G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

G^1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.

Modification of B-Spline Surfaces with Optimization

Algorithms of modifying a surface to approximate some scattered points, or pass through some characteristic points/curves are presented. Similar to variational approach, the algorithms are based on optimization. For the deviation between the modified surface and the original one is adopted as the objective functions, the change of the surface shape is as small as possible with the modified surface satisfying the specified requirements.

Research status and prospects of the fractal analysis of metal material surfaces and interfaces

As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.

G^1 Continuous Condition of B-Spline Surfaces with Double Knots

The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.

Computing B-Spline Surfaces on Transputer Networks

This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.

Triboelectric‘electrostatic tweezers'for manipulating droplets on lubricated slippery surfaces prepared by femtosecond laser processing

The use of‘Electrostatic tweezers'is a promising tool for droplet manipulation,but it faces many limitations in manipulating droplets on superhydrophobic surfaces.Here,we achieve noncontact and multifunctional droplet manipulation on Nepenthes-inspired lubricated slippery surfaces via triboelectric electrostatic tweezers(TETs).The TET manipulation of droplets on a slippery surface has many advantages over electrostatic droplet manipulation on a superhydrophobic surface.The electrostatic field induces the redistribution of the charges inside the neutral droplet,which causes the triboelectric charged rod to drive the droplet to move forward under the electrostatic force.Positively or negatively charged droplets can also be driven by TET based on electrostatic attraction and repulsion.TET enables us to manipulate droplets under diverse conditions,including anti-gravity climb,suspended droplets,corrosive liquids,low-surface-tension liquids(e.g.ethanol with a surface tension of 22.3 mN·m^(-1)),different droplet volumes(from 100 nl to 0.5 ml),passing through narrow slits,sliding over damaged areas,on various solid substrates,and even droplets in an enclosed system.Various droplet-related applications,such as motion guidance,motion switching,droplet-based microreactions,surface cleaning,surface defogging,liquid sorting,and cell labeling,can be easily achieved with TETs.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Additive manufacturing of micropatterned functional surfaces:a review

Over the course of millions of years,nature has evolved to ensure survival and presents us with a myriad of functional surfaces and structures that can boast high efficiency,multifunctionality,and sustainability.What makes these surfaces particularly practical and effective is the intricate micropatterning that enables selective interactions with microstructures.Most of these structures have been realized in the laboratory environment using numerous fabrication techniques by tailoring specific surface properties.Of the available manufacturing methods,additive manufacturing(AM)has created opportunities for fabricating these structures as the complex architectures of the naturally occurring microstructures far exceed the traditional ways.This paper presents a concise overview of the fundamentals of such patterned microstructured surfaces,their fabrication techniques,and diverse applications.A comprehensive evaluation of micro fabrication methods is conducted,delving into their respective strengths and limitations.Greater emphasis is placed on AM processes like inkjet printing and micro digital light projection printing due to the intrinsic advantages of these processes to additively fabricate high resolution structures with high fidelity and precision.The paper explores the various advancements in these processes in relation to their use in microfabrication and also presents the recent trends in applications like the fabrication of microlens arrays,microneedles,and tissue scaffolds.

Automatic Extraction Method of 3D Feature Guidelines for Complex Cultural Relic Surfaces Based on Point Cloud

Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Variations in evaporation from water surfaces along the margins of the Badain Jaran Desert over nearly 60 years and influencing factors

Based on meteorological data collected over nearly 60 years(1960-2017)from four national meteorological stations along the margins of the Badain Jaran Desert,this study analyzed the spatiotemporal variations in evaporation from water surfaces and identified the dominant controlling factors.Methods used included linear trend analysis,linear tendency estimation,the departure method,the rank correlation coefficient-based method,and Multiple Linear Regression(MLR).Results indicate notable spatiotemporal differences in evaporation distribution and evolution.Spatially,average annual evaporation exhibited a pronounced altitude effect,decreasing at a rate of about 8.23 mm/m from east to west with increasing altitude.Temporally,annual evaporation showed significant upward trends after 1996 at the northeastern(Guaizi Lake)and western(Dingxin)margins,with rates of 132 mm/10a and 105 mm/10a,respectively.Conversely,along the northwestern(Ejina Banner)and southern(Alxa Right Banner)margins of the desert,an evaporation paradox was observed,with annual evaporation trending downward at rates of 162 mm/10a and 187 mm/10a,respectively,especially after 1987.The dominant factors controlling evaporation varied spatially:Average annual temperature and relative humidity influended the western margin(Dingxin),average annual temperature was the key factor for the northeastern margin(Guaizi Lake),and average wind speed was crucial for the northern(Ejina Banner)and southern(Alxa Right Banner)margins.

Ultrafast dynamics of femtosecond laser-induced high spatial frequency periodic structures on silicon surfaces

Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.

