Section Curves Research Articles

Flow characteristics inside rectangular Tesla valve with different width-to-narrow ratios

To investigate the influence of the flow channel’s width-to-narrow ratio on the Tesla valve’s flow characteristics, this paper establishes five Tesla valve models with different width-to-narrow ratios. Employing the laminar flow model, CFD methods were used to numerically simulate both the forward and reverse flows through the Tesla valve across a spectrum of width-to-narrow ratios, ranging from 0.2 to 1. The results reveal the flow trends in the straight or arc channels show opposite variation patterns when flowing in forward and reverse directions. The flow rate passing through straight channel is more sensitive to the response of a small width-to-narrow ratio. Irrespective of the flow direction, as the width-to-narrow ratio increases, the fluid flow within the valve demonstrates increasingly pronounced stratification. The pressure curve of the diversion section assumes an “∞” shape in forward flow, whereas in reverse flow, it assumes a “flat plate” shape.

3D young female waist-leg modelling based on a hybrid 3d-scan and 2d-image approach

To enhance the pant fit for individuals, this study proposed a method for constructing a 3D waist-leg mannequin based on body images and 3D point-clouds of young women. A total of 288 females aged 18–25 were measured using 3D body scanner and 2D image-shooting method to obtain 3D point-cloud data and body images. The 3D point-cloud data were analyzed to extract 33 sectional curves, including the cross-sectional curves and crotch curve, to identify key points on each curve. For the body images, key parameters related to curve position and shape, such as height, width, and thickness, were automatically extracted for modelling parameters. Curve generation rules were established based on correlation and regression analysis of the key points. The Individualized 3D mannequin was simulated by adjusting the curve centers at each characteristic position to align with the body images, and was validated by comparing the body sizes of the 3D mannequin with the actual measurements. The results indicated that the final simulated mannequin accurately represents the basic characteristics of the waist-leg shape, with significance values above 0.05, which showed the feasibility of the modelling method. Furthermore, 73.9% of the samples had an absolute error of less than 1 cm between the 3D mannequin and the actual measurements. This study can facilitate 3D body modelling from body images, and provide a reference to develop individualized apparel patterns for clothing customization.

Multistep-Ahead Prediction of Logging-While-Drilling Resistivity Curves Based on Seismic-Guided Seq2Seq-Long Short-Term Memory

Summary High-temperature and high-pressure reservoirs in complex geological conditions present primary targets and significant challenges in deepsea oil and gas exploration. Limited offshore drilling operations and lack of detailed geological data hinder accurate formation pressure prediction using geoguided and offset imaging, increasing drilling hazards. Logging-while-drilling (LWD) technology provides timely and accurate subsurface information. Resistivity closely correlates with formation pressure and lithology, aiding pressure prediction. Therefore, in this study, we developed an ahead prediction workflow for LWD curves using the resistivity curve (RD) as an example. A seismic-guided sequence-to-sequence framework with the long short-term memory model (Seq2Seq-LSTM) is used to predict the RD curve at a constant depth ahead of the drill bit, utilizing the RD curve of drilled sections and seismic attributes. The network structure incorporates a direct-recursive hybrid multistep prediction strategy based on update threshold control (Dir-Rec-Update), aligning with real-time LWD data acquisition for ahead curve prediction. Using real well data cross-prediction, baseline models such as multilayer perceptron (MLP) and extreme gradient boosting (XGBoost) were compared while also investigating the impact of different configurations on the proposed Seq2Seq-LSTM. The results demonstrate that the method outperforms conventional models, with an average performance across multiple wells under a 5-m update threshold: root mean square error (RMSE) of 0.15, correlation coefficient of 0.88, and coefficient of determination of 0.77. The Seq2Seq-LSTM model and Dir-Rec-Update strategy provide accurate LWD curves ahead of the drill bit, enabling advanced drilling decisions and preventing hazards. Advanced technologies such as empirical wavelet transform (EWT) and feature selection enhance the method’s potential for curve ahead-of-time prediction.

Arteriovenous Oscillometric Plethysmography for Fistula Functional Testing.

