Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.

Multi-objective strategy to optimize dithering technique for high-quality three-dimensional shape measurement

Dithering optimization techniques can be divided into the phase-optimized technique and the intensity-optimized technique. The problem with the former is the poor sensitivity to various defocusing amounts, and the problem with the latter is that it cannot enhance phase quality directly nor efficiently. In this paper, we present a multi-objective optimization framework for three-dimensional(3D) measurement by utilizing binary defocusing technique. Moreover, a binary patch optimization technique is used to solve the time-consuming issue of genetic algorithm. It is demonstrated that the presented technique consistently obtains significant phase performance improvement under various defocusing amounts.

Three-Dimensional Measurement and Reconstruction of Fabric Drape Shape

This paper introduces a new method of measuring the three-dimensional drape shape of fabrics with structural light. First, we apply parallel annular structural light to form light and shade alternating contour stripes on the surface of fabrics. We then collect the images of contour stripes using Charge Coupled Device (CCD). Subsequently, we process the images to identify the contour stripes and edges of fabrics, and obtain the fabric contour lines of curved surfaces. Finally, we apply three-dimensional curved surface modeling method based on a network of polar coordinates, and reconstruct the three-dimensional drape shape of fabrics. Experiments show that our method is effective in testing and reconstructing three-dimensional drape shape of fabrics.

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.

Three-dimensional constitutive model for magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy single crystals

Existing experimental results have shown that four types of physical mechanisms, namely, martensite transformation, martensite reorientation, magnetic domain wall motion and magnetization vector rotation, can be activated during the magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy (FSMA) single crystals. In this work, based on irreversible thermodynamics, a three-dimensional (3D) single crystal constitutive model is constructed by considering the aforementioned four mechanisms simultaneously. Three types of internal variables, i.e., the volume fraction of each martensite variant, the volume fraction of magnetic domain in each variant and the deviation angle between the magnetization vector, and easy axis are introduced to characterize the magneto-mechanical state of the single crystals. The thermodynamic driving force of each mechanism and the thermodynamic constraints on the constitutive model are obtained from Clausius's dissipative inequality and constructed Gibbs free energy. Then, thermodynamically consistent kinetic equations for the four mechanisms are proposed, respectively. Finally, the ability of the proposed model to describe the magneto-mechanical deformation of NiMnGa FSMA single crystals is verified by comparing the predictions with corresponding experimental results. It is shown that the proposed model can quantitatively capture the main experimental phenomena. Further, the proposed model is used to predict the deformations of the single crystals under the non-proportional mechanical loading conditions.

Balanced Functional Maps for Three-Dimensional Non-Rigid Shape Registration

Three-dimensional(3D)shape registration is a challenging problem,especially for shapes under non-rigid transformations.In this paper,a 3D non-rigid shape registration method is proposed,called balanced functional maps(BFM).The BFM algorithm generalizes the point-based correspondence to functions.By choosing the Laplace-Beltrami eigenfunctions as the function basis,the transformations between shapes can be represented by the functional map(FM)matrix.In addition,many constraints on shape registration,such as the feature descriptor,keypoint,and salient region correspondence,can be formulated linearly using the matrix.By bi-directionally searching for the nearest neighbors of points’indicator functions in the function space,the point-based correspondence can be derived from FMs.We conducted several experiments on the Topology and Orchestration Specification for Cloud Applications(TOSCA)dataset and the Shape Completion and Animation of People(SCAPE)dataset.Experimental results show that the proposed BFM algorithm is effective and has superior performance than the state-of-the-art methods on both datasets.

Interactions of penny-shaped cracks in three-dimensional solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Three-dimensional spatial multi-point uniform light focusing through scattering media based on feedback wavefront shaping

We use feedback wavefront shaping technology to realize the multi-point uniform light focusing in three-dimensional(3D) space through scattering media only by loading the optimal mask once.General 3D spatial focusing needs to load the optimal mask multiple times to realize the spatial movement of the focal point and the uniformity of multi-point focusing cannot be guaranteed.First,we investigate the effects of speckle axial correlation and different axial distances on 3D spatial multi-point uniform focusing and propose possible solutions.Then we use our developed non-dominated sorting genetic algorithm suitable for 3D spatial focusing(S-NSGA) to verify the experiment of multi-point focusing in 3D space.This research is expected to have potential applications in the fields of optical manipulation and optogenetics.

Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point

A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward.

Modified shape-based method for three-dimensional trajectory design

Although the shape-based method has been proven to be useful for low-thrust trajectory design,and be capable to provide near-optimal solution for a more accurate trajectory optimization method,it is slightly non-effective when used in some 3D cases.In this paper,a modified 3D shape-based method is proposed for earth trajectory design.In this approach,in consideration of the sinusoidal periodic variation in z direction of actual trajectory,a new exponential sinusoid model is chosen for the out-of-plane motion,with four coefficients such that four scalar out-of-plane boundary conditions can be satisfied.After deriving the 3D shape-based procedure,low-thrust trajectory design example with modest inclination change is given.The results demonstrate that this modified approach is feasible for the transfer trajectory design,and comparing to the former shape-based method,the z direction solution is more coincident with the actual situation,furthermore,the solution may be used for further mission planning,trajectory evaluation and optimization.

