Direction Of Normal Vector Research Articles

FACE: Feature-preserving CAD model surface reconstruction

Feature lines play a pivotal role in the reconstruction of CAD models. Currently, there is a lack of a robust explicit reconstruction algorithm capable of achieving sharp feature reconstruction in point clouds with noise and non-uniformity. In this paper, we propose a feature-preserving CAD model surface reconstruction algorithm, named FACE. The algorithm initiates with preprocessing the point cloud through denoising and resampling steps, resulting in a high-quality point cloud that is devoid of noise and uniformly distributed. Then, it employs discrete optimal transport to detect feature regions and subsequently generates dense points along potential feature lines to enhance features. Finally, the advancing-front surface reconstruction method, based on normal vector directions, is applied to reconstruct the enhanced point cloud. Extensive experiments demonstrate that, for contaminated point clouds, this algorithm excels not only in reconstructing straight edges and corner points but also in handling curved edges and surfaces, surpassing existing methods.

Analysis of the Evolution of Calligraphy Creation Style Combined with Numerical Analysis Methods

Abstract The combination of computer technology and calligraphy art is better applied to people’s daily lives while promoting the popularization and development of calligraphy art. In this paper, the mechanical model of the brush tip is constructed on the basis of the spring-vibrator model according to the relationship between the force and the deformation of the brush tip in the real calligraphy creation and drawing. The projection plane is constructed by the method of mapping, and the two-dimensional brush strokes generated on the projection plane are mapped onto the surface of the three-dimensional model in real-time, and the method of minimally enclosing the sphere of the brush tip is used to solve the normal vector direction of the plane. Finally, the orthographic projection of the contact area between the brush and the plane is taken as the brush stroke, and the real brush stroke is simplified to be fitted by two symmetric B-spline curves. The results show that the maximum value of the relevant parameter of the sine equation in the four simulations of the regular script style is 1.5075, which has the best-fitting effect. After 300 iterations of calligraphic creation style evolution, the style recognizability reaches 24.8. The method feeds back the process of recreating calligraphic style and increases the interactivity of calligraphic creation.

The impact of stress on magneto-impedance and achievement of high sensitivity in Co-based ribbons with three-peak behavior

In this paper, the Stress-Magneto-Impedance (S-MI) effect is investigated in Co-based ribbons by varying tensile stress and frequency. The MI changes are obtained as a function of applied stress and frequency ranged between 3.5 and 35 MPa and 1–12 MHz, respectively. Results are interpreted in terms of MI curve changes, modifying the applied mechanical stresses and measurement direction relative to the earth's magnetic field. A correlation between MI response, magnetic properties and tensile stress of the ribbons is illustrated, also the influences of processing and measurement parameters on the corresponding MI response were analyzed. A three-peak behavior is observed, indicating significant sensitivity which can be controlled by the earth's magnetic field to reform the measurement system. Vibrating sample magnetometer analysis results illustrate the magnetic behavior of the ribbon samples for longitudinal and transverse directions of magnetic field and out of plane. Due to the different responses for surface normal vector directions, this work provides useful insights into the fabrication of highly sensitive sensors.

NORMAL CLASSIFICATION OF 3D OCCUPANCY GRIDS FOR VOXEL-BASED INDOOR RECONSTRUCTION FROM POINT CLOUDS

Abstract. In this paper, we present an automated method for classification of binary voxel occupancy grids of discretized indoor mapping data such as point clouds or triangle meshes according to normal vector directions. Filled voxels get assigned normal class labels distinguishing between horizontal and vertical building structures. The horizontal building structures are further differentiated into those with normal directions pointing upwards or downwards with respect to the building interior. The derived normal grids can be deployed in the context of an existing voxel-based indoor reconstruction pipeline, which so far was only applicable to indoor mapping triangle meshes that already contain normal vectors consistently oriented with respect to the building interior. By means of quantitative evaluation against reference data, we demonstrate the performance of the proposed method and its applicability in the context of voxel-based indoor reconstruction from indoor mapping point clouds without normal vectors. The code of our implementation is made available to the public at https://github.com/huepat/voxir.