The aim of the presented prospective observational study was to evaluate the effect of fistula flow on peripheral wave morphology and pulse wave velocity by means of the oscillometric Vicorder®-device with the purpose of fistula surveillance. Digitized and normalized curves of 53 haemodialysis patients at the fistula and non-fistula arm were analysed. Slope parameters and the areas under the curve of characteristic sections of pulse waves as well as the power spectrum of the pulse waves and their first and second derivatives were computed. Furthermore, the amplitude of volumetric change (AMP) was assessed. Duplex sonography served as a reference method. In the comprehensive set of novel pulse wave parameters significant inter-arm differences were demonstrated and a significant delay of the systolic maximum at the fistula arm in comparison to the non-fistula arm (204 ± 3.4 vs. 162 ± 5.3 ms, p < 0.001) was proven. Unexpectedly, pulse wave velocity apparently did not differ between both arms (7.85 vs. 8.05 m/s at the fistula/non-fistula side, p = 0.942). The inter-arm differences of the slope parameters were more pronounced in forearm than in upper arm fistulas. Finally, we showed that the inter-arm difference of AMP correlated with volume flow (r = 0.326 with p = 0.017). Pulse waves as assessed by oscillometric pulse wave analysis have distinct features at fistula and non-fistula arms. This is due to enhanced arteriovenous flow, i.e. in both the brachial artery and the fistula vein. The analysis of those alterations has the potential to assess fistula function.

Strength design of built-up radially battened columns subject to axial compression and arbitrary directional bending moment

Built-up radially battened columns (RBCs), comprising several identical circular steel tubes interconnected by multiple radial-shaped battens, represent an innovative column design that combines aesthetic appeal with exceptional load-bearing capacity. This makes them well-suited for architectural applications in large public buildings such as stations and airports. The axial compressive strength design methods for the built-up RBC have been extensively explored in the authors' prior studies. However, in real-world engineering applications, built-up RBCs may experience simultaneous axial compression and varying directional bending moments, particularly when considering potential eccentric compression or wind and earthquake loads in public buildings. Currently, strength design methods for this loading condition are still lacking. To address this deficiency, this paper primarily delves into the failure mechanism and strength design methods for built-up RBCs experiencing combined axial compression and arbitrary directional bending moments. Initially, the sectional strength of the built-up RBC is investigated by using a shell finite element model (FEM) for the built-up RBC. It is revealed that the compression-bending sectional strength of the built-up RBC exhibits significant differences with varying bending directions and tube numbers. Moreover, in some bending directions, the M-N sectional strength curve of the built-up RBC exhibits convexity. By integrating theoretically derived equations grounded in the principles of materials mechanics with FEM numerical calculations, concise and practical design equations are proposed for accurately predicting the sectional strength of the built-up RBC under combined axial compression and arbitrary directional bending moments. Subsequently, The buckling strength of the built-up RBC is studied using the FEM, considering initial geometrical imperfections consistent with first-order flexural buckling and accounting for geometric nonlinearity. It is noted that the bending direction of the built-up RBC may deviate during loading. Besides, the M-N buckling strength curve of the built-up RBC is not as convex as its M-N sectional strength curve. Based on calculations from numerous examples, practical design equations for predicting the buckling strength for the built-up RBC under axial compression and any directional bending moments are introduced. The key findings of this paper contribute to the compression-bending strength design of RBCs, enriching RBC design theory and promoting the widespread application of built-up RBCs in actual engineering projects.

Design and application of a new type of hierarchical control device

To realize coupling between the yielding and partition failure processes, a new hierarchical control device was designed. The new stage control device comprised an internal and external two-stage structure similar to “piston + sleeve.” Under the action of the surrounding rock pressure, primary yielding occurred first, and the cone slid along the inner wall of the yielding sleeve. With an increase in the surrounding rock pressure, secondary yielding occurred, and the tray slid along the outer wall of the yielding sleeve. The device had a simple mechanical structure and exhibited reliable mechanical properties. It had a convenient and rapid installation process, and the load-displacement curve was obtained by laboratory tensile tests. Mechanical test results showed that the device exhibited a clear function of graded pressure yielding, which was consistent with the designed sectional control curve. The results show that the new hierarchical control device exhibited a good control effect on the surrounding rock and is helpful for TBM in realizing fast driving.

Permeability Prediction of Carbonate Reservoir Based on Nuclear Magnetic Resonance (NMR) Logging and Machine Learning

Reservoir permeability is an important parameter for reservoir characterization and the estimation of current and future production from hydrocarbon reservoirs. Logging data is an important means of evaluating the continuous permeability curve of the whole well section. Nuclear magnetic resonance logging measurement results are less affected by lithology and have obvious advantages in interpreting permeability. The Coates model, SDR model, and other complex mathematical equations used in NMR logging may achieve a precise approximation of the permeability values. However, the empirical parameters in those models often need to be determined according to the nuclear magnetic resonance experiment, which is time-consuming and expensive. Machine learning, as an efficient data mining method, has been increasingly applied to logging interpretation. XGBoost algorithm is applied to the permeability interpretation of carbonate reservoirs. Based on the actual logging interpretation data, with the proportion of different pore components and the logarithmic mean value of T2 in the NMR logging interpretation results as the input variables, a regression prediction model is established through XGBoost algorithm to predict the permeability curve, and the optimization of various parameters in XGBoost algorithm is discussed. The determination coefficient is utilized to check the overall fitting between measured permeability versus predicted ones. It is found that XGBoost algorithm achieved overall better performance than the traditional models.

