Surface Generation Method Research Articles

Design of Random and Deterministic Fractal Surfaces from Voronoi Cells

We show a fractal surface generation method that, unlike other methods, generates both random and deterministic fractals that model natural and architectural elements. The method starts with a succession of sets of sites, which determine, by means of a metric, a succession of Voronoi tessellations of the region where the fractal is defined. For each element of the tessellation sequence we define a tessellation function which depends on each tile. This generates a succession of tessellation functions that will be the parameter of the same seed function. Finally, the fractal is generated by a weighted sum of the seed function evaluated on each value of the succession of parameters. If the sites used to generate the Voronoi tessellation are random, natural elements such as mountains, craters, lakes, etc. are generated; if they are deterministic, architectural and decorative elements are generated. In addition, the designers can control the morphology of the generated fractal by simply varying the metric.

Contact Analysis for Cycloid Pinwheel Mechanism by Isogeometric Finite Element

Cycloid drives are generally used in precision machinery requiring high-reduction ratios, such as robot joint (RV) reducers. The contact stress of cycloidal gears greatly affects lifetime and transmission performance. Traditional finite element method (FEM) has less computational efficiency for contact analysis of complex surface. Therefore, in this paper, isogeometric analysis (IGA) was employed to explore the multi-tooth contact problem of the cycloid pinwheel drive. Based on the nonuniform rational B spline (NURBS) curved surface generation method, the NURBS tooth profile of the cycloid gear was reconstructed. In addition, the NURBS surface of the cycloid gear–pin tooth–output pin was generated via the element splicing method. A geometrical analysis model of cycloid pinwheel drive was established to solve the contact force of the meshing pair under different input angles and compared with the finite element method in terms of convergence, resultant accuracy, and solving timeliness. The results show that isogeometric analysis has higher accuracy and efficiency than the finite element method in calculating the contact stress and contact force. The error of the IGA is only 8.8% for 10 × 10 elements in contact, while the error of the finite element method reaches about 40%. The method can improve the contact simulation accuracy of the cycloid drive and provides a reference for the design evaluation of RV reducer.

FMASketch: Freehand Mid-Air Sketching in AR

Sketching is a common way to depict design ideas freely. Augmented reality technology extends the human–computer interaction space from the screen to the real world, providing a new application space for 3D sketching. However, due to the difficulty of depth perception, it is difficult for sketching strokes to maintain good planar and spatial consistency, making drawing 3D sketches in AR challenging. In this article, we propose FMASketch—a method of drawing mid-air sketches similar to building blocks. The auxiliary surfaces can ensure that the strokes drawn by users can always stay on the same plane as drawing in 2D space. Gestures are used to stitch together multiple drawing planes, and the strokes on the planes form a 3D sketch, which is very similar to how 3D modeling is done on the desktop by drawing different views and assembling them. Experiments have verified the effectiveness of the auxiliary surface generation method and gesture operations in this article. The mid-air sketching method is easy to learn and provides a new idea for rapid modeling in AR scenarios.

Generation of Textured Surfaces by Vibration-Assisted Ball-End Milling

Textured surfaces have been widely applied in many fields due to their excellent functional performances. Although several micro-scale surface texturing techniques have been used to fabricate surface textures, most are either very expensive, have material limitations, or lack flexibility. In this study, a novel textured surface generation method using vibration-assisted ball-end milling with a non-resonant vibrator is proposed. Firstly, the configuration of the vibration-assisted ball-end milling system is introduced. Then, the trajectories of the cutting edges are modeled and analyzed. Furthermore, an analysis of a non-resonant vibrator is conducted. Finally, surface texture machining experiments are conducted, and the feasibility of the proposed vibration-assisted ball-end milling method for surface texture fabrication is verified.

