Geometric Model Research Articles

Geometric Modelling of a Family of 4-Point Ternary Approximating Subdivision Scheme U_φ with Visual Performance

Making signals better than noise in communication has always been challenging for scientists. Researchers have been working on it in different ways. The computer-aided geometric design is a new research field emerging from the collaboration of computer algorithms and mathematical logic towards curve designing, in which the subdivision schemes used have a key position due to their flexible and smooth behaviour. Using parameters in these schemes allows for increased control over designing. A parameterized framework for generating a wide range of subdivision surfaces with tunable degrees of shape control is presented in the family of schemes. The properties of the proposed family make it suitable for use in isogeometric analysis, computer animation, and geometric modelling. The purpose of this paper is to construct and analyze a family of 4-point ternary subdivision schemes to smooth the curves based on the Laurant polynomial. This family is generated by tuning the weight parameter. The scheme is analysed for its different properties. The scheme has continuity. Visual performance of the subdivision scheme is also provided as an application of this proposed study.

Outlier Detection by Energy Minimization in Quantized Residual Preference Space for Geometric Model Fitting

Outliers significantly impact the accuracy of geometric model fitting. Previous approaches to handling outliers have involved threshold selection and scale estimation. However, many scale estimators assume that the inlier distribution follows a Gaussian model, which often does not accurately represent cases in geometric model fitting. Outliers, defined as points with large residuals to all true models, exhibit similar characteristics to high values in quantized residual preferences, thus causing outliers to cluster away from inliers in quantized residual preference space. In this paper, we leverage this consensus among outliers in quantized residual preference space by extending energy minimization to combine model error and spatial smoothness for outlier detection. The outlier detection process based on energy minimization follows an alternate sampling and labeling framework. Subsequently, an ordinary energy minimization method is employed to optimize inlier labels, thereby following the alternate sampling and labeling framework. Experimental results demonstrate that the energy minimization-based outlier detection method effectively identifies most outliers in the data. Additionally, the proposed energy minimization-based inlier segmentation accurately segments inliers into different models. Overall, the performance of the proposed method surpasses that of most state-of-the-art methods.

Construction of multi-component finite element model to predict biomechanical behaviour of breasts during running and quantification of the stiffness impact of internal structure.

This study aims to investigate the biomechanical behaviour and the stiffness impact of the breast internal components during running. To achieve this, a novel nonlinear multi-component dynamic finite element method (FEM) has been established, which uses experimental data obtained via 4D scanning technology and a motion capture system. The data are used to construct a geometric model that comprises the rigid body, layers of soft tissues, skin, pectoralis major muscle, fat, ligaments and glandular tissues. The traditional point-to-point method has a relative mean absolute error of less than 7.92% while the latest surface-to-surface method has an average Euclidean distance (d) of 7.05mm, validating the simulated results. After simulating the motion of the different components of the breasts, the displacement analysis confirms that when the motion reaches the moment of largest displacement, the displacement of the breast components is proportional to their distance from the chest wall. A biomechanical analysis indicates that the stress sustained by the breast components in ascending order is the glandular tissues, pectoralis major muscle, adipose tissues, and ligaments. The ligaments provide the primary support during motion, followed by the pectoralis major muscle. In addition, specific stress points of the breast components are identified. The stiffness impact experiment indicates that compared with ligaments, the change of glandular tissue stiffness had a slightly more obvious effect on the breast surface. The findings serve as a valuable reference for the medical field and sports bra industry to enhance breast protection during motion.

Non-interference slow tool servo turning method for complex surfaces with large undulation changes

Complex curved surface parts are integral to the mechanical industry, demanding precise machining techniques. Multi-axis slow tool servo turning has emerged as an efficient method due to its high precision and quality. However, the challenge of severe tool flank interference arises, especially on surfaces with large undulation changes. Conventional methods, such as increasing tool clearance angles or adding extra tool axes, detrimentally affect machining precision and stability. To address this, a non-interference toolpath planning method is proposed for complex surfaces with large undulation changes. The approach begins with establishing geometric models of the single-point diamond turning tool and typical complex surfaces, followed by analyzing the mechanism and evolution of tool flank interference. By considering geometric parameters and vector relationships, the practical tool clearance angles are calculated. And then a criterion for subregion division is introduced and the non-cutting stroke is designed, accounting for the maximal acceleration of machine tool axis. Multi-pass toolpaths are generated to navigate different subregions while avoiding interference by transforming spindle rotation direction. Furthermore, a method is proposed to optimize toolpath stitching in practical machining regions, ensuring continuous and smooth transitions while maintaining machining precision and surface quality. Experimental validation, conducted on a hyperbolic paraboloid surface with large undulation changes, demonstrates a significant reduction in surface roughness (Sa) from 380.503 nm to 75.664 nm—a reduction of 80.115 %. The proposed method not only enhances machining precision and surface quality but also extends tool life and improves working conditions. This research offers vital guidance for non-interference toolpath planning in engineering practice.

