Free-form Surface Modeling Research Articles

CFD based aerodynamic optimization design

The CFD technology based on the N-S equation plays an extremely important role in the detailed aerodynamic shape design of the complex surface of civil aircraft. In this paper, a consistent parameterization method, response surface model and numerical optimization method are used to conclude the optimization design. The aerodynamic optimization based on CFD, the commonly used CFD methods and free-form surface modeling technology are studied, and the challenges faced in the process of aerodynamic shape optimization of civil aircraft are analyzed. The adoption of a genetic algorithm based on the response surface increases the effectiveness of the entire optimization process.The results show that the adopted design method is effective in solving the problem of complex shape optimization using computationally expensive CFD codes. The advantage of the proposed method is that it can flexibly shape the wing body design and can quickly respond to changes in design requirements during the design process; the proposed method can be used in the design of a wider range of complex aerodynamic shapes.

Generalized Riemann-Liouville fractional Bézier curve and its applications in engineering surface

Modeling of free-form curves and surfaces is vital in the manufacturing industry and engineering. Curves and surfaces that have flexible shapes and adjustable lengths and sizes are a necessity to fulfill the needs of the manufacturing industry. Hence, researchers develop numerous aesthetic Bézier curves and surfaces to have such flexibility and adjustability. In this paper, the generalized Riemann–Liouville fractional Bézier curves and surfaces are proposed in the modeling of complex surfaces. The generalized Riemann–Liouville fractional Bézier curves and surfaces have two outstanding parameters: shape and fractional parameters. Shape parameters are utilized to change the shape of the curves and surfaces without altering the control points hence, adding flexibility in controlling the shape. While fractional parameters are utilized in curves and surfaces’ length and size adjustability. By adjusting the sizes of surfaces via fractional parameters, surfaces with optimal sizes can be modeled. In this paper, five types of engineering surfaces will be modeled, namely ruled surface, swept surface, swung surface, rotation surface, and coons patch. The geometric effects of the implementation of shape and fractional parameters to these engineering surfaces will also be analyzed, thus proving the generalized Riemann–Liouville fractional Bézier surfaces is an excellent tool in designing complex surfaces.

Multi-Objective Optimization via GA Based on Micro Laser Line Scanning Data for Micro-Scale Surface Modeling

Industry 4.0 represents high-level methodologies to make intelligent, autonomous, and self-adaptable manufacturing systems. Additionally, the surface modeling technology has become a great tool in industry 4.0 for representing the surface point cloud. Thus, the micro-scale machining technology requires efficient models to represent micro-scale flat and free-form surfaces. Therefore, it is fundamental to perform surface modeling through artificial intelligence for representing small surfaces. This study addressed multi-objective optimization via genetic algorithms and micro laser line projection to accomplish surface models for representing micro-scale flat and free-form surfaces, where an optical microscope system retrieves micro-scale topography via micro laser line coordinates and the multi-objective optimization constructs the flat and free-form surface models through genetic algorithms and micro-scale topography. The multi-objective optimization determines the surface model parameters through exploration and exploitation, and the solution space is deduced via surface data. The surface model generated through the multi-objective optimization fit accurately to the micro-scale target surface. Thus, the proposed technique enhanced the fitting of micro-scale flat and free-form surface models, which were deduced via gray-level images of an optical microscope. This enhancement was validated by a discussion between the multi-objective optimization via genetic algorithms and the micro-scale surface modeling via optical microscope imaging systems.

Virtual planning and volumetric evaluation of wound healing following regenerative surgical treatment of intrabony periodontal defects