Effect of external prestressing on the special shear lag behavior of precast box girder bridges

The shear lag behavior exhibited by precast segmental box girders (PSBGs) under concentrated external prestressing differs significantly from that observed in box girders subjected to vertical loads. To study the special shear lag behavior of PSBGs under external prestressing, a theoretical analytical method was developed based on the classical energy variational principle. In this analysis, the effect of external prestressing was decomposed into axial compression and bending effects through the equivalent load method. For each of these effects, appropriate longitudinal warping displacement modes were assumed, and the total energy functional expressions of the system under these two effects were further established. The governing differential equations for the two effects were derived using the principle of energy variation. Analytical solutions for the normal stress of the beam section under axial compression and bending effects were deduced, and corresponding boundary conditions were obtained. Subsequently, the normal stress of the section under the two effects was superimposed to obtain the comprehensive normal stress distribution curve of the beam section under external prestressing. The reliability of the theoretical analysis method was validated through a comparison of the theoretical analysis results with experimental and numerical analysis results.

Life cycle costs and mid-term performance of a geogrid-stabilized pavement section, an economical and sustainable approach, case study, RN-39 Honduras

When we talk about mechanical stabilization of granular layers with geogrids in roadway applications, we often mention that these pavements have a better performance along the time and a reduced cost along the whole life cycle. In the last years we have been measuring the International Roughness Index (IRI) of a segment of multi-axial with triangular aperture geogrid-stabilized road of 45.6 km of length and comparing it with a non-stabilized segment of 30.7 km of length, which was constructed in the same period and was commissioned the same year, for the same traffic. In terms of deterioration based on the International Roughness Index (IRI) for each segment, the mechanically stabilized road has shown a better performance than the non-stabilized segment, this publication seeks to show the tendency of the IRI curve for both sections, and the differences in their behavior. In addition, an analysis with the software; Highway Development and Management, version 2.0 (HDM-4) will be conducted to estimate the impact in the road user’s costs which are part of the life cycle cost and compare both sections, as well as an attempt to emulate and calibrate the IRI curve for the stabilized road section. This publication will help pavement engineers, designers, asset managers, highway engineers, departments of transportation and any people involved on roads, to better understand the economic advantages and performance benefits of mechanically stabilized granular layers with multi-axial geogrids on pavements and how they can help building resilient, durable, and sustainable road infrastructures.

Design of broadband gradient resistive film metamaterial absorber based on genetic algorithm

In recent years, electromagnetic (EM) wave absorbing devices based on metamaterials have attracted widespread attention, due to their advantages such as broadband, easy preparation, and flexibility to tailor EM waves. Nevertheless, a review of the existing research reveals that the inherent sub-wavelength characteristics of metamaterials and metasurfaces impose certain constraints on their applications in low-frequency ranges. In order to achieve low detectability that takes into account both low-frequency and broadband absorbing performance, this work, presents a metamaterial absorber based on 5-layer gradient resistance film and dielectric composite structure, as shown in <xref ref-type="fig" rid="FigureAbstract">Fig. (a)</xref>. To begin with, we introduce the structural design of the initial element, and based on this, the transmission line theory and impedance matching principle are used to analyze the strong wave absorption conditions of the absorber element. In terms of the element structure optimization, the genetic algorithm is adopted to globally search for the optimal solution in the multi-variable domain, resulting in the rapid determination of metamaterial elements’ configurations and resistance parameters that meet the design goals. In the simulation, the wave absorption performance and mechanism of the designed absorbing element are also investigated in an in-depth manner. Simulation results show that the designed metamaterial absorber can achieve more than 90% EM wave absorption in a frequency range of 1.62–19.16 GHz (with a relative bandwidth of 168.8%) under normal incidence of linearly polarized plane waves, which effectively expands the absorption bandwidth to the L band and K band. In addition, the simulations for oblique incidence at different polarizations provide strong evidence for the device’s insensitivity to both polarization and angle. The radar cross section (RCS) curves obtained by the time domain (TD) simulation illustrate that the novel structure can achieve more than 10 dB RCS reduction in a frequency range of 1.7–20 GHz. In the device's performance verification process, a metamaterial absorber with 20 × 20 elements and dimensions of 1.566<inline-formula><tex-math id="M1">\begin{document}$ {\lambda }_{l} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M1.png"/></alternatives></inline-formula>×1.566<inline-formula><tex-math id="M2">\begin{document}$ {\lambda }_{l} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M2.png"/></alternatives></inline-formula>× 0.113<inline-formula><tex-math id="M3">\begin{document}$ {\lambda }_{l} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231781_M3.png"/></alternatives></inline-formula> is fabricated and tested by using the bow method reflectivity test system. The absorptivity curves under 5° oblique incidence of different polarizations, show that the proposed metamaterial absorber can realize more than 80% EM absorption in an entire frequency range from 2 to 18 GHz, the test results of different polarizations are basically consistent. The test results at oblique incidence (<i>θ</i> ≥ 30°) show that although the measured and simulated curves exhibit discrepancies in certain frequency bands due to human error or material dispersion characteristics, the overall experimental results are consistent with our expectations, which fully proves that the designed metamaterial absorber has potential application value in the field of low-frequency and broadband EM absorption.