Theoretical Modeling and Surface Roughness Prediction of Microtextured Surfaces in Ultrasonic Vibration-Assisted Milling

Textured surfaces with certain micro/nano structures have been proven to possess some advanced functions,such as reducing friction,improving wear and increasing wettability.Accurate prediction of micro/nano surface textures is of great significance for the design,fabrication and application of functional textured surfaces.In this paper,based on the kinematic analysis of cutter teeth,the discretization of ultrasonic machining process,transformation method of coordinate systems and the cubic spline data interpolation,an integrated theoretical model was established to characterize the distribution and geometric features of micro textures on the surfaces machined by different types of ultrasonic vibration-assisted milling(UVAM).Based on the theoretical model,the effect of key process parameters(vibration directions,vibration dimensions,cutting parameters and vibration parameters)on tool trajectories and microtextured surface morphology in UVAM is investigated.Besides,the effect of phase difference on the elliptical shape in 2D/3D ultrasonic elliptical vibration-assisted milling(UEVAM)was analyzed.Compared to conventional numerical models,the method of the cubic spline data interpolation is applied to the simulation of microtextured surface morphology in UVAM,which is more suitable for characterizing the morphological features of microtextured surfaces than traditional methods due to the presence of numerous micro textures.The prediction of surface roughness indicates that the magnitude of ultrasonic amplitude in z-direction should be strictly limited in 1D rotary UVAM,2D and 3D UEVAM due to the unfavorable effect of axial ultrasonic vibration on the surface quality.This study can provide theoretical guidance for the design and fabrication of microtextured surfaces in UVAM.

Acoustic Bilayer Gradient Metasurfaces for Perfect and Asymmetric Beam Splitting

We experimentally and theoretically present a paradigm for the accurate bilayer design of gradient metasurfaces for wave beam manipulation,producing an extremely asymmetric splitting effect by simply tailoring the interlayer size.This concept arises from anomalous diffraction in phase gradient metasurfaces and the precise combination of the phase gradient in bilayer metasurfaces.Ensured by different diffraction routes in momentum space for incident beams from opposite directions,extremely asymmetric acoustic beam splitting can be generated in a robust way,as demonstrated in experiments through a designed bilayer system.Our work provides a novel approach and feasible platform for designing tunable devices to control wave propagation.

Reconfigurable optical neural networks with Plug-and-Play metasurfaces

In a very recent study,Prof.Lingling Huang and co-workers proposed and demonstrated reconfigurable optical neural networks based on cascaded metasurfaces.By fixing one metasurface and switching the other pluggable metasurfaces,the neural networks,which operate at near-infrared wavelengths,can perform distinct recognition tasks for handwritten digits and fashion products.This innovative device opens up an avenue for all-optical,high-speed,low-power,and multifunctional artificial intelligence systems.

Symmetric alteration of four knots of B-spline and NURBS surfaces

Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

A density functional theory study of polarons on different TiO_(2)surfaces

Polarons are widely considered to play a crucial role in the charge transport and photocatalytic performance of materials,but the mechanisms of their formation and the underlying driving factors remain a matter of controversy.This study delves into the formation of polarons in different crystalline forms of TiO_(2)and their connection with the materials'structure.By employing density functional theory calculations with on-site Coulomb interaction correction(DFT+U),we provide a detailed analysis of the electronic polarization behavior in the anatase and rutile forms of TiO_(2).We focus on the polarization properties of defect-induced and photoexcited excess electrons on various TiO_(2)surfaces.The results reveal that the defect electrons can form small polarons on the anatase TiO_(2)(101)surface,while on the rutile TiO_(2)(110)surface,both small and large polarons(hybrid-state polarons)are formed.Photoexcited electrons are capable of forming both small and large polarons on the surfaces of both crystal types.The analysis indicates that the differences in polaron distribution are primarily determined by the intrinsic properties of the crystals;the structural and symmetry differences between anatase and rutile TiO_(2)lead to the distinct polaron behaviors.Further investigation suggests that the polarization behavior of defect electrons is also related to the arrangement of electron orbitals around the Ti atoms,while the polarization of photoexcited electrons is mainly facilitated by the lattice distortions.These findings elucidate the formation mechanisms of different types of polarons and may contribute to understanding the performance of TiO_(2)in different fields.

Target Detection on Water Surfaces Using Fusion of Camera and LiDAR Based Information

To address the challenges of missed detections in water surface target detection using solely visual algorithms in unmanned surface vehicle(USV)perception,this paper proposes a method based on the fusion of visual and LiDAR point-cloud projection for water surface target detection.Firstly,the visual recognition component employs an improved YOLOv7 algorithmbased on a self-built dataset for the detection of water surface targets.This algorithm modifies the original YOLOv7 architecture to a Slim-Neck structure,addressing the problemof excessive redundant information during feature extraction in the original YOLOv7 network model.Simultaneously,this modification simplifies the computational burden of the detector,reduces inference time,and maintains accuracy.Secondly,to tackle the issue of sample imbalance in the self-built dataset,slide loss function is introduced.Finally,this paper replaces the original Complete Intersection over Union(CIoU)loss function with the Minimum Point Distance Intersection over Union(MPDIoU)loss function in the YOLOv7 algorithm,which accelerates model learning and enhances robustness.To mitigate the problem of missed recognitions caused by complex water surface conditions in purely visual algorithms,this paper further adopts the fusion of LiDAR and camera data,projecting the threedimensional point-cloud data from LiDAR onto a two-dimensional pixel plane.This significantly reduces the rate of missed detections for water surface targets.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.