Our aim was to present a virtual surgical planning process in the regenerative treatment of intrabony periodontal defects and to evaluate volumetric and 3D morphological changes by the superimposition of pre- and post-operative cone-beam computed tomography (CBCT) datasets. Eight intrabony periodontal defects were enrolled in the present investigation. CBCT and intraoral scans (IOS) were taken prior to and 6 months after periodontal regenerative surgery. Utilizing a semi-automatic segmentation method 3D models were generated from CBCT scans using an open-source radiographic image processing software (3D Slicer). Hybrid models were acquired with the superimposition and subsequent free-form surface modeling of the segmented CBCT model and the IOS. Hybrid models visualizing all relevant anatomical structures separately (alveolar bone, teeth, soft tissues) were used to plan each step of the procedure virtually prior to surgery. Superimposition of the pre- and post-operative CBCT scans was performed to validate volumetric and 3D morphological alterations. Based on the hybrid models, periodontal defect morphology was visualized in 3D. Following healing, hard tissue fill averaged at 43.04 mm 3 ± 24.47 mm 3 . Hard tissue resorption could be detected in three cases. Hybrid models acquired with the technique allowed a better understanding of the 3D defect morphology and therefore more precise surgical planning could be performed. With the spatial registration of pre- and post-operative CBCT scans volumetric and 3D morphological alterations could be visualized that provided a better understanding of the healing dynamics.

Increasing optical pose estimation accuracy via freeform design and its application to hand-eye calibration.

For robot-assisted assembly of complex optical systems, the alignment is facilitated by an accurate pose estimation of its components. However, wavefront-based pose estimation is typically ill-conditioned due to the inherent geometry of conventional industrially manufactured optical components. Therefore, we propose a novel approach in this paper to increase wavefront-based pose estimation accuracy via the design of freeform optics. For this purpose, an optimization problem is derived that parameterizes the component's surfaces by a predetermined freeform surface model. To show the efficacy of our approach, we provide simulation results to compare the pose estimation accuracy for a variety of optical designs. As an application example for the resulting improved pose estimation, a hand-eye calibration of a wavefront sensor is performed. This calibration originates from the field of robotics and represents the identification of a sensor coordinate system with respect to a global reference frame. For quantitative evaluation, the calibrating results are first presented with the aid of simulation data. Finally, the practical feasibility is demonstrated using a conventional industrial robot and additively manufactured freeform lenses.

Cutting Force Modeling and Experimental Study for Ball-End Milling of Free-Form Surfaces

In order to improve the machining quality and efficiency and optimize NC machining programming, based on the existing cutting force models for ball-end, a cutting force prediction model of free-form surface for ball-end was established. By analyzing the force of the system during the cutting process, we obtained the expression equation of the instantaneous undeformed chip thickness during the milling process and then determined the rule of the influence of the lead angle and the tilt angle on the instantaneous undeformed chip thickness. It was judged whether the cutter edge microelement is involved in cutting, and the algorithm flow chart is given. After that, the cutting force prediction model of free-form surface for ball-end and pseudocodes for cutting force prediction were given. MATLAB was used to simulate the prediction force model. Finally, through the comparative analysis experiment of the measured cutting force and the simulated cutting force, the experimental results are basically consistent with the theoretical prediction results, which proves that the model established in this paper can accurately predict the change of the cutting force of the ball-end cutter in the process of milling free-form surface, and the error of the cutting force prediction model established in this paper is reduced by 15% compared with the traditional cutting force prediction model.

Digital Hybrid Model Preparation for Virtual Planning of Reconstructive Dentoalveolar Surgical Procedures

Virtual, hybrid three-dimensional (3D) model acquisition is presented in this article, utilizing the sequence of radiographic image segmentation, spatial registration, and free-form surface modeling. Firstly cone-beam computed tomography datasets were reconstructed with a semi-automatic segmentation method. Alveolar bone and teeth are separated into different segments, allowing 3D morphology, and localization of periodontal intrabony defects to be assessed. The severity, extent, and morphology of acute and chronic alveolar ridge defects are validated concerning adjacent teeth. On virtual complex tissue models, positions of dental implants can be planned in 3D. Utilizing spatial registration of IOS and CBCT data and subsequent free-form surface modeling, realistic 3D hybrid models can be acquired, visualizing alveolar bone, teeth, and soft tissues. With the superimposition of IOS and CBCT soft tissue, thickness above the edentulous ridge can be assessed about the underlying bone dimensions; therefore, flap design and surgical flap management can be determined, and occasional complications may be avoided.