Neutron resonance cross sections evaluation based on the phase shift deep neural network

Neutron resonance cross sections are essential in many nuclear science and application fields. Evaluated nuclear libraries usually derive neutron resonance parameters using R-matrix theory. However, determining these parameters and reconstructing the pointwise cross sections required for transport calculations is a time-consuming process. This paper presents a new method for fitting neutron resonance cross sections by using a phase shift deep neural network (PhaseDNN). The network presents resonance cross sections based on its network parameters. This approach allows for the quick calculation of cross section values from the given network parameters. Additionally, PhaseDNN can fit network parameters to experimental data to obtain a smooth resonance cross section curve. Therefore, it has the potential to be an alternative to R-matrix theory.

Three-Dimensional Profiling of Drilled Shafts Based on Four-Point Ultrasonic Measurement

Drilled piles are one of the most important foundation systems, and the shapes of the shafts prior to casting have a significant impact on their quality. In order to better obtain geometrical information on the shafts, this study proposes a profiling approach based on four-point ultrasonic measurement. First, data from horizontal sections are fitted using least squares to obtain sectional contour curves. Vertical contours are generated by iterative fitting to ensure the smoothness of the curves. Data-processing software is then used to merge the horizontal sectional curves and the vertical curves into a three-dimensional image that approximates the actual contours of the shaft.

Experimental study on high-temperature resistance of alkali-activated slag concrete block masonry

The use of blast furnace slag improves resource utilization and supports the achievement of sustainable development goals. The use of alkali-activated slag cementitious material (AASCM) provides a new direction for improving the fire resistance of masonry structures. The masonry investigated in this study was alkali-activated slag crushed aggregate concrete masonry (ASCCM) in which aggregates of blocks and mortars were crushed and screened using AASCM paste specimens. The compression behavior of 12 specimens during and after exposure to high temperatures, specifically 300, 500, 600, 700, 800, and 900°C was investigated. The specimens were maintained under the target temperature for 2 h. The compressive strength and axial deformation of the specimen were recorded. The compressive strength losses during exposure to 300, 500, 600, 700, 800, and 900°C are 15.9, 20.3, 38.3, 43.9, 63.3 and 73.8%, respectively. The compressive strength losses after exposure to 300, 500, 600, 700, 800, and 900°C are 10.6, 15.8, 34.0, 37.2, 58.6 and 72.2%, respectively. The rate of loss in elastic modulus is greater than that in compressive strength. During exposure to 300, 500, 600, 700, 800, and 900°C, the loss rates of elastic modulus are 56.5, 74.4, 83.3, 86.3, 92.9 and 93.9%, respectively. After exposure to 300, 500, 600, 700, 800, and 900°C, the loss rates of elastic modulus are 49.6, 67.3, 77.5, 82.0, 90.7 and 94.5%, respectively. The peak compressive strain values are 9.9 and 11.1 times that at room temperature. Equations for calculating the compressive strength, elastic modulus, peak compressive strain, and ascending section curve of the stress–strain relationship with temperature were derived. The research results provide a new choice for high temperature resistant masonry materials, and provide theoretical basis and data support for the application of AASCM in masonry structures in high-temperature environments.

