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.

Fast B-spline surface extraction algorithm of seismic volume data on GPU

In the process of seismic data interpretation, the extraction of a horizon or a fault is generally needed. In this paper we present a fast extraction method. First select some feature points interactively, then reconstruct the surface according to the selected feature points by using B-spline interpolation curve or surface. In order to solve the error-drawing problem appeared in the process of interactive rendering, which is caused by the change of sampling interval as the view point changes, we combine shear-warp and splatting algorithm to render the surface. The rendering of seismic data and specific surface in our work are achieved on GPU platform using CUDA programming language, which make it able to meet the requirements of real-time rendering.

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.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

Geometric Calibration of LensUsing B-Spline Surface Fitting

A new lens calibration method which is suitable for all kinds of cameras is presented. Based on the global and local adjustable feature of B-spline surface, this method does not require the determination of distortion model of the camera lens. By applying B-spline surface fitting, all kinds of lens distortion models can be simulated. The control points of B-spline surface are estimated inversly from the feature points of detected lines. Then by moving the control points, straight line features in the image can be retrieved. Compared with traditional calibration method, this method has its unique advantage that need no corresponding points between image and scene. Experimental results show the effectiveness of the method.

An Algorithm of B-Spline Surface Interpolation

A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors and twist vector at each positions. Single surface interpolation approach is easier to ensure the smoothness of the interpolating surface than multi-patches method. This algorithm can be used to solve the approximating problem of B-spline approximation of general parametric surface.

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.

3D Printing of Tough Hydrogel Scaffolds with Functional Surface Structures for Tissue Regeneration

Hydrogel scaffolds have numerous potential applications in the tissue engineering field.However,tough hydrogel scaffolds implanted in vivo are seldom reported because it is difficult to balance biocompatibility and high mechanical properties.Inspired by Chinese ramen,we propose a universal fabricating method(printing-P,training-T,cross-linking-C,PTC&PCT)for tough hydrogel scaffolds to fill this gap.First,3D printing fabricates a hydrogel scaffold with desired structures(P).Then,the scaffold could have extraordinarily high mechanical properties and functional surface structure by cycle mechanical training with salting-out assistance(T).Finally,the training results are fixed by photo-cross-linking processing(C).The tough gelatin hydrogel scaffolds exhibit excellent tensile strength of 6.66 MPa(622-fold untreated)and have excellent biocompatibility.Furthermore,this scaffold possesses functional surface structures from nanometer to micron to millimeter,which can efficiently induce directional cell growth.Interestingly,this strategy can produce bionic human tissue with mechanical properties of 10 kPa-10 MPa by changing the type of salt,and many hydrogels,such as gelatin and silk,could be improved with PTC or PCT strategies.Animal experiments show that this scaffold can effectively promote the new generation of muscle fibers,blood vessels,and nerves within 4 weeks,prompting the rapid regeneration of large-volume muscle loss injuries.

Microstructure evolution of 7050 aluminum forgings during surface cumulative plastic deformation

To elucidate the mechanisms of regulating the microstructure uniformity in 7050 aluminum forgings through surface cumulative plastic deformation(SCPD),the microstructure under different solution treatments was investigated using metallographic observation(OM),electron backscatter diffraction(EBSD),transmission electron microscopy(TEM),and X-ray diffraction(XRD).The findings demonstrate that the most uniform microstructure in the forgings is achieved with a solution treatment at 470℃for 30 min.The SCPD process generates a significant number of needle-shaped precipitates,resulting in a higher dislocation density and stored energy.Solution treatments alleviate the pinning effect of second-phase particles and facilitate static recrystallization(SRX)in forgings,leading to a reduction in grain size.Additionally,mechanical testing results demonstrate 7%−13%increase in tensile strength and more uniform elongation of the forgings in different directions.

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.

Effect of surface crack on the bearing capacity of strip footing placed on rock mass

In hilly regions,the existence of surface cracks in rock mass induces a potential threat to structural stability.Thus,the present research aims to explore the impact of surface cracks on the loadbearing capacity of strip footing placed on the rock mass.By taking into account the various boundary constraints across the surface of crack edges,the study investigates the presence of two categories of surface cracks,namely(1)separated crack,and(2)fine crack.The lower bound limit analysis is employed in conjunction with the finite element method(LBFELA)to conduct the numerical analysis.In order to evaluate rock mass yielding,the power conic programming(PCP)method is utilized to implement the generalized Hoek-Brown(GHB)failure criterion.The stability of the strip footing is analyzed by determining the bearing capacity factor(Nσγ),which is presented in the form of design charts by varying the strength parameters of rock,including the Geological Strength Index(GSI),Hoek-Brown material parameter(mi),Disturbance factor(D),and Normalised Uniaxial Compressive Strength(σci/γB),whereγis the unit weight of rock mass,and B is the width of strip footing.The study also investigates the impact of cracks on strip footings,considering different positions of the crack(LC)and depths of the crack(DC).The results demonstrate that the influence of the fine crack is only noticeable until the LC/B ratio reaches 6.However,for the separated crack,its impact remains significant even when the LC/B ratio exceeds 16.The appearance of fine crack at the edge of the footing results in a decrease in the magnitude Nσγof up to 45%,indicating a substantial reduction in the stability of the footing.The failure patterns are presented and discussed in detail for various cases in this study to examine the effect of surface cracks on the strip footing and to address the extent of the plastic collapse.