Curvature Singularity of Space Curves and Its Relationship to Computational Mechanics

Abstract Curve geometry plays a fundamental role in many aspects of analytical and computational mechanics, particularly in developing new data-driven science (DDS) approaches. Furthermore, curvature and torsion of space curves serve as deformation measures that need to be properly interpreted, shedding light on the significance of relationship between differential-geometry curve framing methods and computational-mechanics motion description. Alternate space-curve framing methods were proposed to address the existence of Frenet frame at isolated zero-curvature points. In this paper, both mechanics and differential-geometry approaches are used to establish Frenet-frame continuity and the existence of Serret-Frenet equations at curvature-vanishing points for curves with arbitrary parameterization. Frenet–Euler angles, referred to for brevity as Frenet angles, are used to define curve geometry, with particular attention given to the definition of Frenet bank angle used to prove the existence of curve normal and binormal vectors at curvature-vanishing points. Solving curvature-singularity problem and using mechanics description based on Frenet angles contributes to successful development and computer implementation of new DDS approaches based on analysis of recorded motion trajectories (RMT). Centrifugal-inertia force is always in direction of curve normal vector, and in most applications, this force is continuous and approaches zero value as curve curvature approaches zero. Discontinuity in definition of Frenet frame can negatively impact the quality of numerical results that define RMT curves. The study also demonstrates that Frenet-frame curvature singularity can be solved without need for integrating curve torsion, which is not, in general, an exact differential.

Improving the staircase approximation for wettability implementation of phase-field model: Part 1 – Static contact angle

In this study, two schemes to treat fluid-solid interaction on complex boundaries are proposed and solved in the framework of lattice Boltzmann method. The schemes are applied on the phase-field-based wettability implementation methods for binary and ternary fluids to simulate static contact angle on a circular surface generated by the staircase approximation. For the binary system, surface-energy and geometric wetting conditions are adopted, while for the ternary system, surface-energy model with two discretization schemes resulting in explicit and implicit wetting conditions are developed and examined. It is proven that the implicit wetting condition approximating the value of order parameters on the boundary node, as the average of their value between the neighboring fluid node and solid node, enhances the accuracy of predicted contact angles. For modeling of contact angle on the circular surface and identifying the direction of normal vectors required for incorporating wetting condition, the gradient of fluid-solid field is calculated. Two methods namely, round-off and interpolation describing how the information of neighboring nodes given the direction of normal vector on the boundary nodes should be used, are discussed. It is illustrated that results of the interpolation method exhibit a good agreement with the analytical solution as opposed to the round-off when tested in the case of static contact angle on a circular surface for both binary and ternary systems. Finally, it is shown incorporating different wetting conditions with the appropriate way of handling normal vectors and in combination with the conservative phase-field model can model static contact angle at high-density ratios for both binary and ternary fluids with good accuracy.

A novel probability iterative closest point with normal vector algorithm for robust rail profile registration

Regular inspection of rail wear is very important to ensure the safety of railway transportation. Rail profile registration is a key step in rail wear measurement. However, the accuracy of rail profile registration cannot be guaranteed due to soil and corrosion on the rail waist. To solve this problem, a new rail profile registration method based on probability iterative closest point algorithm with normal vector direction (N-PICP) is proposed in this paper. First, rail profile data is obtained using a line structured light measurement system. Then, the rail profile data is divided into rail head and rail waist according to the distance between adjacent points. The data of the rail waist is used to register with the corresponding part of the standard profile data by N-PICP. Finally, the rail head data is also converted according to the calculated transformation matrix. The experimental results demonstrate that the proposed method can realize the registration of the rail profile with a high precision and strong robustness.

Generating the tool path directly with point cloud for aero-engine blades repair

Aero-engine is an essential component of the aircraft. Due to the high cost of raw materials and precise structure, the maintenance cost of aero-engine is great. By repairing worn blades rather than replacing them with new ones, the aero-engine maintenance cost can be reduced effectively. For repairing worn blades, existing methods mainly generate tool path based on the reconstructed surface with the aid of CAM software. In this paper, an effective tool path generation method for repairing blades after additive manufacturing process is presented, which overcomes the low efficiency and complicated process weakness of existing methods. The tool path is generated directly with point clouds without surface fitting. By splitting point cloud and analyzing geometric parameters of points, machining areas could be recognized from the entire blade model. The cutter location point is generated by extending on the normal vector direction of the corresponding point. The five-axis tool path could be obtained by connecting cutter location points in turns. Tool path optimization is further studied after the generation process. These algorithms eliminate the time consumption caused by surface fitting operations, and could generate five-axis tool paths for repairing aero-engine blades efficiently.

OPTIMIZATION ALGORITHM OF TILTED IMAGE MATCHING BASED ON ADAPTIVE INITIAL OBJECT ASPECT

Abstract. When adopting the matching method of the least squares image based on object-patch to match tilted images, problems like the low degree of connection points for images with the discontinuity of depth or the discrepancy in elevation or low availability of aerotriangulation points would frequently appear. To address such problems, a tilted-image-matching algorithm based on an adaptive initial object-patch is proposed by this paper. By means of the existing initial values of the interior and exterior orientation elements of the tilted image and the information of object points generated in the matching process, the algorithm takes advantage of the method of multi-patch forward intersection and object variance partition so as to adaptively calculate the elevation of the object-patch and the initial value of the normal vector direction angle. Furthermore, this algorithm aims to solve the problem of difficulties in matching the tilted image with its corresponding points brought about by the low accuracy of the initial value of the tilted image when adopting the matching method of the least squares image based on object-patch to match the tilted image with high discrepancy in elevation. We adopt the algorithm as proposed in this paper and the least squares image matching method in which the initial state of the object-patch is horizontal to the object-patch respectively to conduct the verification process of comparing and matching two groups of tilted images. Finally, the effectiveness of the algorithm as proposed in this paper is verified by the testing results.