Geometrical and Mechanical Modeling of Polymeric Multi-Ply Yarns

Geometrical and Mechanical Modeling of Polymeric Multi-Ply Yarns

Innovative claw rotor design for claw vacuum pump and its power consumption analysis

The claw vacuum pump is extensively utilized in semiconductor, photovoltaic and aerospace industries because of its dry oil-free and compact structure. In order to reduce the power consumption of the claw vacuum pump caused by its special mixing process during operation, a novel pair of claw rotors was proposed. This innovation involves replacing the conventional circular arc at the dedendum of the claw rotors with an eccentric circular arc. A geometric model of the novel claw rotor was established, and the geometric characteristics of both the novel and conventional claw rotors were compared. Subsequently, the optimal design parameters were determined. The pressure distribution and power consumption of two claw vacuum pumps were analyzed with numerical simulations. Study results indicates that the power consumption of the proposed claw vacuum pump in the mixing process is reduced by 72.3 %, and the total power consumption is reduced by 12.6 % compared to the conventional pump. The study is of great significance for reducing power consumption of the claw vacuum pumps and improving application.

Interfacial delamination mechanism of thermal barrier coatings with real microstructure considering gradient thermal and growth strains based on the fracture phase field

The interface of atmospheric plasma spray (APS) thermal barrier coatings (TBCs) is highly irregular and rough, while their microstructure is porous and extremely uneven. This complexity leads to intricate patterns during the growth of thermally grown oxide (TGO), the distribution and evolution of the generated stress, as well as the initiation and expansion of cracks. Along these lines, in this work, a phase-field theory considering both the thermal gradient strain and TGO growth was established to thoroughly investigate the interface oxidation cracking in TBCs. More specifically, a two-dimensional geometric model of APS TBCs was established, incorporating real interface morphology and microstructure. Numerical simulations and experiments were also conducted to study the temperature and stress distribution, as well as the underlying mechanism of interface cracking during the service of TBCs. The results indicated that at high temperatures, the bottom temperature of the top coating (TC) layer with a porosity of 3.1% and a thickness of 200 μm was approximately 5 °C lower than that of the TC layer without porosity. Compared to the ideal model without pores, the model considering the real microstructure, with the presence of microcracks in the TC, makes it easier for the normal stress in the TGO at the peak region to be released. The inter-lamella cracks (Type A) in the TC near the peaks initiated earliest, followed by the creation of inter-lamella cracks at other locations, accompanied by the appearance of lamella-fracture cracks (Type B), inter-lamella to interfacial cracks (Type C), inter-lamella to TGO cracks (Type D), and internal TGO cracks (Type E). The coalescence of all these types of cracks will ultimately lead to coating failure.

Lung divisions for models of cardiopulmonary interaction – preliminary tests

Abstract Introduction: The perfusion of a part of the lung depends on its distance from the pulmonary trunk (differences in vascular resistance) and on the horizontal plane (differences in hydrostatic pressure). The aim of this study was to determine the geometric parameters characterising their positions and sizes in order to analyse the diffusion of the ventilation/perfusion ratio. Material and methods: A developed virtual respiratory system has been supplemented with an appropriate model of pulmonary circulation that uses a lung outline that is divided into parts based on an anatomical atlas and a CT image; it comprises a 3D geometric model of the lungs that was developed using the Inventor CAD software (Autodesk, Inc, San Francisco, USA). Each panel was divided into 2 horizontal and 8 vertical parts; the 16-part division was then modified. Results: When taking human lungs as a research object and simulating their accompanying physical, biological, or biochemical phenomena, one necessary task is to construct a spatial model of the lungs that takes into account, and maintains awareness of, the limitations of the source of data that is relied upon. The developed modified geometric model of lung division turned out to be useful and was successfully applied to a virtual patient, among others, as part of the VirRespir project. Conclusions: Finally, we can conclude that the virtual cardiorespiratory system thus elaborated may serve as a proper tool for the preliminary analysis of such complex interactions, considering the elaborated model of the lung’s divisions and its future improvements.