Molecular electronic stopping cross section for H and He beams colliding with water: projectile charge state contribution

Abstract When an ion beam impinges on a target material, electron stripping and capture processes involve different charge fraction states in the beam, such that each projectile charge state produces a different energy-loss. In this work, the energy deposition of swift hydrogen and helium ion beams colliding with a water target in the gas phase is studied. The electronic structure of the molecular target is represented in terms of core, bond, and lone pair orbital decomposition within a Harmonic Oscillator representation. In this way, the stopping cross section becomes only a function of the orbital mean excitation energy, I 0i . The ion beam charge fraction compositions colliding on water is determined from the work of Wedlund et al (2019) Astronomy & Astrophysics, 630, A36) by accounting for the electron transfer cross sections. We find that the larger the projectile charge state, the larger the electronic stopping cross section and that the beam charge fraction determines the position of the maximum of the electronic stopping curve. Also, in agreement with the experiment, evidence is given on the dominant role of the largest projectile charge state in defining the stopping cross section for high energy collisions, while for low collision energies it is the lowest charge state together with all possible charge states contributing at the maximum of the electronic stopping cross section curve. Our results are reported and compared to available experimental data showing an excellent agreement to the available literature.

Study on Nonlinear Vibration of Vertical Lifting Section of Bulk Grain Entrainment Ship Unloader

In view of the prominent problem that nonlinear vibration of a belt conveyor can easily occur during the vertical grain-conveyance process due to the coupling effect of airflow clamping and traction of the conveyor belt, which seriously affects the efficiency and stability of conveying materials by the belt conveyor, a method of solving the vibration analysis of the vertical lifting section of the bulk grain belt unloader by using nonlinear vibration is proposed. Firstly, based on the laminated plate theory, the vertical lifting belt and the grain material clamped by the belt are laminated. The nonlinear vibration differential equation of the vertical lifting section of the bulk grain-carrying ship unloader is established by elastic–plastic mechanics, and solved by perturbation theory and Galerkin discrete analysis. The vibration response curve and structural natural frequency of the vertical lifting section of the bulk grain-carrying machine are obtained by numerical solution, and the influence of the volume content of the clamped material on the vibration response and structural natural frequency of the lifting section is analyzed. This study provides theoretical support for the design of pressure-supply parameters, overall structure and operation parameters of the subsequent entrainment ship unloader, promotes the rapid development of the entrainment ship unloader, provides theoretical support for the design, manufacture, later operation, and maintenance of the entrainment ship unloader, and thus provides equipment and technical support for building an efficient and intelligent port.

Fano's last Fano

In 1949, Fano published his last paper on 3 -folds with canonical sectional curves. There, he constructed and described a 3 -fold of degree 22 in a projective space of dimension 13 with canonical curve section, which we like to call Fano's last Fano . We report on Fano's construction and we provide various (in our opinion missing) proofs in modern language. Moreover, we try to use results and techniques available at that time. After that we construct Fano's last Fano with modern tools, in particular, via the Hilbert scheme of zero cycles on a rational surface; as a consequence we easily point out the corresponding example in the Mori–Mukai classification.

Revisiting the luminescence properties of Er3+, Tm3+ and Ho3+ doped Bi4Ge3O12 rod-type crystal fibers for the laser application

BGO single crystals doped with Er3+, Tm3+ and Ho3+ rare-earth ions were prepared in the form of rod-type crystal fibers via the micro-pulling down technique to perform an extensive investigation of their visible, near- and mid-infrared luminescence properties and to really decide on their interest as solid-state laser media in the various spectral domains. Revisiting and completing the absorption spectra already available in the literature led to the derivation of more reliable “effective” radiative lifetimes and branching ratios. Registration of the fluorescence decays of the most important emitting levels versus dopant concentrations led for the first time to an unambiguous determination of “intrinsic” emission lifetimes – corresponding to negligible contributions from inter-ionic energy-transfers - and non-radiative multiphonon relaxation rates. Such data also allowed for the determination of the dominant phonon energy which comes into play in the electron-phonon coupling responsible for these multiphonon relaxation processes and for its lattice vibration origin, i.e. a high phonon energy of the order of 820 cm−1 corresponding to the coupling between bending vibrations of (GeO4)4- tetrahedra and vibrations corresponding to motions of these (GeO4)4- tetrahedra against the Bi3+ ions for which the rare-earth dopant ions substitute. Using the above data and different methods for the calibration of the registered emission spectra in cross section unit and for the derivation of gain cross section curves finally show that mid-infrared emissions of Er:BGO, Tm:BGO and Ho:BGO around 1.55 μm, 1.9 μm and 2 μm, respectively, occur with comparable gain cross sections as in the most important reference mid-infrared laser materials, although over slightly shifted thus complementary spectral domains. It is shown that potentialities also exist with Tm:BGO in the blue, deep-red and near-infrared spectral domains around 470 nm, 800 nm and 1.45 μm, by pumping the crystals with conventional pump sources and using some suitable co-dopants to avoid detrimental self-terminating processes.

