Normal Vector Calculation Research Articles

Numerical simulation of dry laser derusting process based on SPH method

Laser cleaning is an efficient, environmental-friendly, and non-contact surface treatment technology. Laser radiation and heating cause the surface material to heat up and gasify, separating it from the substrate. Traditional mesh-based numerical methods are difficult to effectively simulate the evolution of erosion crater and the splashing phenomenon. In this study, a meshfree method, the smoothed particle hydrodynamics (SPH) method, is used to establish the numerical model of the interaction between the laser beam and the targeted material and to investigate the removal process of the rust layer under different laser operating conditions. In consideration of the coupling effect of laser absorption, heat transfer, and material phase change, the SPH modeling procedure and corresponding numerical scheme for heat transfer and heat-absorption-induced phase change are introduced. Additionally, a surface particle detection algorithm and surface normal vector calculation method are proposed to accurately compute the complex surface geometry of the erosion crater, which realizes the dynamic coupling of laser-energy absorption and laser-beam direction. The established SPH model is then used to simulate the temperature distribution of the rust layer under the action of a laser beam, and the influence of laser energy, beam overlap rate, and beam direction on the removal efficiency is analyzed. This study applies the meshfree SPH method to the study of laser rust removal process, verifies the accuracy of the surface detection algorithm, captures the spatter behavior of material particles after phase change, and reflects the advantages of the meshfree method in solving such problems.

Generation of 3D geotechnical particles using random angular bend algorithm

AbstractGeo‐materials are generally regarded as multi‐phase structural systems, which are composed of particles, pores, and fissures. Generally, the shape and size of particles have considerable influence on the physical and mechanical properties of geo‐materials. Based on the theory of random angular bend (RAB) algorithm, this paper presented a method to finely generate the three‐dimensional (3D) random particle model via the superposition of two‐dimensional (2D) particle profiles, and this proposed method was coded in Python. According to the generation procedure, the relevant point cloud data should be generated, and with the aid of the point cloud normal vector calculation and Poisson reconstruction technique, the required 3D particle profiles can be obtained. Subsequently, three shape descriptors are selected to describe the shape characteristics of generated particles, and accordingly, the quantitative relationships between the shape descriptors and the input controlling parameters are established to accurately control the shape of generated particles. Finally, the generated geo‐material particles are implemented into the particle flow code (PFC3D) to construct the clump library, and an example about a 3D soil–rock mixture model was taken to validate the performance of the proposed method for numerical simulation. The results show that this study provides a useful strategy for the simulation of the geo‐materials based on the RAB theory.

Lambertian Reflection Separation Under High Reflectiveness for Worn Surface Reconstruction With Insufficient Samples

Compared with 2D images, 3D image based worn inspection can provide more profound information regarding the in-suit endoscope examination of mechanical parts. With photometric stereo vision, 3D topography can be reconstructed from 2D images with minimal cost. However, this promising technology is limited by the imprecion in calculating normal vector due to the high reflectiveness of worn surfaces. An innovative model is here developed to separate Lambertian reflection from photometric images. The Lambertian reflection variations are estimated by fusing multiple photometric images, while the constants are extracted from the general plane base of worn surfaces. Considering a small sample set of worn surfaces, hybrid samples, including the real and the simulated images, are adopted for parameter optimization with feature-level alignment. Moreover, a label-free prediction loss function is constructed to constrain the optimization direction via real samples. The constructed model is obtained from training 20,000 simulated samples and 1,000 real samples. The results indicate that high reflectiveness can be addressed by separating the Lambertian reflections. Comparatively, the model can improve the normal vector calculation with lower average error than other existing algorithms.