ECG imaging as a real time tool to guide left bundle branch pacing implant in patients with left bundle branch block and resynchronization therapy indication

Abstract Background Left bundle branch pacing (LBBP) has emerged as a promising alternative technique for cardiac resynchronization therapy (CRT). ECG imaging (ECGI) may provide an accurate assessment of electrical resynchronization using real-time maps during LBBP implant. Purpose To evaluate the usefulness of ECGI to guide LBBP implant, by analyzing the ventricular activation times and the degree of resynchronization at each screwing step during the lead implant. Methods Four patients with CRT indication and left bundle branch block (LBBB) referred for LBBP were prospectively enrolled. ECGI was performed during the implant procedure. Cardiac signals were recorded using ECGI and projected into an artificial intelligence-derived geometric model. Thus, generating imageless and non-invasive activation maps at defined stages during lead screwing: basal rhythm (LBBB), right ventricular (RV) septum, mid-septal, deep-septal, and finally pacing from the left bundle branch (according with guidelines ECG criteria). The following parameters were measured: a) total activation time (TAT); b) left ventricular activation time (LVAT); c) left ventricular dyssynchrony index (LVDI) (as a quantifier of intraventricular dyssynchrony); d) ventricular electrical uncoupling (VEU); and e) histogram overlap between LV and RV distribution (the last 2 markers of interventricular dyssynchrony). Results The study cohort comprised men with a median age of 68 [Q1 59- Q3 79], with a median basal LBBB QRS duration of 175 ms [160-188] and a median LVEF of 32% [28-39]. A shortening of the activation times and a decrease in intra and interventricular dyssynchrony was achieved when the final lead position was reached. See the results in Figure 2. Conclusion Real-time and imageless ECGI system may offer a novel approach for guiding LBBP and it is useful to ensure left ventricular resynchronization.ECGI to guide LBBP implantActivation and dyssynchrony measurements

In vivo mechanical response of thigh soft tissues under compression: A two-layer model allows an improved representation of the local tissue kinematics

Biomechanical parameters have the potential to be used as physical markers for prevention and diagnosis. Finite Element Analysis (FEA) is a widely used tool to evaluate these parameters in vivo. However, the development of clinically relevant FEA requires personalisation of the geometry, boundary conditions, and constitutive parameters. This contribution focuses on the characterisation of mechanical properties in vivo which remains a significant challenge for the community. The aim of this retrospective study is to evaluate the sensitivity of the computed elastic parameters (shear modulus of fat and muscle tissues) derived by inverse analysis as a function of the geometrical modelling assumption (homogenised monolayer vs bilayer) and the formulation of the cost function. The methodology presented here proposes to extract the experimental force-displacement response for each tissue layer (muscle and fat) and construct the associated Finite Element Model for each volunteer, based on data previously collected in our group (N = 7 volunteers) as reported in (Fougeron et al., 2020). The sensitivity analysis indicates that the choice of the cost function has minimal impact on the topology of the response surface in the parametric space. Each surface displays a valley of parameters that minimises the cost function. The constitutive properties of the thigh (reported as median ± interquartile range) were determined to be (μ=198±322Pa,α=37) for the monolayer and (μmuscle=1675±1127Pa,αmuscle=22±14,μfat=537±1131Pa,αfat=32±7) for the bilayer. A comparison of the homogenised monolayer and bilayer models showed that adding a layer reduces the error on the local force displacement curves, increasing the accuracy of the local kinematics of soft tissues during indentation. This allows for an increased understanding of load transmission in soft tissue. The comparison of the two models in terms of strains indicates that the modelling choice significantly influences the localization of maximal compressive strains. These results support the idea that the biomechanical community should conduct further work to develop reliable methodologies for estimating in vivo strain in soft tissue.

Enhancing endoscopic scene reconstruction with color-aware inverse rendering through neural SDF and radiance fields.