Plant Leaf Image Reconstruction Based on Point Cloud Characteristics

We present a method of leaf image reconstruction for plants whose midribs are close to straight. First, tangerine leaves are used as an example to illustrate the geometric and leaf-shape features of such leaves and suggest an extraction method using principal component analysis. Hence, this method was used to extract the geometric features, and additional methods such as coordinate conversion, mathematical morphology, and scan line analysis were applied to extract the leaf shape features. Then, based on these leaf shape features, a Bezier deformation function of the tangerine leaf edges and their curved Bezier deformation function in the normal vector direction were employed to obtain a parametric equation of the leaves according to their rectangular deformation. Finally, a simple illumination model for the leaves is presented. The reconstruction results show that the method is highly efficient and geometrically realistic. These results will be useful for the further study of plant leaf image reconstruction.

Two-dimensional ultrasound-computed tomography image registration for monitoring percutaneous hepatic intervention.

Deformable registration of ultrasound (US) and contrast enhanced computed tomography (CECT) images are essential for quantitative comparison of ablation boundaries and dimensions determined using these modalities. This comparison is essential as stiffness-based imaging using US has become popular and offers a nonionizing and cost-effective imaging modality for monitoring minimally invasive microwave ablation procedures. A sensible manual registration method is presented that performs the required CT-US image registration. The two-dimensional (2D) virtual CT image plane that corresponds to the clinical US B-mode was obtained by "virtually slicing" the 3D CT volume along the plane containing non-anatomical landmarks, namely points along the microwave ablation antenna. The initial slice plane was generated using the vector acquired by rotating the normal vector of the transverse (i.e., xz) plane along the angle subtended by the antenna. This plane was then further rotated along the ablation antenna and shifted along with the direction of normal vector to obtain similar anatomical structures, such as the liver surface and vasculature that is visualized on both the CT virtual slice and US B-mode images on 20 patients. Finally, an affine transformation was estimated using anatomic and non-anatomic landmarks to account for distortion between the colocated CT virtual slice and US B-mode image resulting in a final registered CT virtual slice. Registration accuracy was measured by estimating the Euclidean distance between corresponding registered points on CT and US B-mode images. Mean and SD of the affine transformed registration error was 1.85±2.14 (mm), computed from 20 coregistered data sets. Our results demonstrate the ability to obtain 2D virtual CT slices that are registered to clinical US B-mode images. The use of both anatomical and non-anatomical landmarks result in accurate registration useful for validating ablative margins and comparison to electrode displacement elastography based images.

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

SummaryConsideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second‐order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a1 and a2, control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a2 as well as the first mode by the parameter a1. The third parameter, θ0, expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal‐stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.

Correlation of fabric tensors for granular materials using 2D DEM

Soil fabric anisotropy can be quantitatively assessed by means of fabric tensors introduced as internal variables in constitutive models and defined by unit vectors along the directions of different orientation microstructural entities such as particle long axes, inter-particle contact normal vectors and void vectors. The most common choice is a fabric tensor based on contact normal directions. However, contact normal directions are more difficult to determine experimentally, due to difficulties associated with accurate measurement of tangent contact planes. The main scope in this study is to seek for possible correlations for fabric tensors defined using different fabric entities, i.e., contact normal, void and particle orientation vector directions, and based on this correlation to suggest the two latter instead of the first one because of the easiness of their measurements. The void fabric is defined using a very recent contribution of the authors concerning a modified and a novel approach of the scan line method for the determination of appropriate void vectors by means of 2D discrete element method analysis. In this very recent work of the authors, a first qualitative correlation was detected between contact normal and void fabric for both the void fabric tensors used therein. Given that this observation concerned only one 2D test, the current work aims at presenting an extended parametric analysis on the correlation of fabric tenors for all the above-mentioned fabric entities.