Surface integrity in 3D ultrasonic vibration-assisted turning driven by two actuators

The surface integrity of machined parts is critical to their in-service function, longevity and overall performance. The integrity of the surface is dominantly affected by the chip formation process that can be significantly altered and controlled, among other methods, by ultrasonic vibration assistance. This work will explore the integrity of surfaces generated in three-dimensional ultrasonic vibration-assisted turning (3D-UVAT). The integrity of the obtained workpiece surfaces will be systematically explored in terms of surface roughness, the microstructure of the surface obtained by heat-assisted turning, surface hardness and wettability. A comparative assessment with other surface generation methods, i.e., common turning (CT), one-dimensional (UVAT) and two-dimensional elliptical ultrasonic vibration-assisted turning (EUAT) is also given. The results show that 3D-UVAT can reduce the depth of surface damage and enhance the hydrophobicity of the surface while reducing surface roughness.

A study on longitudinal motion stability of a variable-structure SWATH USV with and without twin hydrofoils

The form-changeable unmanned surface vehicle (USV) have a high research enthusiasm due to its far-ranging applicability, strong combat capability and low operating cost. This paper constructs a variable-structure Small Waterplane Area Twin Hull (SWATH) USV with twin hydrofoils, and aims at assessing its longitudinal motion stability (LMS) in the catamaran-form state (CFS) by parametric model and CFD method. The parametric representation of the torpedo, double struts and hydrofoils was conducted by uniform B-spline curves, 3-D coordinates conversion and surface generation method. The CFD code was verified, and used to calculate the LMS of the vessel with different strut configurations, form-states and CG position. Based on numerical results, the causes of different instability behaviors were expounded. Further, the LMS of the models with and without hydrofoils was compared at Fr = 0.1–0.8, the adjustment method of fore and aft hydrofoils to sailing attitudes was explained, the rational allocation of attack angles was also offered. The results show that the slender double struts arranged at both ends of torpedo is more conducive to the LMS and resistance, the vessel should sail in the CFS of γs ≤ 10° at Fr > 0.6; the hydrofoils slightly weakens the LMS at low Fr, makes the bow appear slight updip at Fr = 0.4–0.6, but still can sails stably; adjusting attack angles can inhibit the instability, and the most effective allocation of the fore and aft hydrofoil's attack angles is linearly arranged at Fr = 0.7, 0.8, also the adjusting can reduce the upward trim at Fr = 0.9, 1.0, but the hull is lifted higher and arises the bow updip due to the free surface suction force, at this time, the attack angle's graduation should be refined to realize the finer adjustment to the dynamic trim.

A simulation study on stress-seepage characteristics of 3D rough single fracture based on fluid-structure interaction

This paper expounds on the process of deformation and seepage field change of single coarse fracture under normal stress and puts forward a numerical simulation framework based on fluid-structure coupling method to reasonably link contact deformation of fracture surface with seepage field change. The geometric model of a three-dimensional rough single fracture surface with controllable JRC is established based on the random surface generation method. The numerical test model of radiation flow of single fracture in rough rock is constructed, which is consistent with the laboratory test. Through carrying out numerical simulation tests of different JRC and normal stress conditions, this paper discusses the phenomenon and intrinsic nature of the influence of JRC on fracture seepage characteristics. The increase in eddy current intensity and eddy current area ratio is the inherent characteristics of the seepage field characteristics after JRC increases. With the rise of energy loss, the macroscopic seepage flow decreases. In addition, with the advantage of the fluid-structure interaction method, the fracture deformation characteristics under different normal stresses are reflected by the ratio of the contact area. The correlation among fracture surface deformation, velocity vector, and seepage pressure are analyzed. Finally, the cubic polynomial correlation between gap width ratio and contact area ratio is established and verified. It is of positive significance to quantify the influence of coarse single fracture contact ratio on deformation-seepage coupling characteristics under normal stress.