Robotic direct grinding for unknown workpiece contour based on adaptive constant force control and human–robot collaboration

PurposeIn customized production such as plate workpiece grinding, because of the diversity of the workpiece shapes and the positional/orientational clamping errors, great efforts are taken to repeatedly calibrate and program the robots. To change this situation, the purpose of this study is to propose a method of robotic direct grinding for unknown workpiece contour based on adaptive constant force control and human–robot collaboration.Design/methodology/approachFirst, an adaptive constant force controller based on stiffness estimation is proposed, which can distinguish the contact of the human hand and the unknown workpiece contour. Second, a normal vector search algorithm is developed to calculate the normal vector of the unknown workpiece contour in real-time. Finally, the force and position are controlled in the calculated normal and tangential directions to realize the direct grinding.FindingsThe method considers the disturbance of the tangential grinding force and the friction, so the robot can track and grind the workpiece contour simultaneously. The experiments prove that the method can ensure the force error and the normal vector calculating error within 0.3 N and 4°. This human–robot collaboration pattern improves the convenience of the grinding process.Research limitations/implicationsThe proposed method realizes constant force grinding of unknown workpiece contour in real-time and ensures the grinding consistency. In addition, combined with human–robot collaboration, the method saves the time spent in repeated calibration and programming.Originality/valueCompared with other related research, this method has better accuracy and anti-disturbance capability of force control and normal vector calculation during the actual grinding process.

Scanning Path Planning of the Robot for Breast Ultrasound Examination Based on Binocular Vision and NURBS

Ultrasonic scanning is the most commonly used method for detecting breast cancer. Traditional breast ultrasound mainly relies on manual examination, which requires doctors with rich clinical experience. The scanning path planning of the robot for breast ultrasound examination based on binocular vision and non-uniform rational B-Splines (NURBS) is proposed in this paper to solve the limitations of traditional examination methods. First, breast images are acquired by the binocular camera. The depth information of the images is obtained through stereo matching, and the 3D point cloud reconstruction of the breast model is completed. Second, the spatial index algorithm based on the K-dimension tree (Kd-tree) and uniform sampling method are selected to denoise and down-sample the point cloud model to complete the preliminary optimization of the model. The point cloud information for the scanning path is extracted according to the method of point cloud extraction and the principle of normal vector calculation. Then, the interpolation optimization of the scanning path based on the NURBS curve is completed. The optimized scanning path is transformed into the robot motion path. Finally, the robot motion is simulated and analyzed, and the experimental results show that the rationality of robot operation and the smoothness of robot motion meet the requirements of path planning defined in this paper. The error analysis experiment shows that the path planned by this method can ensure the efficiency and accuracy of ultrasound examination.

Differential-geometry-based surface normal vector calculation method using a time-of-flight camera.

A surface normal vector of an object is often needed to detect an orientation of the object. A simple calculation method of the surface normal vector by means of a time-of-flight (ToF) camera is thus proposed here, using a coordinate transformation of three-dimensional irregular points acquired by the ToF camera to regular grid representation. Each point of the regular grid representation has a depth (distance from the camera) defined on the regular grid. The surface normal vector on the regular grid can be derived based on differential geometry with partial derivatives of the depth, and can then be in the form of the discretized Fourier transformation to which the fast Fourier transformation algorithm is applicable. The method of the surface normal vector calculation is thus theoretically derived. Validation of the method is also experimentally performed.

Automatic identification and characterization of discontinuities in rock masses from 3D point clouds

The routine application of remote surveying techniques which can quickly acquire 3D digital data with high resolution, in particular digital photogrammetry, light detection and ranging (LiDAR) and unmanned aerial vehicle (UAV) for rock mass characterization has rapidly grown over the past decade. In this paper, a new method for automatic identification and interpretation of rock mass discontinuities, clustering of discontinuity sets and characterization of discontinuity orientation, persistence and spacing using 3D point clouds, is presented. The proposed method is based on a four-stage procedure consisting of: (1) normal vector calculation using the iterative reweighted plane fitting (IRPF) method, (2) discontinuity sets clustering by fast search and find of density peaks (CFSFDP) algorithm, and Fisher’s K value iterative calculation to eliminate noise points, (3) discontinuity segmentation using density-ratio based method, and discontinuity plane fitting using the random sample consensus (RANSAC) algorithm, (4) persistence and spacing calculation using the theory of analytic geometry. The method is applied to two case studies (i.e. rock slopes) and compared with the results from previous studies and from manual survey. It is concluded that the proposed method is reliable and yields a great accuracy for automatic identification of discontinuities in rock masses.