Physically‐based Book Simulation with Freeform Developable Surfaces

AbstractReading books or articles digitally has become accessible and widespread thanks to the large amount of affordable mobile devices and distribution platforms. However, little effort has been devoted to improving the digital book reading experience, despite studies showing disadvantages of digital text media consumption, such as diminished memory recall and enjoyment, compared to physical books. In addition, a vast amount of physical, printed books of interest exist, many of them rare and not easily physically accessible, such as out‐of‐print art books, first editions, or historical tomes secured in museums. Digital replicas of such books are typically either purely text based, or consist of photographed pages, where much of the essence of leafing through and experiencing the actual artifact is lost. In this work, we devise a method to recreate the experience of reading and interacting with a physical book in a digital 3D environment. Leveraging recent work on static modeling of freeform developable surfaces, which exhibit paper‐like properties, we design a method for dynamic physical simulation of such surfaces, accounting for gravity and handling collisions to simulate pages in a book. We propose a mix of 2D and 3D models, specifically tailored to represent books to achieve a computationally fast simulation, running in real time on mobile devices. Our system enables users to lift, bend and flip book pages by holding them at arbitrary locations and provides a holistic interactive experience of a virtual 3D book.

Automatic determination of part build orientation for laser powder bed fusion

ABSTRACT In this paper, an automatic determination method of part build orientation for laser powder bed fusion is presented. This method includes two steps. First, an existing facet clustering-based approach is applied to automatically generate the alternative orientations of a laser powder bed fusion part. Second, support volume, volumetric error, surface roughness, build time and build cost are considered. Their values in each alternative orientation are estimated by certain estimation models. The weights of these factors are determined via pairwise comparison. The weighted sum model is used to calculate a summary value of the factors in each alternative orientation. According to the calculated summary values, an optimal orientation to build the part is generated. To demonstrate the method, a set of part orientation cases are tested, and effectiveness analysis and efficiency and characteristic comparisons are reported. The demonstration results suggest that the proposed method can work for both regular and freeform surface models, produce stable and reasonable results and provide desired efficiency.

Automatic generation of alternative build orientations for laser powder bed fusion based on facet clustering

ABSTRACT In this paper, a novel facet clustering based method is proposed to generate alternative build orientations for laser powder bed fusion. This method consists of two steps. First, a hierarchical clustering algorithm is applied to divide facets of the design model in standard tessellation language format into different clusters, each of which shares a similar normal vector. Second, alternatives of each cluster are computed and the final set of alternative build orientations is generated by combining and refining the alternatives from all clusters. To illustrate and validate the method, a set of examples including both regular and freeform surface models are tested, and qualitative and quantitative comparisons between the method and the existing methods are reported. The results suggest that the proposed method is feasible and effective for both regular and freeform surface parts. It is evident that the proposed method can output stable results, provide satisfying efficiency, and work well with facet clusters of varying probability density.

Optimized free-form surface modeling of point clouds from laser-based measurement

Freeform parameterizations to reproduce structure deformation are increasingly important topics in laser-scanner-based deformation analyses. High-accuracy assurance of free-form surface approximation is extremely critical for reliable deformation analysis. One main challenge in this field is the model selection. Improper model complexity could result in under-fitting the real object shape or overfitting data noises, and thus a failure of deformation analysis. A multi-sensor system could integrate advantages of different sensors and improve the quality of mission completed. This paper combines terrestrial laser scanning (TLS) and laser tracker (LT) technologies, to enhance high-accuracy surface modeling in deformation analysis. A surface-based B-spline approximation and a multi-sensor system are investigated, the latter of which focuses mainly on the combination of TLS and LT technologies. The innovation of this paper is that the surface-based B-spline approximation is validated and optimized with LT corner cube reflectors. Hypothesis testing is adopted to select the best parameter setting by judging most consistency of TLS and LT in various epochs. In the B-spline surface modeling, both instrumental and numerical uncertainties are considered. We use the instrumental uncertainty model based on intensity value, as well as numerical uncertainty based on adjustment theories. A sampling strategy is proposed to avoid data gaps and obtain even distributed data points.