3shape Trios 3口内扫描和传统硅橡胶在牙体缺损修复中的失败原因分析

目的分析并比较3shape Trios 3口内扫描和传统硅橡胶在牙体缺损修复中的失败原因,为临床取模以及口内扫描仪性能改善提供参考依据。方法回顾性分析2021年1月至2023年10月实施口腔固定修复治疗并返工的200例患者为研究对象,以取模方式将其分为口扫组(n=97)和硅橡胶组(n=103)。口扫组给予3shape Trios 3口内扫描,硅橡胶组给予传统硅橡胶。比较两组在牙体缺损修复中的失败原因。结果两组的牙体缺损修复失败分布情况比较,差异具有统计学意义(P<0.05);口扫组中,龈下缺损修复失败占比高于龈上(P<0.05)。两组的龈下缺损修复失败原因比较,差异具有统计学意义(P<0.05)。结论相较于传统硅橡胶,3shape Trios 3口内扫描在龈上缺损修复中更有优势,但在龈下缺损修复中,硅橡胶应用效果更佳。

Optimized dithering technique in frequency domain for high-quality three-dimensional depth data acquisition

On the basis of the objective functions,dithering optimization techniques can be divided into the intensity-based optimization technique and the phase-based optimization technique.However,both types of techniques are spatial-domain optimization techniques,while their measurement performances are essentially determined by the harmonic components in the frequency domain.In this paper,a novel genetic optimization technique in the frequency domain is proposed for highquality fringe generation.In addition,to handle the time-consuming difficulty of genetic algorithm(GA),we first optimize a binary patch,then join the optimal binary patches together according to periodicity and symmetry so as to generate a full-size pattern.It is verified that the proposed technique can significantly enhance the measured performance and ensure the robustness to various amounts of defocusing.

Three-dimensional Computational Fluid Dynamics Modeling of Two-phase Flow in a Structured Packing Column

Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

Three-Dimensional and Cross-sectional Characteristics of Normal Grain Growth Based on Monte Carlo Simulation

An appropriate Monte Carlo method was developed to simulate the three-dimensional normal grain growth more completely. Comparative investigation on the three-dimensional and the cross-sectional characteristics of normal grain growth was done. It was found that the time exponent of grain growth determined from cross-section exhibits the same rule of increasing slowly with time and approaching the theoretical value n = 0.5 of steadygrain growth as the three-dimensional (3-D) system. From change of the number of grains per unit area with timemeasured in cross-section, the state of 3-D normal grain growth may be predicted. The gtain size distribution incross-section is different from that in 3-D system and can not express the evolution characteristic of the 3-D distribution. Furthermore, there exists statistical connection between the topological parameters in cross-section and thosein three-dimensions.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

The three-dimension model for the rock-breaking mechanism of disc cutter andanalysis of rock-breaking forces

To study the rock deformation with three- dimensional model under rolling forces of disc cutter, by car- rying out the circular-grooving test with disc cutter rolling around on the rock, the rock mechanical behavior under rolling disc cutter is studied, the mechanical model of disc cutter rolling around the groove is established, and the the- ory of single-point and double-angle variables is proposed. Based on this theory, the physics equations and geometric equations of rock mechanical behavior under disc cutters of tunnel boring machine （TBM） are studied, and then the bal- ance equations of interactive forces between disc cutter and rock are established. Accordingly, formulas about normal force, rolling force and side force of a disc cutter are de- rived, and their validity is studied by tests. Therefore, a new method and theory is proposed to study rock- breaking mech- anism of disc cutters.

Dynamic Characteristic Mechanism of Atrial Septal Defect Using Real-Time Three-Dimensional Echocardiography and Evaluation of Right Ventricular Functions

