Nonuniform Rational B-splines Model Research Articles

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

SummaryAn efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR) is proposed to construct mapping between the mesh before modification and after modification during the optimization process. Subsequently, MG‐IGR is utilized to reanalyze the modified design efficiently by reusing the initial evaluated results. Moreover, the proposed MG‐IGR also eliminates the restriction of mesh consistency. In this framework, the structure can be designed directly through parameterized control of the non‐uniform rational B‐spline (NURBS) model, and the MG‐IGR fast solver enables any metaheuristic algorithm to perform the optimization procedure. Moreover, the accuracy of the simulation can be guaranteed by the NURBS model and the convergence criterion of the MG. Finally, two geometric optimization examples are presented to validate the performance of the developed framework.

Optimized Design Method for Profile Extrusion Die Based on NURBS Modeling

For optimization design of polymer extrusion dies, dimensional accuracy is critical to product quality of the extrudate. The extrusion dies used to be a regular geometrical profile, which is mostly composed by a straight line. Traditional optimization methods for extrusion die design used to have poor controllability when dealing with a curved profile. In this paper, the response surface optimization method is used to find out an optimal solution of the design of the extrusion die. Firstly, the Latin Hypercube Sampling method is used to generate the experiment samples for the design of experiments. Secondly, ANSYS Polyflow software is adopted to execute the computational fluid dynamics analysis. Thirdly, the Kriging method is used to generate the response surface. Finally, nonlinear programming by using Quadratic-Lagrangian algorithm is applied to find out the optimal solution. It is worth noting that Non-uniform Rational B-Splines (NURBS) modeling is used to optimize flow channel of an extrusion die in order to obtain a qualified extrudate. Thus, design variables for the optimization involve control points of the NURBS curve of the inlet cross-section. Meanwhile, two new objective functions, including minimization of point displacement and minimization of dimensional tolerance are proposed in the optimization process. Compared with existing objective functions of flow balancing and homogeneous die swell, the new objective functions of minimization of point displacement and minimization of dimensional tolerance have significant advantages of strong adaptability, more precise shape of the extrudate and fast convergence, which significantly improve efficiency of the optimization design and thus lower manufacturing costs of the extrusion die.

Real-Time Visual Tracking of Dynamic Surgical Suture Threads.

In order to realize many of the potential benefits associated with robotically assisted minimally invasive surgery, the robot must be more than a remote controlled device. Currently, using a surgical robot can be challenging, fatiguing, and time consuming. Teaching the robot to actively assist surgical tasks, such as suturing, has the potential to vastly improve both patient outlook and the surgeon's efficiency. One obstacle to completing surgical sutures autonomously is the difficulty in tracking surgical suture threads. This paper presents novel stereo image processing algorithms for the detection, initialization, and tracking of a surgical suture thread. A Non Uniform Rational B-Spline (NURBS) curve is used to model a thin, deformable, and dynamic length thread. The NURBS model is initialized and grown from a single selected point located on the thread. The NURBS curve is optimized by minimizing the image matching energy between the projected stereo NURBS image and the segmented thread image. The algorithms are evaluated using suture threads, a calibrated test pattern, and a simulated thread image. Additionally, the accuracy of the algorithms presented are validated as they track a suture thread undergoing translation, deformation, and apparent length changes. All of the tracking is in real-time. Note to Practioners: Abstract-The problem of tracking a surgical suture thread was addressed in this work. Since the suture thread is highly deformable, any tracking algorithm must be robust to intersections, occlusions, knot tying, and length changes. The detection algorithm introduced in this paper is capable of distinguishing different threads when they intersect. The tracking algorithm presented here demonstrate that it is possible, using polynomial curves, to track a suture thread as it deforms, becomes occluded, changes length, and even ties a knot in real time. The detection algorithm can enhance directional thin features while the polynomial curve modeling can track any string like structure. Further integration of the polynomial curve with a feed-forward thread model could improve the stability and robustness of the thread tracking.

Research on Security Assessment of Highway Slope Protection by using NURBS modeling: an Ecological Perspective

Virtual reality means that people use the computer to visualize complex data and realtime interaction. In this paper, the authors proposed a 3D geological modeling for slope engineering by using Non-Uniform Rational B-Splines (NURBS) surface function. By analyzing the commonly used 3D data structure, we construct a 3D solid modeling of complex slope, which combined with the advantages of NURBS surface and B-Rep entity. The results show that the realization of 3D geological visualization can be used as the decision basis for the slope engineering construction. At the same time, the author analyzed the greening slope that could prevent water and soil loss, and put forward the importance of slope greening protection from the view of ecological protection.