Improvement of Simultaneous 5-Axis Controlled Machining Accuracy by CL-Data Modification

As the motion accuracy of 5-axis machining centers directly influences the geometrical shape accuracy of the machined workpieces, accuracy enhancement of the 5-axis machining centers is strongly needed. To improve the shape accuracy during the machining by a 5-axis machine tool, a method that modifies the CL-data based on the motion trajectory errors normal to the machined surface at each command point has been proposed. In this study, the proposed method is applied to simultaneous 5-axis controlled machining to improve motion accuracy. A normal vector calculation method for the simultaneous 5-axis controlled motion is newly proposed, and the compensation method is applied to turbine blade machining by 5-axis controlled motion. Measurement tests of the cutting motion for blade shape machining by a ball-end mill were carried out with a different control mode of NC. The CL-data for the machining tool path was also modified based on the calculated trajectory of the tool center point. Experimental results reveal that the feed speed and machining accuracy significantly depend on the control mode of NC, and that the shape accuracy can be improved by applying the proposed compensation method without any decrease in motion speed.

A study on the control strategies of a series–parallel hybrid platform for blade polishing

Blades are key components of turbines, aircraft engines, and high-speed ship propulsion systems, such that their manufacturing quality has a considerable influence on a machine’s performance. This paper presented a series–parallel hybrid platform that employed abrasive belt as the tool and integrated the measuring equipment to achieve in-situ measurement for blade polishing. It studied the control strategies for solving the processing parameters aiming to the characteristics of the alternate measurement and processing in the process of polishing. According to singularity analysis of the parallel mechanism, the platform structure parameters were appropriately optimized to avoid the singular position. Then, based on the in-situ measuring data of the blade contour, a method was proposed for calculating the normal vector of machining points, while the platform kinematics were studied, and the total machining allowance was determined by comparing the actual and ideal contour profiles of the blade. Finally, a testing experiment was performed to validate the proposed method of the normal vector calculation, and blade polishing experiment was conducted on the developed platform, which proved the effectiveness and feasibility of the platform.

Neural networks for determining the vector normal to the surface in CFD, LBM and CA applications

PurposeThe well-known discrete methods of computational fluid dynamics (CFD), lattice Boltzmann method (LBM), cellular automata (CA), volume-of-fluid (VoF) and others rely on several parameters describing the boundary or the surface. Some of them are vector normal to the surface, coordinates of the point on the surface and the curvature. They are necessary for the reconstruction of the real surface (boundary) based on the values of the volume fractions of several cells. However, the simple methods commonly used for calculations of the vector normal to the surface are of unsatisfactory accuracy. In light of this, the purpose of this paper is to demonstrate a more accurate method for determining the vector normal to the surface.Design/methodology/approachBased on the thesis that information about the volume fractions of the 3 × 3 cell block should be enough for normal vector determination, a neural network (NN) was proposed for use in the paper. The normal vector and the volume fractions of the cells themselves can be defined on the basis of such variables as the location of the center and the radius of the circumference. Therefore, the NN is proposed to solve the inverse problem – to determine the normal vector based on known values of volume fractions. Volume fractions are inputs of NNs, while the normal vector is their output. Over a thousand variants of the surface location, orientations of the normal vector and curvatures were prepared for volume fraction calculations; their results were used for training, validating and testing the NNs.FindingsThe simplest NN with one neuron in the hidden layer shows better results than other commonly used methods, and an NN with four neurons produces results with errors below 1° relative to the orientation of the normal vector; for several cases, it proven to be more accurate by an order of magnitude.Practical implicationsThe method can be used in the CFD, LBM, CA, VoF and other discrete computational methods. The more precise normal vector allows for a more accurate determination of the points on the surface and curvature in further calculations via the surface or interface tracking method. The paper contains the data for the practical application of developed NNs. The method is limited to regular square or cuboid lattices.Originality valueThe paper presents an original implementation of NNs for normal vector calculation connected with CFD, LBM and other application for fluid flow with free surface or phase transformation.