The dynamic characteristics of the area of the atrial septal defect（ASD） were evaluated using the technique of real-time three-dimensional echocardiography（RT 3DE）, the potential factors responsible for the dynamic characteristics of the area of ASD were observed, and the overall and local volume and functions of the patients with ASD were measured. RT 3DE was performed on the 27 normal controls and 28 patients with ASD. Based on the three-dimensional data workstations, the area of ASD was measured at P wave vertex, R wave vertex, T wave starting point, and T wave terminal point and in the T-P section. The right atrial volume in the same time phase of the cardiac cycle and the motion displacement distance of the tricuspid annulus in the corresponding period were measured. The measured value of the area of ASD was analyzed. The changes in the right atrial volume and the motion displacement distance of the tricuspid annulus in the normal control group and the ASD group were compared. The right ventricular ejection fractions in the normal control group and the ASD group were compared using the RT 3DE long-axis eight-plane（LA 8-plane） method. Real-time three-dimensional volume imaging was performed in the normal control group and ASD group（n=30）. The right ventricular inflow tract, outflow tract, cardiac apex muscular trabecula dilatation, end-systolic volume, overall dilatation, end-systolic volume, and appropriate local and overall ejection fractions in both two groups were measured with the four-dimensional right ventricular quantitative analysis method（4D RVQ） and compared. The overall right ventricular volume and the ejection fraction measured by the LA 8-plane method and 4D RVQ were subjected to a related analysis. Dynamic changes occurred to the area of ASD in the cardiac cycle. The rules for dynamic changes in the area of ASD and the rules for changes in the right atrial volume in the cardiac cycle were consistent. The maximum value of the changes in the right atrial volume occurred in the end-systolic period when the peak of the curve appeared. The minimum value of the changes occurred in the end-systolic period and was located at the lowest point of the volume variation curve. The area variation curve for ASD and the motion variation curve for the tricuspid annulus in the cardiac cycle were the same. The displacement of the tricuspid annulus exhibited directionality. The measured values of the area of ASD at P wave vertex, R wave vertex, T wave starting point, T wave terminal point and in the T-P section were properly correlated with the right atrial volume（P〈0.001）. The area of ASD and the motion displacement distance of the tricuspid annulus were negatively correlated（P〈0.05）. The right atrial volumes in the ASD group in the cardiac cycle in various time phases increased significantly as compared with those in the normal control group（P=0.0001）. The motion displacement distance of the tricuspid annulus decreased significantly in the ASD group as compared with that in the normal control group（P=0.043）. The right ventricular ejection fraction in the ASD group was lower than that in the normal control group（P=0.032）. The ejection fraction of the cardiac apex trabecula of the ASD patients was significantly lower than the ejection fractions of the right ventricular outflow tract and inflow tract and overall ejection fraction. The difference was statistically significant（P=0.005）. The right ventricular local and overall dilatation and end-systolic volumes in the ASD group increased significantly as compared with those in the normal control group（P=0.031）. The a RVEF and the overall ejection fraction decreased in the ASD group as compared with those in the normal control group（P=0.0005）. The dynamic changes in the area of ASD and the motion curves for the right atrial volume and tricuspid annulus have the same dynamic characteristics. RT 3DE can be used to accurately evaluate the local and overall volume and functions of the right ventricle. The local and overall volume loads of the right ventricle in the ASD patients increase significantly as compared with those of the normal people. The right ventricular cardiac apex and the overall systolic function decrease.

Clinical Value of Stereoscopic Three-dimensional Echocardiography in Assessment of Atrial Septal Defects: Feasibility and Efficiency

Stereoscopic three-dimensional echocardiography（S-3DE） is a novel displaying technol-ogy based on real-time 3-dimensional echocardiography （RT-3DE）. Our study was to evaluate the feasibility and efficiency of S-3DE in the diagnosis of atrial septal defect （ASD） and its use in the guidance for transcatheter ASD occlusion. Twelve patients with secundum ASD underwent RT-3DE examination and 9 of the 12 were subjected to transcatheter closure of ASD. Stereoscopic vision was generated with a high-performance volume renderer with red-green stereoscopic glasses. S-3DE was compared with standard RT-3D display for the assessment of the shape, size, and the surrounding tis-sues of ASD and for the guidance of ASD occlusion. The appearance rate of coronary sinus and the mean formation time of the IVC, SVC were compared. Our results showed that S-3DE could measure the diameter of ASD accurately and there was no significant difference in the measurements between S-3DE and standard 3D display （2.89±0.73 cm vs 2.85±0.72 cm, P〉0.05; r=0.96, P〈0.05）. The appearance of coronary sinus for S-3DE was higher as compared with the standard 3D display （93.3% vs 100%）. The mean time of the IVC, SVC for S-3DE monitor was slightly shorter than that of the standard 3D display （11.0±3.8 s vs 10.3±3.6 s, P〉0.05）. The mean completion time of interven-tional procedure was shortened with S-3DE display as compared with standard 3D display （17.3±3.1 min vs 23.0±3.9 min, P〈0.05）. Stereoscopic three-dimensional echocardiography could improve the visualization of three-dimensional echocardiography, facilitate the identification of the adjacent structures, decrease the time required for interventional manipulation. It may be a feasible, safe, and efficient tool for guiding transcatheter septal occlusion or the surgical interventions.

Inversion of source mechanism of 1989 Loma Prieta earthquake by three-dimensional FEM Green's function

Based on three-dimensional joint finite element, this paper discusses the theory and methodology about inversionof geodetic data. The FEM and inversion formula is given in detail; also a related code is developed. By use of theGreen's function about 3-D FEM, we invert geodetic measurementS of coseismic deformation of the 1989 Ms=7. 1Loma Prieta earthquake to datermine itS source mechanism. The result indicates that the slip on the fault plane isvery heterogeneous. The maximum slip and shear stress are located about 10 kin to northwest of the eathquakesource, the stress drop is about more than 1 MPa.