Robust flow-guided neural prediction for sketch-based freeform surface modeling

Sketching provides an intuitive user interface for communicating free form shapes. While human observers can easily envision the shapes they intend to communicate, replicating this process algorithmically requires resolving numerous ambiguities. Existing sketch-based modeling methods resolve these ambiguities by either relying on expensive user annotations or by restricting the modeled shapes to specific narrow categories. We present an approach for modeling generic freeform 3D surfaces from sparse, expressive 2D sketches that overcomes both limitations by incorporating convolution neural networks (CNN) into the sketch processing workflow. Given a 2D sketch of a 3D surface, we use CNNs to infer the depth and normal maps representing the surface. To combat ambiguity we introduce an intermediate CNN layer that models the dense curvature direction, or flow, field of the surface, and produce an additional output confidence map along with depth and normal. The flow field guides our subsequent surface reconstruction for improved regularity; the confidence map trained unsupervised measures ambiguity and provides a robust estimator for data fitting. To reduce ambiguities in input sketches users can refine their input by providing optional depth values at sparse points and curvature hints for strokes. Our CNN is trained on a large dataset generated by rendering sketches of various 3D shapes using non-photo-realistic line rendering (NPR) method that mimics human sketching of free-form shapes. We use the CNN model to process both single- and multi-view sketches. Using our multi-view framework users progressively complete the shape by sketching in different views, generating complete closed shapes. For each new view, the modeling is assisted by partial sketches and depth cues provided by surfaces generated in earlier views. The partial surfaces are fused into a complete shape using predicted confidence levels as weights. We validate our approach, compare it with previous methods and alternative structures, and evaluate its performance with various modeling tasks. The results demonstrate our method is a new approach for efficiently modeling freeform shapes with succinct but expressive 2D sketches.

Research on Laser Additive and Milling Subtractive Composite Remanufacturing Process of Compressor Blade

As an important energy conversion mechanism, centrifugal compressors play an important role in the national economy. The blade is one of the most critical components of the compressor. Damaged blades contain extremely high added value for remanufacturing. Thus, remanufacturing research on damaged and retired impeller/blade is getting more and more attention. Laser additive and milling subtractive composite remanufacturing technology is an effective means to achieve metal parts remanufacturing. In this paper, an advanced methodology for the remanufacturing of complex geometry and expensive components via reverse engineering, free-form surface modeling, laser additive repaired and machining is presented. The approach involves the integration of 3D non-contact digitization to obtain the point cloud data of damaged parts, adaptive free-form surface reconstruction to get the digital model of damage location, and laser additive manufacturing process containing slicing and path planning and subsequent multi-axis milling operation. The methodology has been successfully implemented on thin-curved centrifugal compressor blades. The results have shown that the composite remanufacturing method is an effective solution to realize the remanufacturing of damaged blades, and can be applied to the remanufacturing of other complicated parts.

Isogeometric shape design optimization of nanoscale structures using continuum-based shell theory considering surface effects

Considering surface effects on nanoscale structures, an isogeometric shape optimization method is developed for curved structures using Naghdi’s shell formulation. Since the curved structures are very sensitive to geometrical changes, the geometric exactness of isogeometric approach successfully prevents the loss of higher-order geometric information in design sensitivity analysis (DSA). A direct differentiation method is employed for the DSA, where the control points are selected as the design variables and describe the flexible modeling of free-form shell surfaces. Through numerical examples, we verified the accuracy of isogeometric analysis whose framework shows better convergence rate than finite element analysis due to the exact geometry and the higher order geometric information in the DSA formulation. The surface Lamé constants turns out to alter the ratio between the portion of membrane and bending energies. Also, the optimal shape is dependent on the residual surface stress that affects its stress state.