Fast Reconstruction Model of the Ship Hull NURBS Surface with Uniform Continuity for Calculating the Hydrostatic Elements

The fast reconstruction of the ship hull nonuniform rational B-spline (NURBS) surface with uniform continuity is essential for calculating hydrostatic elements such as waterplane area and molded volume in real time. Thus, this study proposes a fast reconstruction model with uniform continuity to solve the problem of uniform continuity and splicing in the separate model of hull bow and stern surfaces. The proposed model includes the NURBS curve generation (UCG) algorithm with uniform continuity and the hybrid NURBS surface generation (HSG) algorithm. The UCG algorithm initially fits the feature points using the global interpolation algorithm and then precisely constructs straight-line segments in the curve using the improved flattening algorithm. In comparison, the HSG algorithm adaptively selects the surface knot vectors according to the parameters of the section curves. In this study, the profile of discontinuous compartments is uniformly expressed, effectively avoiding various articulation problems in separation modeling. The results of comparative experiments show that the NURBS surface generated using the HSG algorithm can accurately express the characteristics of various parts of the hull with uniform continuity, and the calculation speed of the proposed model can be increased by up to 8.314% compared with the existing best-performing algorithms. Thus, the proposed model is effective and can improve computational efficiency to a certain extent. The NURBS surfaces generated by the proposed model can be further applied to calculating the hydrostatic elements of hulls and compartments.

Reparameterization of B-spline surface and its application in ship hull modeling

NURBS are widely used in the design of free curves and surfaces and have been the industrial standard for product design in CAD/CAM. Ship hull surfaces are complex doubly-curved surfaces and usually decomposed into patches based on feature curves. Due to the topologically rectangular limitations of tensor-product NURBS surfaces and the inevitable problem of surface merging caused by decomposition, the reconstruction of ship hull still remains a complicated problem. The theoretical research of merging NURBS surfaces is relatively comprehensive, but the difficulty lies in how to merge surfaces defined in different knot vectors at the common boundary curve since control meshes form T-junctions. This paper proposes a methodology of reparameterizing B-spline surfaces, using a fast progressive-iterative approximation (FPIA) method to refit section curves or isoparametric curves with constraints, thus making the topological structure of control meshes regular, uniform and orthogonal. Subsequently, a KCS container ship with bulbous bow and stern is utilized as an illustration for reconstructing with B-splines. The lighting effects and lines plan derived from the hull surface demonstrate that this approach can achieve fair, smooth and watertight surfaces. The approach exhibits strong robustness, versatility and generalization ability, and provides theoretical innovation and practical design methods for representing and reconstructing complex ship hull.

Prediction of condylar movement envelope surface based on facial morphology

The present study aimed to predict the envelope surfaces from facial morphology. Condylar envelope surfaces for 34 healthy adults were formed and simplified as sagittal section curves. Cephalometric and maximum mandibular moving distances measurement were performed on the participants. There was no statistically significant difference (p = 0.763) between the left and right maximum lateral movements. There was a statistically significant difference in the mandibular body length between the sexes. The envelope surfaces were divided into type 1 with Hp2 ≥ 1/3 Hp1 and type 2 with Hp2 < 1/3 × Hp1. SNA and SNB for type 2 were significantly greater than those for type 1 (p < 0.001). Therefore, the participants were divided into four groups based on gender and envelope surface morphology. The curves could be fitted using the second-order Fourier function (R-square ≥0.95). Six facial parameters were selected and a matrix was used to map facial morphology to the envelope surface. Individual sagittal curves were predicted using the matrix and facial parameters, and the envelope surface was predicted using the curve and the condyle model. Deviation analysis for the predicted envelope surface using the actual envelope as a reference was carried out (root mean square = 0.9970 mm ± 0.2918 mm). This method may lay a foundation for the geometric design of artificial fossa components of temporomandibular joint replacement systems. It may improve prosthesis design without flexible tissue repair and guide the movement of the artificial joint head.