Rapid measurement of the three-dimensional distribution of leaf orientation and the leaf angle probability density function using terrestrial LiDAR scanning

At the plant or stand level, leaf orientation is often highly anisotropic and heterogeneous, yet most analyses neglect such complexity. In many cases, this is due to the difficulty in measuring the spatial variation of the leaf angle distribution function. There is a critical need for a technique that can rapidly measure the leaf angle distribution function at any point in space and time. A new method was developed and tested that uses terrestrial LiDAR scanning data to rapidly measure the three-dimensional distribution of leaf orientation for an arbitrary volume of leaves. The method triangulates laser-leaf intersection points recorded by the LiDAR scan, which allows for easy calculation of normal vectors. As a byproduct, the triangulation also yields continuous surfaces that reconstruct individual leaves. In order to produce a probability density function for leaf orientation from triangle normal vectors, it is critical that the proper weighting be applied to each triangle. Otherwise, results will heavily bias toward normal vectors pointed toward the the LiDAR scanner. The method was validated using artificially generated LiDAR data where the exact leaf angle distributions were known, and in the field for an isolated tree and a grapevine canopy by comparing LiDAR-generated distribution functions to manual measurements. The artificial test cases demonstrated the consistency of the method, and quantitatively showed that errors in the predicted leaf angle distribution functions decreased as scan resolution was increased or as the density of leaves was increased. The isolated tree field validation showed qualitatively similar trends between manual and LiDAR measurements of distribution functions. Manual measurements of leaf orientation in the vineyard were shown to have large errors due to high leaf curvature, which illustrated the benefits of the more detailed LiDAR measurement method.

A Surface Normal On-Machine Measuring Method Using Eddy-Current (EC) Sensor Array

Normal vector measurements of the machining point and attitude adjustments of the end effector are key aspects to meet the technological requirements of hole verticality in auto-drilling and the residual wall thickness in mirror milling. In this paper, a surface normal on-machine measuring method using an EC sensor array is proposed. The influences of the object surface inclination and the sensor array arrangement on the performance of EC displacement sensors were investigated, and the sensor measuring errors from coupling interference were effectively eliminated. Moreover, a practical calibration algorithm was established in which the positions of the EC sensors in a normal vector calculation model were accurately corrected. The feasibility of the measuring method was validated through a calibration experiment, as well as a measurement experiment based on the calibration results. The accuracy of a normal vector measurement is improved when applying the accuracy compensation and position calibration algorithm of an EC array to engineering practices.

Modelling the Flow in a Transonic Diffuser with One Reynolds-Stress and Two Eddy-Viscosity Models

Turbulence modeling combined with the mass averaged Navier-Stokes equations and detailed comparisons with experimental data are presented for a transonic flow in a converging diverging diffuser for two different inlet Mach numbers. Three low-Reynolds number turbulence models, which do not use the concept of the wall distance and wall normal vector calculation are adopted: a linear eddy-viscosity model, a cubic non-linear eddy-viscosity model and a non-linear Reynolds-stress model. The compressibility effects due to the mean density variations are incorporated in a subsonic pressure-based flow solver through minor modifications to the pressure velocity-coupling algorithm and by introducing the dilatation-dissipation of turbulence to the equations of the turbulent models. Grid dependency studies were conducted and detailed velocity and pressure coefficient distributions are presented in comparison with available experimental data providing also information for the boundary layer development on the diffuser walls in the region downstream the shock wave. The final results are very promising concerning the capability of the turbulence models to capture the compressibility effects in transonic flows when they are incorporated with appropriate modifications in a pressure-based flow solver.

