accounting for the measurements' stochastic properties as well as propagating them on the surfaces' control points. A parametric comparison of two B-spline surfaces can be made on the basis of these estimated control points. This approach is advantageous with regard to the transition of the space-continuous deformation analysis to a point-based task, thus ensuring the applicability of the well-established congruency model. The influence of the structure's geometry on the surfaces' control points is investigated using terrestrial laser scans of a clinker facade. Points measured in the joints are eliminated using an own developed segmentation approach. A comparison of the results obtained from segmented as well as from unsegmented laser scans for the B-spline approximation and the subsequent deformation analysis provides information about the structure-related influence. An aqueduct arc is used as measuring object in this study. For the intended comparison, data sets, which contain possible influences due to changes of the mechanical loads, are analysed. [ABSTRACT FROM AUTHOR]