Vibration safety assessment and parameter analysis of buried oil pipelines based on vibration isolation holes under strong surface impact

Strong surface impact will produce strong vibration,which will pose a threat to the safety of nearby buried pipelines and other important lifeline projects.Based on the verified numerical method,a comprehensive numerical parameter analysis is conducted on the key influencing factors of the vibration isolation hole(VIH),which include hole diameter,hole net spacing,hole depth,hole number,hole arrangement,and soil parameters.The results indicate that a smaller ratio of net spacing to hole diameter,the deeper the hole,the multi-row hole,the hole adoption of staggered arrangements,and better site soil conditions can enhance the efficiency of the VIH barrier.The average maximum vibration reduction efficiency within the vibration isolation area can reach 42.2%.The vibration safety of adjacent oil pipelines during a dynamic compaction projection was evaluated according to existing standards,and the measurement of the VIH was recommended to reduce excessive vibration.The single-row vibration isolation scheme and three-row staggered arrangement with the same hole parameters are suggested according to different cases.The research findings can serve as a reference for the vibration safety analysis,assessment,and control of adjacent underground facilities under the influence of strong surface impact loads.

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.

Quasi-Developable B-Spline Surface Design with Control Rulings

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible.Specifically,the terminal ruling lines are treated as hard constraints.Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control,our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings.We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications.The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control(CNC)flank milling.

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.

A facile strategy for tuning the density of surface-grafted biomolecules for melt extrusion-based additive manufacturing applications

Melt extrusion-based additive manufacturing(ME-AM)is a promising technique to fabricate porous scaffolds for tissue engi-neering applications.However,most synthetic semicrystalline polymers do not possess the intrinsic biological activity required to control cell fate.Grafting of biomolecules on polymeric surfaces of AM scaffolds enhances the bioactivity of a construct;however,there are limited strategies available to control the surface density.Here,we report a strategy to tune the surface density of bioactive groups by blending a low molecular weight poly(ε-caprolactone)5k(PCL5k)containing orthogonally reactive azide groups with an unfunctionalized high molecular weight PCL75k at different ratios.Stable porous three-dimensional(3D)scaf-folds were then fabricated using a high weight percentage(75 wt.%)of the low molecular weight PCL 5k.As a proof-of-concept test,we prepared films of three different mass ratios of low and high molecular weight polymers with a thermopress and reacted with an alkynated fluorescent model compound on the surface,yielding a density of 201-561 pmol/cm^(2).Subsequently,a bone morphogenetic protein 2(BMP-2)-derived peptide was grafted onto the films comprising different blend compositions,and the effect of peptide surface density on the osteogenic differentiation of human mesenchymal stromal cells(hMSCs)was assessed.After two weeks of culturing in a basic medium,cells expressed higher levels of BMP receptor II(BMPRII)on films with the conjugated peptide.In addition,we found that alkaline phosphatase activity was only significantly enhanced on films contain-ing the highest peptide density(i.e.,561 pmol/cm^(2)),indicating the importance of the surface density.Taken together,these results emphasize that the density of surface peptides on cell differentiation must be considered at the cell-material interface.Moreover,we have presented a viable strategy for ME-AM community that desires to tune the bulk and surface functionality via blending of(modified)polymers.Furthermore,the use of alkyne-azide“click”chemistry enables spatial control over bioconjugation of many tissue-specific moieties,making this approach a versatile strategy for tissue engineering applications.

Spatial Variation in CO_(2) Concentration Improves the Simulated Surface Air Temperature Increase in the Northern Hemisphere

The increasing concentration of atmospheric CO_(2) since the Industrial Revolution has affected surface air temperature.However,the impact of the spatial distribution of atmospheric CO_(2) concentration on surface air temperature biases remains highly unclear.By incorporating the spatial distribution of satellite-derived atmospheric CO_(2) concentration in the Beijing Normal University Earth System Model,this study investigated the increase in surface air temperature since the Industrial Revolution in the Northern Hemisphere(NH) under historical conditions from 1976-2005.In comparison with the increase in surface temperature simulated using a uniform distribution of CO_(2),simulation with a nonuniform distribution of CO_(2)produced better agreement with the Climatic Research Unit(CRU) data in the NH under the historical condition relative to the baseline over the period 1901-30.Hemispheric June-July-August(JJA) surface air temperature increased by 1.28℃ ±0.29℃ in simulations with a uniform distribution of CO_(2),by 1.00℃±0.24℃ in simulations with a non-uniform distribution of CO_(2),and by 0.24℃ in the CRU data.The decrease in downward shortwave radiation in the non-uniform CO_(2) simulation was primarily attributable to reduced warming in Eurasia,combined with feedbacks resulting from increased leaf area index(LAI) and latent heat fluxes.These effects were more pronounced in the non-uniform CO_(2)simulation compared to the uniform CO_(2) simulation.Results indicate that consideration of the spatial distribution of CO_(2)concentration can reduce the overestimated increase in surface air temperature simulated by Earth system models.