Calculation of the interface curvature and normal vector with the level-set method

This article addresses the use of the level-set method for capturing the interface between two fluids. One of the advantages of the level-set method is that the curvature and the normal vector of the interface can be readily calculated from the level-set function. However, in cases where the level-set method is used to capture topological changes, the standard discretization techniques for the curvature and the normal vector do not work properly. This is because they are affected by the discontinuities of the signed-distance function half-way between two interfaces. This article addresses the calculation of normal vectors and curvatures with the level-set method for such cases. It presents a discretization scheme based on the geometry-aware curvature discretization by Macklin and Lowengrub [1]. As the present scheme is independent of the ghost-fluid method, it becomes more generally applicable, and it can be implemented into an existing level-set code more easily than Macklin and Lowengrub’s scheme [1]. The present scheme is compared with the second-order central-difference scheme and with Macklin and Lowengrub’s scheme [1], first for a case with no flow, then for a case where two drops collide in a 2D shear flow, and finally for a case where two drops collide in an axisymmetric flow. In the latter two cases, the Navier–Stokes equations for incompressible two-phase flow are solved. The article also gives a comparison of the calculation of normal vectors with the direction difference scheme presented by Macklin and Lowengrub in [2] and with the present discretization scheme. The results show that the present discretization scheme yields more robust calculations of the curvature than the second-order central difference scheme in areas where topological changes are imminent. The present scheme compares well to Macklin and Lowengrub’s method [1]. The results also demonstrate that the direction difference scheme [2] is not always sufficient to accurately calculate the normal vectors.

Accurate 3D comparison of complex topography with terrestrial laser scanner: Application to the Rangitikei canyon (N-Z)

Surveying techniques such as terrestrial laser scanner have recently been used to measure surface changes via 3D point cloud (PC) comparison. Two types of approaches have been pursued: 3D tracking of homologous parts of the surface to compute a displacement field, and distance calculation between two point clouds when homologous parts cannot be defined. This study deals with the second approach, typical of natural surfaces altered by erosion, sedimentation or vegetation between surveys. Current comparison methods are based on a closest point distance or require at least one of the PC to be meshed with severe limitations when surfaces present roughness elements at all scales. To solve these issues, we introduce a new algorithm performing a direct comparison of point clouds in 3D. The method has two steps: (1) surface normal estimation and orientation in 3D at a scale consistent with the local surface roughness; (2) measurement of the mean surface change along the normal direction with explicit calculation of a local confidence interval. Comparison with existing methods demonstrates the higher accuracy of our approach, as well as an easier workflow due to the absence of surface meshing or Digital Elevation Model (DEM) generation. Application of the method in a rapidly eroding, meandering bedrock river (Rangitikei River canyon) illustrates its ability to handle 3D differences in complex situations (flat and vertical surfaces on the same scene), to reduce uncertainty related to point cloud roughness by local averaging and to generate 3D maps of uncertainty levels. We also demonstrate that for high precision survey scanners, the total error budget on change detection is dominated by the point clouds registration error and the surface roughness. Combined with mm-range local georeferencing of the point clouds, levels of detection down to 6mm (defined at 95% confidence) can be routinely attained in situ over ranges of 50m. We provide evidence for the self-affine behaviour of different surfaces. We show how this impacts the calculation of normal vectors and demonstrate the scaling behaviour of the level of change detection. The algorithm has been implemented in a freely available open source software package. It operates in complex 3D cases and can also be used as a simpler and more robust alternative to DEM differencing for the 2D cases.