NURBS modeling and isogeometric shell analysis for complex tubular engineering structures

We present an approach to construct NURBS (Non-Uniform Rational B-Splines) surfaces for tubular engineering structures. Isogeometric shell analysis using degenerated NURBS elements for tubular structures is also presented. We developed an automatic and simple algorithm to reconstruct multiple $$C^0$$ continuous NURBS surfaces using the skeleton withdrawn from the trimmed CAD model. Isogeometric shell analysis based on Reissner–Mindlin theory was applied to the reconstructed model. To verify the efficiency of the present method, we constructed the CAD model of the car body of an electric car and simulate the deformation of an electric car using isogeometric shell analysis.

NURBS-based geometric inverse reconstruction of free-form shapes

In this study, a geometric inverse algorithm is proposed for reconstructing free-form shapes (curves and surfaces) in space from their arbitrary perspective images using a Non-Uniform Rational B-Spline (NURBS) model. In particular, NURBS model is used to recover information about the required shape in space. An optimization problem is formulated to fit the NURBS to the digitized data in the images. Control points and weights are treated as the decision variables in the optimization process. The 3D shape reconstruction problem is reduced to a problem that comprises stereo reconstruction of control points and computation of the corresponding weights. The correspondence between the control points in the two images is obtained using a third image. The performance of the proposed algorithm was validated by taking several examples based on the synthetic and real images. Comparisons were made with a point-based method in terms of various types of errors.

Automatic Initialization and Dynamic Tracking of Surgical Suture Threads.

In order to realize many of the potential benefits associated with robotically assisted minimally invasive surgery, the robot must be more than a remote controlled device. Currently using a surgical robot can be challenging, fatiguing, and time consuming. Teaching the robot to actively assist surgical tasks, such as suturing, has the potential to vastly improve both patient outlook and the surgeon's efficiency. One obstacle to completing surgical sutures autonomously is the difficulty in tracking surgical suture threads. This paper proposes an algorithm which uses a Non-Uniform Rational B-Spline (NURBS) curve to model a suture thread. The NURBS model is initialized from a single selected point located on the thread. The NURBS curve is optimized by minimizing the image match energy between the projected stereo NURBS image and the segmented thread image. The algorithm is able to accurately track a suture thread as it translates, deforms, and changes length in real-time.

Fitting NURBS using separable least squares techniques

We consider the problem of fitting a non-uniform rational B-spline (NURBS) curve to a set of data points by determining the control points and the weights using techniques aimed for solving separable least squares problems. The main technique under consideration is the variable projection method which utilises that the NURBS model depends linearly on its control points but non-linearly on the weights. The variable projection method can be used with the Gauss-Newton algorithm but also with Newton’s algorithm. We investigate the efficiency of the different algorithms when fitting NURBS and observe that the variable projection methods do not perform as well as reported for its use on, e.g., exponential fitting problems.

Development of a Rat Computational Phantom Using Boundary Representation Method for Monte Carlo Simulation in Radiological Imaging

Computational models for small experimental animals are important in medical imaging and radiation dosimetry researches. The boundary representation method by use of nonuniform rational B-splines (NURBS) is adopted in this paper to develop a rat computational phantom based on the previously obtained segmentation data for cryosectional color photographic images of an adult male Sprague-Dawley rat. Continuous two-dimensional contours for a total of 14 major structures were outlined from the downscaled anatomical atlas, corresponding to a voxel size of 0.2 times 0.2 times 0.2 mm3 and stacked to reconstruct the three-dimensional (3-D) shapes. The NURBS model was then appropriately fitted through the surface of each organ. Monte Carlo simulation of cone beam X-ray computed tomography was performed focusing on the thorax region to demonstrate the usefulness of the computational phantom in radiological imaging. The integrated whole-body geometry is presented with smooth internal and exterior boundaries. Organ centroid coordinates and volume information are tabulated for future comparison purposes. The rat phantom can be used in 3-D dose calculation and other computational applications as well.