Virtual surgical training is crucial for enhancing minimally invasive surgical skills. Traditional geometric reconstruction methods based on medical CT/MRI images often fall short in providing color information, which is typically generated through pseudo-coloring or artistic rendering. To simultaneously reconstruct both the geometric shape and appearance information of organs, we propose a novel organ model reconstruction network called Endoscope-NeSRF. This network jointly leverages neural radiance fields and Signed Distance Function (SDF) to reconstruct a textured geometric model of the organ of interest from multi-view photometric images acquired by an endoscope. The prior knowledge of the inverse correlation between the distance from the light source to the object and the radiance improves the real physical properties of the organ. The dilated mask further refines the appearance and geometry at the organ's edges. We also proposed a highlight adaptive optimization strategy to remove highlights caused by the light source during the acquisition process, thereby preventing the reconstruction results in areas previously affected by highlights from turning white. Finally, the real-time realistic rendering of the organ model is achieved by combining the inverse rendering and Bidirectional Reflectance Distribution Function (BRDF) rendering methods. Experimental results show that our method closely matches the Instant-NGP method in appearance reconstruction, outperforming other state-of-the-art methods, and stands as the superior method in terms of geometric reconstruction. Our method obtained a detailed geometric model and realistic appearance, providing a realistic visual sense for virtual surgical simulation, which is important for medical training.

Geometric growth of the normal human craniocervical junction from 0 to 18 years old.

The craniocervical junction (CCJ) forms the bridge between the skull and the spine, a highly mobile group of joints that allows the mobility of the head in every direction. The CCJ plays a major role in protecting the inferior brainstem (bulb) and spinal cord, therefore also requiring some stability. Children are subjected to multiple constitutive or acquired diseases involving the CCJ: primary bone diseases such as in FGFR-related craniosynostoses or acquired conditions such as congenital torticollis, cervical spine luxation, and neurological disorders. To design efficient treatment plans, it is crucial to understand the relationship between abnormalities of the craniofacial region and abnormalities of the CCJ. This can be approached by the study of control and abnormal growth patterns. Here we report a model of normal skull base growth by compiling a collection of geometric models in control children. Focused analyses highlighted specific developmental patterns for each CCJ bone, emphasizing rapid growth during infancy, followed by varying rates of growth and maturation during childhood and adolescence until reaching stability by 18 years of age. The focus was on the closure patterns of synchondroses and sutures in the occipital bone, revealing distinct closure trajectories for the anterior intra-occipital synchondroses and the occipitomastoid suture. The findings, although based on a limited dataset, showcased specific age-related changes in width and closure percentages, providing valuable insights into growth dynamics within the first 2 years of life. Integration analyses revealed intricate relationships between skull and neck structures, emphasizing coordinated growth at different stages. Specific bone covariation patterns, as found between the first and second cervical vertebrae (C1 and C2), indicated synchronized morphological changes. Our results provide initial data for designing inclusive CCJ geometric models to predict normal and abnormal growth dynamics.

Estimated Fetal Radiation Dose From 18 F-FDG PET/CT During the Second and Third Trimesters of Pregnancy.

Data published in the literature concerning the doses received by fetuses exposed to a 18 F-FDG PET are reassuring but were obtained from small and heterogeneous cohorts, and very few data are available concerning the fetal dose received after exposure to both PET and CT. The present study aimed to estimate the fetal dose received following a PET/CT exposure using methods that include anthropomorphic phantoms of pregnant women applied on a large cohort. This retrospective multicenter study included 18 pregnant patients in the second and third trimesters. For PET exposure, the fetal volume and mean concentration of radioactivity in the fetus were measured by manually drawing regions of interest. Those data, combined with the time-integrated activities of the fetus and the mother's organs, were entered into the OLINDA/EXM software 2.0 to assess the fetal dose due to PET exposure. To estimate the fetal dose received due to CT exposure, 2 softwares were used: CT-Expo (based on geometric phantom models of nonpregnant patients) and VirtualDose (using pregnant patient phantoms). The fetal dose exposure for PET/CT examination in the second trimester ranged from 5.7 to 15.8 mGy using CT-Expo (mean, 11.6 mGy) and from 5.1 to 11.6 mGy using VirtualDose (mean, 8.6 mGy). In the third trimester, it ranged from 7.9 to 16.6 mGy using CT-Expo (mean, 10.7 mGy) and from 6.1 to 10.7 mGy using VirtualDose (mean, 7.6 mGy). The estimated fetal doses were in the same range of those previously published and are well below the threshold for deterministic effects. Pregnancy does not constitute an absolute contraindication for a clinically justified hybrid 18 F-FDG PET/CT.