Application of intelligent virtual reality technology in Clothing virtual wear and color saturation after COVID-19 epidemic situation

The COVID-19 epidemic has brought a huge impact to the clothing industry. Because of the inconveniences caused by countermeasures, clothing consumers can’t go to physical stores to try on, so it is urgent to develop a virtual clothing trial system. In addition, online fitting and online shopping gradually become the trend of clothing consumption. Based on virtual reality technology, this paper proposes a virtual clothing fitting system, and studies the color saturation in the process. In this paper, a method of parametric drawing of garment characteristic curve is proposed, and the shape of garment is designed by using control vertices. Based on this, this paper presents four forms of sutured parabola space and their control point solving algorithm. According to the principle of scale method, a three-dimensional coordinate transformation model of feature points is established. The model can calculate the coordinates of each characteristic value point of clothing according to the body shape information provided by customers and the empirical formula of different clothing styles, and then reverse calculate the curve control point. Furthermore, Bezier surface generation method is used to fit the control points. After the surface patches are spliced, the 3D rigid clothing model can be obtained. Experiments show that the method of personalized clothing modeling in this paper is efficient and accurate, which can be further extended to the observation system with larger degree of freedom.

Effect of geometry error on accuracy of large-diameter pads used for CMP dressing

Large-diameter polishing pads play an important role in chemical mechanical polishing (CMP) and are vital to large-aperture plane optics. The surface profile of a wafer is closely related to the profile accuracy of the polyurethane pad. To attain a high-precision surface, the polishing pad is dressed using a diamond dresser. In the present study, a pad dressing model was proposed as a means of analysing how any geometry errors in the polishing machine affect the profile accuracy by observing the trajectory of the moving dresser tool. Based on the spherical surface generation method, the influence of any tilt and motion error on the profile accuracy of the pad was studied. To verify the accuracy of the model, a variety of analyses and dressing experiments were performed using PPS100 and KPJ1700 CMP machines. The results of these experiments showed that the proposed model could effectively predict the profile accuracy of the pad after the dressing process. However, because of uncertainty in the measurements, there was a degree of error between the predicted and measured values, although this was never > 5%. Moreover, the results demonstrated that the main geometry error was the dressing spindle’s tilt angle which, if minimised, resulted in a higher dressing profile accuracy for the polyurethane pad.

Local T-spline surface skinning with shape preservation

Surface skinning is a surface generation method that uses a set of given cross-sectional curves, and it is widely used in free-form surface design. In the B-spline surface skinning, the given B-spline curves should be compatible, that is, the curves should have the same degree and knot sequence. While making the curves compatible, lots of control vertices are generated. Although T-spline surface skinning methods have been introduced to reduce the number of control vertices, the T-spline skinning method that was proposed by Nasri et al. (2012) can generate a wiggled surface when the given B-spline curves are not sufficiently compatible. The intermediate cross sections that were introduced for T-spline surface skinning cannot preserve the shape of the given B-spline curves if the adjacent B-spline curves do not have sufficient common knots, and it can cause wiggles on the surface. In this paper, we analyze this issue and suggest a modified method to remove the wiggles on the skinned T-spline surface. Furthermore, we propose an algorithm for shape preservation of the surface. Our approach is verified by suggesting some examples compared to the Nasri et al. (2012)’s method.

Geometrical characteristic-based stream surface of 3D flow field

This paper addressed a novel stream surface generation method to represent the structure of flow field smoother, feature more prominently and better visual clarity than the conventional triangulate method. To have a nice expressive force in the visualization of 3D flow field, first a strategy for adaptive streamline based on geometrical characteristic in 3D flow field space is presented to show a clear flow field pattern and the important flow features in our algorithm. Characteristics such as Euclidean distance between adjacent streamlines, curvature and torsion of each individual streamline are considered as influence factors to determine the number of seed points in the focused regions. Then, in the process of stream surface generation, an adaptive triangulation technique based on geometrical characteristic of streamlines is adopted to keep the structural continuity, smoothness, concavity and convexity of stream surface. At last, the whole algorithm is implemented using CUDA, and it can effectively shorten the lag phase appeared in the process of interaction with the control line and parameter modification. Compared with conventional triangulate method, comprehensive experiments conducted on dataset of delta-wing show that the proposed algorithm can better reflect the underlying properties of the flow field and greatly improve the readability of 3D flow field dataset.

Adaptive multi-hypar structure

ABSTRACTThis paper is concerned with developing an adaptive structure that can offer morphologically flexible, structurally effective and architecturally viable solution. For this purpose, a multi-hypar structure serving as an adaptive roof for exhibition pavilions is proposed. In the first part of the paper, geometric design principles of the multi-hypar surface created by ruled surface generation method is analysed. In order to investigate the morphology of multi-hypar, a parametric model is built. In the second part, the proposed multi-hypar structure is introduced which provides a variety of geometric configurations for changing conditions. Its structural mechanism and transformation capability are presented as well. In the last part, a set of structural analysis is carried out to examine the feasibility of the proposed structure at different geometric configurations. The result obtained with the analysis demonstrates that planar configuration of the structure has the least efficient structural shape among the others, but the structure fulfils the strength and stiffness criteria in all configurations.

Surface generation of freeform surfaces in diamond turning by applying double-frequency elliptical vibration cutting

A new freeform surface generation method for the difficult-to-cut materials is proposed in this paper. Fast tool servo and slow slide servo diamond turning are the main generation technologies for freeform surfaces, whereas they cannot machine the freeform surfaces of difficult-to-cut materials very effectively. On the other hand, elliptical vibration cutting has demonstrated its excellent performance in material processing, especially for the difficult-to-cut materials. Nevertheless, it is unable to generate the freeform surfaces very successfully. Therefore, this paper proposes the double-frequency elliptical vibration cutting method for the freeform surface diamond machining on the difficult-to-cut materials, which provides the high-frequency elliptical vibration to improve the machinability in material removal and the low-frequency reciprocating movements for the freeform surface profile generation. The relative movements between the tool and the workpiece are analyzed, and because of the Y direction elliptical vibration, the cutting plane does not always cross the workpiece center, which makes the tool path generation, the tool geometry selection and the surface topography prediction very different from those in the conventional fast tool servo or slow slide servo diamond turning. A new tool path generation method is proposed, and the selection of the tool geometry parameters is discussed. The surface generation process is analyzed, based on which the topography model for the machined surfaces is constructed. Three typical freeform surfaces are machined on the die steel workpieces, which verifies the feasibility of the proposed tool path generation strategies. In addition, the experimental results agree well with the surface topography predictions, which validates the effectiveness of the topography model. This model also applies to the diamond turning processes with tool motion in the Y direction, such as turning with EVC.

Computer Aided Design of Centrifugal Fan Impeller Using CATIA Software

In this paper, the 3D model of the centrifugal fan impeller will be obtained using CAD software (CATIA). The blade will be obtained with 4 design methods: constant blade width and variable blade angle; hyperbolic blade width and variable blade angle; hyperbolic blade width and constant blade angle; linear blade width and variable blade angle. A comparative analysis of the weight of the blade, as well as of the weight of the rotor composed by cascade of blades, front and rear shrouds will be presented. Two materials have been used for all the elements of the centrifugal fan impeller: steel and aluminium. For computational purposes the MATLAB programming language will be used. The centrifugal fan blade will be designed as untwisted geometry with =2 reference curves (one on the rear shroud and the other one on the front shroud) with different numbers of reference points ={5, 10, 20, 30, 40, 50}. After running the MATLAB script file, the coordinates of reference points of the blade will be obtained for all 4 blade design methods. The transfer of the reference points coordinates from MATLAB workspace to CATIA has been performed using the automatic surface generation method, via an EXCEL macro file. This is the recommended method especially for a big number of reference points.