SU-FF-J-107: 4D Predictive Patient-Specific Anatomical Model Based On 4D CT Data: A Feasibility Study

Purpose: To construct a patient‐specific 4D predicting geometry model based on 4D CT data. Material and methods: Patient's contours were re‐sampled and reconstructed using Non‐Uniform Rational B‐Spline (NURBS) surface. The breathing curve associated with the patient was predicted using Kalman filter and fitted using precise cosine functions. The 4D NURBS model was generated using 3D NURBS surface models in different phases. Results: The percent differences of the volume and the distances of the COM (center of mass) for all structures in phase P0 and P50 shows the model accurate within 5% for volume and 1 mm in three x, y, z directions. With the expense of sampling and reconstructing time, the percentage difference can be further improved. Conclusion: This study demonstrated the feasibility of constructing a patient‐specific 4D predicting geometry model based on 4D CT data. The model was controlled by the patient's breathing curve. Since the breathing curve can be predicted using the Kalman filter and approximated using the cosine function, the model is predictive of patient's lung motion. NURBS control points can reconstruct the anatomical deformations precisely and quickly with affordable computing power and time, therefore, the model has the potential for real‐time controlling and guiding of the radiation delivery.

A general, accurate procedure for calculating molecular interaction force

The determination of molecular interaction forces, e.g., van der Waals force, between macroscopic bodies is of fundamental importance for understanding sintering, adhesion and fracture processes. In this paper, we develop an accurate, general procedure for van der Waals force calculation. This approach extends a surface formulation that converts a six-dimensional (6D) volume integral into a 4D surface integral for the force calculation. It uses non-uniform rational B-spline (NURBS) surfaces to represent object surfaces. Surface integrals are then done on the parametric domain of the NURBS surfaces. It has combined advantages of NURBS surface representation and surface formulation, including (1) molecular interactions between arbitrary-shaped objects can be represented and evaluated by the NURBS model further common geometries such as spheres, cones, planes can be represented exactly and interaction forces are thus calculated accurately; (2) calculation efficiency is improved by converting the volume integral to the surface integral. This approach is implemented and validated via its comparison with analytical solutions for simple geometries. Calculation of van der Waals force between complex geometries with surface roughness is also demonstrated. A tutorial on the NURBS approach is given in Appendix A.

MODELING WITH NURBS SURFACES USED FOR THE CALCULATION OF RCS

In this paper, the edge-facet model is transformed to the Non-Uniform Rational B-Spline (NURBS) model. The parameters of the knot vectors and the control points of NURBS are computed based on the data points on the surface of a target, and the NURBS model is constructed with the parameters. The degrees of the two parametric directions of a NURBS surface and the B-spline basis function are also analyzed. The relative errors between the NURBS models and the real models prove that the modeling method proposed in this paper is exact. Finally, the results of the Radar Cross Section (RCS) computed by the Physical Optics (PO) method with NURBS models are illustrated, and the results prove that the modeling method is of high precision and can be widely used in computational electromagnetics techniques.

Shape Reconstruction of Three-Dimensional Conducting Curved Plates Using Physical Optics, NURBS Modeling, and Genetic Algorithm

A microwave inverse scattering problem including a method for shape reconstruction of three-dimensional electrically large conducting patches with simple geometries using genetic algorithm is presented. Unknown shape reconstruction algorithm starts from the knowledge of the simulated radar cross-section (RCS) data through back-scattering far-field computation using physical optics approximation. The forward problem involves the computation of the multiple-frequency and multiple-direction RCS of three-dimensional large conducting patches modeled by nonuniform rational B-spline (NURBS) surfaces. The control points of NURBS are the geometrical parameters, which are optimized for the shape reconstruction procedure. The extended stationary phase method and critical cases, which occur in physical optics computations in the forward problem, are also discussed. Noise effect and the influence of increment in the number of control points of a NURBS over the inversion algorithm are investigated as well. Numerical results are presented to verify the operation of the proposed algorithm

Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model

Analytical reconstruction of 3D curves from their stereo images is an important issue in computer vision. We present an optimization framework for such a problem based on a nonuniform rational B-spline (NURBS) curve model that converts reconstruction of a 3D curve into reconstruction of control points and weights of a NURBS representation of the curve, accordingly bypassing the error-prone point-to-point correspondence matching. Perspective invariance of NURBS curves and constraints deduced on stereo NURBS curves are employed to formulate the 3D curve reconstruction problem into a constrained nonlinear optimization. A parallel rectification technique is then adopted to simplify the constraints, and the Levenberg-Marquardt algorithm is applied to search for the optimal solution of the simplified problem. The results from our experiments show that the proposed framework works stably in the presence of different data samplings, randomly posed noise, and partial loss of data and is potentially suitable for real scenes.