Numerical simulation of forced ventilation fire suppression for wing leading edge pool fires

In order to meet the requirements of the flammable liquid fire prevention regulations under AC25-863, which stipulates that in the event of ignition, the ignition and its harm of leaked flammable liquids should be minimized, this study investigates the impact on the aircraft structure and the suppression process of wing leading edge pool fires of flammable liquid leakage under forced ventilation fire suppression. Geometric modeling of the wing leading edge in the flammable liquid leakage area is performed, and the burning conditions of the flame under different conditions are simulated. The heat release rate per unit area of the pool fire surface is set to 396.67 kW/m, with ventilation speeds ranging from 0 to 3.1 m/s. Through the analysis of simulation charts and data, it is observed that as the forced ventilation rate increases, the pool fire gradually tends towards a trend of suppression

CMC strength and damage prediction considering thermal mechanic coupling effect

Continuous Fiber Reinforced Ceramic Matrix Composites (CMC) confront significant and undeniable elevated thermal gradient. In this study, a periodic RVE geometrical model was simplified based on the XCT scanning images of 2.5D woven CMC, and the model of the thermal structural strength of 2.5D woven CMC under the influence of fine-scale temperature fields was developed. In conjunction with the temperature distribution of the aero-engine turbine working state, ten sets of temperature field conditions were established and the model of thermal structural strength of 2.5D woven CMC under the influence of fine-scale temperature fields was developed. The effects of the overall temperature level, the form of the temperature difference and the size of the temperature difference on the tensile curve, the failure limits, the form of damage evolution, and the distribution of the failure unit at the time of failure of the 2.5D woven CMC were discussed. It was found that the temperature field induced by temperature difference in the thickness direction has a more significant effect on the tensile mechanical properties of the material, which is a key consideration for the structural design process using this material.

Design and analysis of a solid surface deployable antenna mechanism based on flasher rigid origami

This study proposes a mechanism for solid surface deployable antennas based on flasher rigid origami. The mechanism scheme design and degree-of-freedom analysis were conducted utilizing a Kirigami release constraint strategy. Subsequently, a spatial geometric model of the key points was established incorporating the folding and unfolding characteristics and geometric relationships within the mechanism. Furthermore, a comprehensive 3D model of the antenna was developed by determining the hinge locations, geometric parameters, and driving mechanism, followed by a kinematic simulation analysis. Finally, a prototype was constructed, and a microgravity deployment experiment was conducted to verify the feasibility of the mechanism.

A Geometric Model for Polarization Imaging on Projective Cameras

A Geometric Model for Polarization Imaging on Projective Cameras

Classical limits of Hilbert bimodules as symplectic dual pairs

Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic structures of the relevant types of models. Previously, it has been shown that one can functorially associate certain symplectic dual pairs to Hilbert bimodules through strict deformation quantization. We show that, in the inverse direction, strict deformation quantization also allows one to functorially take the classical limit of a Hilbert bimodule to reconstruct a symplectic dual pair.

Adding mechanobiological cell features to finite element analysis of an immediately loaded dental implant.

Finite element analysis (FEA) has been used to analyze the behavior of dental materials, mainly in implantology. However, FEA is a mechanical analysis and few studies have tried to simulate the biological characteristics of the healing process of loaded implants. This study used the rule of mixtures to simulate the biological healing process of immediate implants in an alveolus socket and bone-implant junction interface through FEA. Three-dimensional geometric models of the structures were obtained, and material properties were derived from the literature. The rule of mixtures was used to simulate the healing periods-immediate and early loading, in which the concentration of each cell type, based on in vivo studies, influenced the final elastic moduli. A 100 N occlusal load was simulated in axial and oblique directions. The models were evaluated for maximum and minimum principal strains, and the bone overload was assessed through Frost's mechanostat. There was a higher strain concentration in the healing regions and cortical bone tissue near the cervical portion. The bone overload was higher in the immediate load condition. The method used in this study may help to simulate the biological healing process and could be useful to relate FEA results to clinical practice.

On tiling spherical triangles into quadratic subpatches

Various interpolation and approximation methods arising in several practical applications in geometric modeling deal, at a particular step, with the problem of computing suitable rational patches (of low degree) on the unit sphere. Therefore, we are concerned with the construction of a system of spherical triangular patches with prescribed vertices that globally meet along common boundaries. In particular, we investigate various possibilities for tiling a given spherical triangular patch into quadratically parametrizable subpatches. We revisit the condition that the existence of a quadratic parameterization of a spherical triangle is equivalent to the sum of the interior angles of the triangle being π, and then circumvent this limitation by studying alternative scenarios and present constructions of spherical macro-elements of the lowest possible degree. Applications of our method include algorithms relying on the construction of (interpolation) surfaces from prescribed rational normal vector fields.