Research on Key Factors in Shader Programming of Dynamic Water Surface

Research on real time dynamic water surface is a hotspot in the study of virtual reality with very broad application prospect. With the rapid development of calculating ability of GPU (Graphics Processing Unit) and the development of HLSL (High-Level Shader Language), the tasks such as vertex shader ,pixel shader, calculation of normal vector, dynamic texture mapping and calculation of water reflections and refractions can be done by GPU. In our research we studied the key factors affecting the effect of dynamic water surface and indicated that the writer presents some opinions which can generate more accurate reflections and refractions of water through adjusting light intensity and colorimchy by lighting and perturbing 2D texture mapping with normal mapping. A shader program in Virtools has been written and applied in virtual reality project. In the actual operation the effect is real and the rendering speed has greatly increased.

A Traditional Quadrilateral NURBS Surfaces Generation Method using MATLAB

NURBS surface is defined as a bi-parameter condition, so you can construct a NURBS surface may be calculated surface points the two aspects of some parameters of the algorithm. Build the way surface grid method has higher accuracy than. Also, when the surface of the normal vector calculation pointed out that the surface point can be got. It is to alleviate the surface of the isometric construction. The results show that NURBS surface generation method is effective and strategy, and by adjusting the produce come quadrilateral surface is feasible to control some of the areas.

Die surface design optimization accommodating springback assisted by an automatic surface generator

One of manufacturing problems in sheet metal forming is springback. This elastic recovery occurs when unloading the formed part off the tooling dies, resulting in shape inaccuracies. Optimizing the geometry surfaces of the tools can be used to accommodate the springback, so that after the unloading process, the formed part meets the target shape. This paper presents an optimization method to modify the geometry surfaces of the tooling dies based on springforward simulations assisted by an automatic surface generator during the process. In the optimization cycle, new sets of upper and lower die surfaces are required. An automatic surface generation method based on normal vector has been developed to create new finite elements of the new surfaces. The normal vector calculation of the deformed elements after springback generates new upper and lower surfaces with uniform gaps. The new generated elements can be used directly during the optimization cycle. For testing and verification purposes, the method is applied in various complicated surfaces. The test results show that this method is able to generate a uniform gap in a corner with 90 degrees angle, without discontinuity in any elements. The application in optimization to minimize the springback is conducted in hat- shape problem. The result shows that the automatic mesh generator works effectively during the optimization cycle. The distortion error after springback can be significantly minimized.

Transformation and Normal Vector Calculation of Parametrically Defined Surfaces Based on Dual Vectors and Screw Theory: Application to Phong's Shading Model

Abstract This paper presents a new approach for the transformation and normal vector calculation algorithms of parametrically defined surfaces via dual vectors and line transformations. The surface is defined via dual points, the transformation is performed by rotations and translations based on screw theory while normal vector calculation is utilized for shading based on Phong's illumination model. The main benefit of this approach lies into the compactness of the surface's representation since geometrical characteristics, such as tangent vectors, that are necessary for shading algorithms, are included within its definition. An extensive comparison is performed between the proposed approach and the traditional homogeneous model, presenting the merits of our approach. Analytical and experimental determination of the computational cost via computer implementation of 3D surface transformation and shading is presented. Point‐based methods for the representation, transformation and shading of parametrically defined surfaces are compared to the introduced line‐based methods (dual quaternions and dual orthogonal matrices). It is shown that the simplified rendering procedure of 3D objects, is considerably faster using screw theory over the traditional point‐based structures.

An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids

We present an adaptive coupled level-set/volume-of-fluid (ACLSVOF) method for interfacial flow simulations on unstructured triangular grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a discontinuous Galerkin finite element method. The volume fraction advection is performed using a Lagrangian–Eulerian method. The interface is reconstructed based on both the level set and the volume fraction information. In particular, the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction. Different from previous works, we have developed an analytic method for finding the line constant on triangular grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. The level set function is finally reinitialized to the signed distance to the reconstructed interface. Since the level set function is continuous, the normal vector calculation is easy and accurate compared to a classic volume-of-fluid method, while tracking the volume fraction is essential for enforcing mass conservation. The method is also coupled to a finite element based Stokes flow solver. The code validation shows that our method is second order and mass is conserved very accurately. In addition, owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately.