Surface Generation Method Research Articles

Derived Metric Tensors for Flow Surface Visualization.

Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.

An adaptive potential energy surface generation method using curvilinear valence coordinates

An automatic Born-Oppenheimer potential energy surface (PES) generation method AGAPES is presented designed for the calculation of vibrational spectra of large rigid and semi-rigid polyatomic molecules within the mid-infrared energy range. An adaptive approach guided by information from intermediate vibrational calculations in connection with a multi-mode expansion of the PES in internal valence coordinates is used and its versatility is tested for a selection of molecules: HNO, HClCO, and formaldoxime. Significant computational savings are reported. The possibility of linear scaling of the sampling grid size with the molecular size due to decrease of correlation of remote coordinates in large molecules is examined and finally, possible improvements are suggested.

Biomolecular surface construction by PDE transform.

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson-Nernst-Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable, and efficient approach for biomolecular surface generation in Cartesian meshes.

A Traditional Quadrilateral NURBS Surfaces Generation Method using MATLAB

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

An experimental study of contact pressure distribution in panel stamping operations

This paper presents an analysis of the dynamic contact pressure distribution at the sheet metal-tooling interface in normal and defective panel stamping operations. Specifically, the stamping of a 1.27 × 20 × 15 cm rectangular aluminum alloy panel has been simulated using finite-element modeling methods. The modeling results are leveraged to determine the forces acting on sensors embedded in the die structure. Based on these results, a customized stamping test bed has been designed, which incorporates an array of force sensors embedded into the stamping die to enable online measurement of the forces in the die. The force measurements are processed by the thin plate spline numeric surface interpolation method to evaluate a continuous contact pressure distribution map of the die cavity. The pressure distribution in the die cavity in normal and defective scenarios has been presented along with a suggested volume thresholding method for automated defect detection. By leveraging the numeric surface generation method to analyze experimental data, the present study establishes the basis for intelligent tooling and in-process monitoring for improved observability in sheet metal stamping.

TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique.

Qualified, stable, and efficient molecular surface meshing appears to be necessitated by recent developments for realistic mathematical modeling and numerical simulation of biomolecules, especially in implicit solvent modeling (e.g., see a review in B. Z. Lu et al. Commun. Comput. Phys. 2008, 3, 973-1009). In this paper, we present a new method: tracing molecular surface for meshing (TMSmesh) the Gaussian surface of biomolecules. The method computes the surface points by solving a nonlinear equation directly, polygonizes by connecting surface points through a trace technique, and finally outputs a triangulated mesh. TMSmesh has a linear complexity with respect to the number of atoms and is shown to be capable of handling molecules consisting of more than one million atoms, which is usually difficult for the existing methods for surface generation used in molecular visualization and geometry analysis. Moreover, the meshes generated by TMSmesh are successfully tested in boundary element solutions of the Poisson-Boltzmann equation, which directly gives rise to a route to simulate electrostatic solvation of large-scale molecular systems. The binary version of TMSmesh and a set of representative PQR benchmark molecules are downloadable at our Web page http://lsec.cc.ac.cn/∼lubz/Meshing.html .

An interior surface generation method for all-hexahedral meshing

This paper describes an all-hexahedral generation method focusing on how to create interior surfaces. It is well known that a solid homeomorphic to a ball with even number of bounding quadrilaterals can be partitioned into a compatible hexahedral mesh where each associated hexahedron corresponds to the intersection of three interior surfaces that are dual to the original hexahedral mesh. However, no such method for creating dual interior surfaces has been developed for generating all-hexahedral meshes of volumes covered with simply connected quadrilaterals. We generate an interior surface as an orientable regular homotopy (or more definitively a sweep) by splitting a dual cycle into several pieces at self-intersecting points and joining the three connected pieces, if the self-intersecting point-types are identical, while we generate a non-orientable surface (containing Mobius bands) if the self-intersecting point-types are distinct. Stitching these simple interior surfaces together allows us to compose more complex interior surfaces. Thus, we propose a generalized method of generating a hexahedral mesh topology by directly creating the interior surface arrangement. We apply the present framework to Schneiders’ open pyramid problem and show an arrangement of interior surfaces that decompose Schneiders’ pyramid into 146 hexahedra.

On-line measurement of contact pressure distribution at tool–workpiece interfaces in manufacturing operations

A new method is proposed for determining the contact pressure distribution (CPD) between the tool and the workpiece in sheet metal forming processes. Contact pressure is measured at discrete points at the tool–workpiece interface by sensors that are structurally embedded beneath the tooling surface. An analytical framework is developed for determining the pressure values between the sensing points through the construction of continuous CPD maps. This is achieved using the Thin Plate Spline (TPS) surface generation method, which creates temporal snapshots of the CPD during a forming process. The effectiveness of this technique is illustrated for a panel stamping operation.

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

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

Utilisation du quadrangle « discrete shear » pour la génération des surfaces d’influence des efforts de plaque

Concept of influence surface is the appropriate tool to determine the extreme structural response values of structures under the effect of moving loads. The action of road traffic moving on bridge deck is computed this way. Influence surface generation method is based on Maxwell-Betti’s theorem of reciprocity. This paper presents the use of the « discrete shear » formulation of a thick plate quadrangle finite element to generate the influence surfaces of internal forces in a slab bridge using the Code_Aster free software.

Direct generation method of NURBS boundary surface

Because of the complexity of Non-Uniform Rational B-splines (NURBS) surface, the conventional NURBS surface generation method usually first constructs a Coons surface and then changes it into NURBS surface, which adds the operation complexity. To address this problem, an NURBS boundary surface direct generation method was proposed, which can directly construct a NURBS boundary surface by using four NURBS boundary curves. Compared with the traditional method,it need not convert Coons surface to NURBS surface and have a low computing cost. The experiments show the proposed method is simple and convenient, but the generated surface still has a high quality and good continuity.

Geometric parameter optimization in multi-axis machining

This paper presents a systematic method for the determination of optimal geometric machining parameters in multi-axis machining. Machining accuracy is considered to be determined by a set of geometric parameters: the design parameters of the cutter, the positioning of the cutter, the orientation of the cutter etc. First, we formulate the general nonlinear constrained optimization model of the machining process. The optimal machining result is expected to produce the least deviation between the designed surface and the actual surface. This objective is accomplished by minimizing the deviation between the designed surface and the actual surface during machining. The details of how to characterize and calculate the deviation is then discussed for both ruled surface milling and general free-form surface milling. The swept surface is developed based on robotic manipulation and is used to model the actual surface. A signed distance function is constructed to perform the comparison which returns the signed distance from each sampled point to the designed surface. The direct search algorithm (Nelder–Mead simplex algorithm and pattern search algorithm in this paper) is used to solve our optimization problems due to possible discontinuity of the objective function and large nonlinearity of the problem. Three numerical examples and necessary comparisons are given to demonstrate the effectiveness of our method. The first example shows the generation of the swept volume of a filled-end cutter. The second example employs the swept surface generation method to solve a parameter optimization problem. Sensitivity analysis is performed for the parameters critical to machining accuracy. The third example optimizes the cutter orientation relative to the part surface to minimize the kinematics error caused by kinematics transformation and interpolation of multi-axis machines.

Precision Grinding of Concave Spherical Surface of High-Alumina

The performances of high-alumina ceramic are analyzed such as physical and mechanical property. In consideration of its brittleness-ductility change, the critical cutting depth agc of high-alumina ceramic is 3μm. When the cutting depth of single grain is less than the critical cutting depth of alumina ceramic in precision manufacturing, the material is wiped off with ductility. So the cutting depth of single grain agm should be selected within 0.1~2.5μm.Grinding wheel sharp edge is utilized for the spherical surface generation cutting. The ceramic-bonded fine grain diamond wheel is selected after considering manufacturing technology, machining parameters, its making and mending. The granularity of grinding wheel is M1~M5 and the consistence is 125%. The method of spherical surface generation cutting and the effect of high-alumina ceramic ductile machining were verified by the experiment of high-alumina ceramic precision grinding using precision grinding machine MGK1420. The result shows that the surface quality is very high and achieves the requirements.

An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis

An improved harmony search algorithm is proposed which is found to be more efficient than the original harmony search algorithm for slope stability analysis. The effectiveness of the proposed algorithm is examined by considering several published cases. The improved harmony search method is applied to slope stability problems with five types of procedure for generating trial slip surfaces. It is demonstrated that the improved harmony search algorithm is efficient and effective for the minimization of factors of safety for various difficult problems, and the method of generating the trial failure surfaces can be important in the minimization process.

A novel method for mathematical modeling of a form-cutting-tool of the optimum design

A method that pertains to design of the optimal form-cutting-tool for machining of a given sculptured surface on a multi-axis NC machine is discussed in the paper. The results reported in the paper are based in much on the author’s previous work in the field of R -mapping of a sculptured surface onto the machining surface of cutting tools. Mathematical foundations of a novel method of experimental modeling of the interaction of the form-cutting-tool and the work are disclosed. The last method is of critical importance for the experimental determination of the rate of conformity functions, those essential for consequent use of R -mapping of surfaces. The presented geometric criteria is helpful for designers since the maximal rate of conformity of the generating surface of the form-cutting-tool to the sculptured surface is a prerequisite for the development of extremely efficient machining operations, and in solving design problems. The results of the research reported in this paper can be considered as a portion of the DG/K -method of surface generation on a multi-axis NC machine earlier developed 1 The DG/K -method of surface generation is based on fundamental results obtained in differential geometry of surfaces and in kinematics of multi-parametric motion of a rigid body in E 3 space (See: Radzevich, S.P., Sculptured Surface Machining on Multi-Axis NC Machine. Monograph , Kiev, Vishcha Shkola Publishers, 1991, 192p. – Copy of the monograph is available from the library of congress, and Radzevich, S.P., Fundamentals of Surface Generation. Monograph , Kiev, Rastan, 2001, 592p. – Copy of the monograph is available from The Library of Congress). 1 by the author. The method is based on the extensive use of reliable results worked out in classical differential geometry of surfaces. Topics covered in the paper enables one designing the form-cutting-tool for optimal machining of a given sculptured surface on a multi-axis NC machine. The usefulness of the approach is verified from two simple examples that are clear and easy for understanding.

On Satisfaction of the Fifth Necessary Condition of Proper Part Surface Generation in Design of Plunge Shaving Cutter for Finishing of Precision Involute Gears

In this paper, a novel modified scheme and effective computer representation for design of a plunge shaving cutter is presented. The paper aims to develop a novel design of shaving cutter for plunge shaving of precision involute gears. The study is carried out on the premise of satisfaction of the fifth necessary condition of proper part surface generation (PSG) when designing the plunge shaving cutter. In the current study, the author’s earlier developed DG/K method of surface generation is used together with the principal elements of analytical mechanics of gears. (The DG/K method is based on fundamental results obtained in differential geometry of surfaces, and on kinematics of multi-parametric motion of a rigid body in the E3 space. The interested reader may wish to go for details to the monograph: Radzevich, S.P., Fundamentals of Surface Generation, Monograph, Kiev, Rastan, 2001, 592 pp., and to: Radzevich, S.P., Sculptured Surface Machining on Multi-Axis NC Machine, Monograph, Kiev, Vishcha Schola, 1991, 192 pp.) In the particular case under consideration, the method employs (a) an analytical description of the gear tooth surface to be machined, (b) configuration of the plunge shaving cutter relative to the involute gear, (c) analytical representation of the coordinate systems transformations, and (d) the fifth condition of proper PSG that is adapted to finishing of precision involute gears. The fifth condition of proper PSG is investigated in the paper. On the premise of the obtained results of the investigation, a novel design of plunge shaving cutter for finishing of precision involute gears is proposed. The developed novel design of plunge shaving cutter can be used on shaving machines available on the market, e.g. on Gleason’s new Genesis™ 130SV computer numerical control (CNC) shaving machine.

Validity of Hybrid Models for the Bidirectional Reflectance of Coated Rough Surfaces

Modeling of the bidirectional reflectance of thin-film coatings on rough surfaces has been an important and challenging problem. In the past, there have been studies that use thin-film optics to take account of the coating-induced interference effects and the geometric optics approximation to model the surface roughness. In an effort to delineate the validity regime of the hybrid method, the predicted bidirectional reflectance is compared with that obtained from the rigorous electromagnetic-wave solution for one-dimensional rough surfaces, considering the effect of coating thickness and roughness parameters. Two hybrid models are implemented using the Monte Carlo ray-tracing algorithm: the surface generation method and microfacet slope method. The former relies on statistically generated surfaces according to the root-mean-square roughness and the autocorrelation length, whereas the latter uses the microfacet whose orientation is stochastically determined, when a ray hits the surface, according to the slope distribution without creating deterministic rough surfaces a priori. The validity regimes of the hybrid models are established for silicon dioxide films on silicon substrates. The advantages and disadvantages of each hybrid model are discussed. Some useful guidelines are provided for the simulation of optical scattering from coated rough surfaces.

Interactive design using higher order PDEs

This paper extends the PDE method of surface generation. The governing partial differential equation is generalised to sixth order to increase its flexibility. The PDE is solved analytically, even in the case of general boundary conditions, making the method fast. The boundary conditions, which control the surface shape, are specified interactively, allowing intuitive manipulation of generic shapes. A compact user interface is presented which makes use of direct manipulation and other techniques for 3D interaction.

On harmonic and biharmonic Bézier surfaces

We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bézier surfaces. The main result we report here is that any biharmonic Bézier surface is fully determined by the boundary control points. We compare the new method, by way of practical examples, with some related methods such as surfaces generation using discretisation masks and functional minimisations.

Structural MR image processing using the brains2 toolbox

Medical imaging has opened a new door into biomedical research. In order to study various diseases of the brain and detect their impact on brain structure, robust and user friendly image processing packages are required. These packages must be multi-faceted to distinguish variations in size, shape, volume, and the ability to detect longitudinal changes over the course of an illness. This paper describes the brains2 image processing package, which contains both manual and automated tools for structural identification, methods for tissue classification and cortical surface generation. These features are described in detail, as well as the reliability of these procedures.