A Novel Transformable Structural Mechanism for Doubly Ruled Hypar Surfaces

A novel structural mechanism (SM) that is capable of transforming itself into various hyperbolic paraboloid (hypar) geometries is introduced in this paper. Composed of straight bars and novel joint types, the SM is designed based on the ruled surface generation method. Thus, the paper first investigates the geometrical properties and morphology of the hypar surface. Second, it constructs the SM and discusses its transformation capability with respect to its kinematic properties. Then, it presents a parametric model not only to analyze the geometry and possible configurations of the SM but also to prepare a model for the structural analysis. Finally, a transformable shelter structure is proposed as an architectural application of the SM and its feasibility is tested based on the structural analysis conducted in different configurations of the structure. According to the results of the structural analysis, the strength, and the stiffness of the structure are discussed in detail.

Creation of user-defined freeform feature from surface models based on characteristic curves

This paper proposes a novel method for the creation of user-defined freeform feature (UDFFF) from existing surface model. The developed methodology has four major steps: selecting the region of interest (ROI), obtaining the characteristic curves from the surface model, reconstructing the ROI surface, and parameterizing the UDFFF. To quickly create UDFFF on the ROI, the representation of freeform feature based on characteristic curves is proposed. First, the characteristic curves of ROI are obtained automatically or by a small amount of human–computer interaction. In particular, user can directly and easily draw the curves on surface to satisfy the designer's requirements. Second, from the set of characteristic curves that is obtained, freeform surface is reconstructed by a suitable surface generation method, e.g., sweeping, revolving, skinning, and filling. Finally, parameterization of the freeform feature is configured, which primarily involves establishing parameters and building the mappings between feature parameters and shape data. Moreover, according to the degrees of freedom, two types of parameterization of freeform features may be described: one (low degrees of freedom) can be accurately described by the characteristic curves and the other (high degrees of freedom) can be approximated with these curves. The proposed UDFFF creation method has been tested with examples based on the surface models. Experience with our prototype system indicates that it allows untrained users to create UDFFFs from the surface models.

One‐step Fabrication of Nanoporous Black Silicon Surfaces for Solar Cells using Modified Etching Solution

Currently, a conventional two‐step method has been used to generate black silicon (BS) surfaces on silicon substrates for solar cell manufacturing. However, the performances of the solar cell made with such surface generation method are poor, because of the high surface recombination caused by deep etching in the conventional surface generation method for BS. In this work, a modified wet chemical etching solution with additives was developed. A homogeneous BS layer with random porous structure was obtained from the modified solution in only one step at room temperature. The BS layer had low reflectivity and shallow etching depth. The additive in the etch solution performs the function of pH‐modulation. After 16‐min etching, the etching depth in the samples was approximately 200 nm, and the spectrum‐weighted‐reflectivity in the range from 300 nm to 1200 nm was below 5%. BS solar cells were fabricated in the production line. The decreased etching depth can improve the electrical performance of solar cells because of the decrease in surface recombination. An efficiency of 15.63% for the modified etching BS solar cells was achieved on a large area, p‐type single crystalline silicon substrate with a 624.32‐mV open circuit voltage and a 77.88% fill factor.

High-order fractional partial differential equation transform for molecular surface construction.

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

High-order fractional partial differential equation transform for molecular surface construction

Abstract Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Local quasigeoid model creation from astrogeodetic measurements

This article describes the process of creation and testing of a local quasigeoid model using the astrogeodetic method known as astronomical levelling. The process used here was based on astronomical levelling principles combined with the least square adjustment in a triangular network and a common method of surface generation. Using this method, the authors have created a quasigeoid model of a small portion of the city of Brno. This model covers an area of approximately 1 × 2 km and is based on the astronomically determined vertical deflection at 11 stations. The average distance between the astrogeodetic stations was 500 m, which is an unusually high density (5.5 stations per km2). This high geo-spatial data density input made it possible to generate a quasigeoid model of height difference precision at mm-level over few km.