Research and application on force control of industrial robot polishing concave curved surfaces

In order to improve the quality of the industrial robot automatic polishing on curved surfaces and ensure the constant polishing pressure during polishing process, a method for polishing complex concave cavity surfaces with industrial robot is proposed in this article. The method can achieve stable force control and precise position control and is easy to be realized online. In order to ensure the removal rate uniformity of surface material at different normal vectors, a method for adjusting the speed of motorized spindle in real time according to the surface normal vector is proposed. After planning the trajectory and normal vectors, combined with the feedback force signal from the sensor and the proportional–integral controller in the direction of the normal vector, the robot terminal tool corrects the trajectory in the direction of the surface normal vector, indirectly realizing force control between the tool and the surface. The robot polishing system with different polishing tools has different system stiffness. In order to ensure the polishing system with different stiffness to have a better tracking performance of the contact force, an adaptive proportional–integral control algorithm proposed in this article can be used to evaluate the stiffness of polishing system and to adjust proportional–integral parameters. The simulation and experimental results indicate that the method can realize the polishing of concave cavity surface commendably.

The Similarity Comparison Algorithm of Free-Form Surfaces with Single Curvature Feature

This paper studies the shape similarity evaluation of free-form surfaces expressed by B-spline with single curvature feature and proposes a similarity evaluation algorithm based on curvature feature. Firstly, we calculate the normal vector direction of the two surfaces compared, and use it as the Z axis, so that the two surfaces are aligned on the Z axis. Then, the two surfaces are cut with planes that all perpendicular to the Z axis, and the intersection sets of two surfaces are obtained respectively. Finally, we design the similarity algorithm of plane curves to realize the similarity comparison of corresponding curves in the two sets of intersection, and which is used as the basis for evaluating the similarity between two surfaces. The algorithm transforms the problem of similarity comparison between 3D surfaces into two dimensional space by plane cutting method, and reduces the complexity of the problem effectively. The algorithm only needs to align one coordinate axis in the process of posture adjustment, so it is easy to implement. In order to test the effect of the algorithm, simulation experiments on different type of single curvature feature B-spline surfaces are carried out. The results show that the proposed similarity comparison algorithm of free-form surfaces is feasible and effective.

A Volumetric Fusing Method for TLS and SFM Point Clouds

A terrestrial laser scanning (TLS) point cloud acquired from a given ground view is incomplete because of severe occlusion and self-occlusion. The models reconstructed by aligning the cross-source point clouds [TLS and structure-from-motion (SFM) point clouds] provide a more complete large-scale outdoor scene. However, because of differences in nonrigid deformation, stratified redundancy of alignment is inevitable and ubiquitous. Therefore, this paper presents a volumetric fusing method for cross-source three-dimensional reconstructions. To eliminate the stratification of aligned cross-source point clouds, we propose a graph-cuts method with boundary constraints for blending the two cross-source point clouds. Then, to reduce the gaps that exist in the blending results, we develop a progressive migration method combined with the local average direction of normal vectors to smooth the unconnected boundary. Finally, experimental results demonstrate the effectiveness of eliminating stratification with the proposed blending algorithm, and the progressive migration method achieves a smooth connection in the boundary of the blended point clouds.

A scale space approach for exploring structure in spherical data

A novel scale space approach, SphereSiZer, is proposed for exploring structure in spherical data, that is, directional data on the unit sphere of the three-dimensional Euclidean space. The method finds statistically significant gradients of the smooths of the probability density function underlying the observed data. Bootstrap is used to establish significance and inference is summarized with planar maps of contour plots of smooths of the data, overlaid with arrows that indicate the directions and magnitudes of the significant gradients. An effective way to explore such maps is a movie where each frame corresponds to a fixed level of smoothing, that is, a particular spatial scale on the sphere. The SphereSiZer is demonstrated using simulated data as well as two real-data examples. The first example examines the distribution of infant head normal vector directions. The presence of local maxima in the normal vector distribution may indicate head deformity, such as severe flatness or asymmetry. The second example considers the distribution of earthquakes in the Northern Hemisphere.

Surface reconstruction from unorganized points with l0 gradient minimization

To reconstruct surface from unorganized points in three-dimensional Euclidean space, we propose a novel efficient and fast method by using l0 gradient minimization, which can directly measure the sparsity of a solution and produce sharper surfaces. Therefore, the proposed method is particularly effective for sharpening major edges and removing noise. Unlike the Poisson surface reconstruction approach and its extensions, our method does not depend on the accurate directions of normal vectors of the unorganized points. The resulting algorithm is developed using a half-quadratic splitting method and is based on decoupled iterations that are alternating over a smoothing step realized by a Poisson approach and an edge-preserving step through an optimization formulation. This iterative algorithm is easy to implement. Various tests are presented to demonstrate that our method is robust to point noise, normal noise and data holes, and thus produces good surface reconstruction results.

A Method for Normal Direction Judge Applied in Electrocardiographic Problem

Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.

Evaluation of Circular Motion Path in NC Machine Tools based on Normal Vector Direction Changes

Evaluation of Circular Motion Path in NC Machine Tools based on Normal Vector Direction Changes