MATEC Web of Conferences – General and efficient algorithms for handling intricate situations in trimmed surface rendering

Trimmed surfaces have been widely used in complicated product design in mechanical engineering especially in complex free form surface models of CAD/CAM/CAE. Focusing on the deficiencies of the algorithms available in published literatures when handling some intricate situations, this paper proposes a more general and efficient algorithm of trimmed surface rendering (ATSR). The ATSR is a general algorithm that can deal with most intricate situations, which frequently occur in practical engineering that no special attention has been paid to in references at hand, as well as common situations. Furthermore, this paper presents a new algorithm for the nodes of polygon connecting into elements (ANCE). The ANCE can handle most tricky polygons appearing in the process of rendering and achieve successful triangulation for the to-be-rendered surface. Preferable results are obtained in the case studies, which indicate that the algorithms (ATSR and ANCE) are efficient and effective in handling complicated as well as common trimmed surface models in real engineering industry.

Research on Preprocessing Techniques of 3D Laser Scanning Data

3D laser scanning point cloud data is the basis of free-form surface modeling technique. This paper focuses on the preprocessing of the original point cloud data. Techniques including denoising step using wavelet transform, data reduction and mending using Image ware are discussed in details. Surface reconstruction is finally achieved to demonstrate that the proposed data preprocessing methods improve the easy realization of point cloud data with higher accuracy and faster speed, and thus take a closer step towards the real applications in 3D laser scanning field.

An effective freeform surface retrieval approach for potential machining process reuse

With the increasing of the machining process data, which are the direct and effective carrier of knowledge, intelligence and experience of skilled engineers, machining process data-driven intelligent machining process planning is becoming more and more important in manufacturing industries. One of the key technologies is to retrieve the similar geometry with machining process reuse value in a fine manner. However, existing 3D CAD model retrieval methods for manufacturing reuse mainly focus on the parts composed of non-freeform surface features machined with 2 1/2-axis CNC milling, while the parts including complex freeform surfaces accounted for a large proportion are little involved. In this paper, a novel freeform surface retrieval approach for potential machining process reuse is presented. First, similar tensor field pattern freeform surface feature is introduced to represent the complex freeform surface into structured freeform surface model. Then, freeform surface content code for accelerating freeform surface retrieval is given to filter out unmatched freeform surfaces efficiently. Moreover, the principal pathline indicating the overall evolution trend of feature pathlines is extracted and represented using D2 shape descriptor to establish the feature similarity assessment model. Finally, sub-graph isomorphism-based matched feature pairs extraction algorithm is presented to calculate the similarity between matched freeform surfaces. A prototype system based on CATIA has been developed to verify the effectiveness of the proposed approach.

Bivariate splines over triangular meshes for freeform surface modeling with sharp features

ABSTRACTThis paper presents a novel scheme for constructing bivariate spline surfaces over triangular meshes which are topologically equivalent to a disk. The core part of the scheme is a set of knot selection rules that define local configurations of a triangulation called the directed-one-ring-cycle (D1RC) configurations and bivariate splines defined over a D1RC configuration that are new non-tensor-product splines and possess many nice properties of a univariate B-spline. Using D1RC splines, we take an input triangular mesh as a control mesh and define a bivariate spline surface from the control mesh, which mimics the standard NURBS modeling. Moreover, we can introduce sharp features into the overall smooth spline surface by simply setting special D1RC configurations. As a result, the proposed scheme can define spline surfaces in a way similar to that of NURBS, but has less restriction on the connectivity of the input control mesh.

Approximation of minimal toric Bézier patch

Toric Bézier patches are a multi-sided generalization of classical rational Bézier patches which are widely used in free-form surface modeling. In this article, we study the problem of finding the patch with minimal area among all possible toric Bézier patches with the given boundaries, that is, the Plateau–toric Bézier problem, and obtain an approximation of minimal toric Bézier patch. Some representative examples are given to verify our results.

Modeling of Complex and Freeform Surfaces by using Reverse Engineering Approach

Reverse Engineering is extensively used technology by both research and industries for rapid development of product. In Reverse engineering with the help of already, existing product a new product is developed. To develop a new product CAD model is necessary. For this purpose already existing object is scanned using CMM machine, laser scanner etc. Output of Scanner is Point cloud data. It is big challenge to get CAD model from point cloud data. Various techniques called segmentation technique are available to convert point cloud in to surface or solid geometry. This paper reviews the reverse engineering and various segmentation techniques from the literature. Case study carried out to convert point cloud data in to CAD model by using FreeCAD Software.