Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.This research work has received funding from the project PDE-GIR (Partial Differential Equations for Geometric modelling, Image processing, and shape Reconstruction) of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 778035, the Spanish Ministry of Economy and Competitiveness (Computer Science National Program) under Grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE), and the project #JU12, jointly supported by public body SODERCAN of the Regional Government of Cantabria and European Funds FEDER (SODERCAN/FEDER UE). We also thank Toho University, Nihon University, and the Symmetry 2018, 10, 58 23 of 25 University of Cantabria for their support to conduct this research wor

Isogeometric Design, Analysis and Optimisation of Lattice-Skin Structures

The advancements in additive manufacturing techniques enable novel designs using lattice structures in mechanical parts, lightweight materials, biomaterials and so forth. Lattice-skin structures are a class of structures that couple thin-shells with lattices, which potentially combine the advantages of the thin-shell and the lattice structure. A new and systematic isogeometric analysis approach that integrates the geometric design, structural analysis and optimisation of lattice-skin structures is proposed in the dissertation. In the geometric design of lattice-skin structures, a novel shape interrogation scheme for splines, specifically subdivision surfaces, is proposed, which is able to compute the line/surface intersection efficiently and robustly without resorting to successive refinements or iterations as in Newton-Raphson method. The line/surface intersection algorithm involves two steps: intersection detection and intersection computation. In the intersection detection process, a bounding volume tree of k-dops (discrete oriented polytopes) for the subdivision surface is first created in order to accelerate the intersection detection between the line and the surface. The spline patches which are detected to be possibly intersected by the line are converted to Bézier representations. For the intersection computation, a matrix-based algorithm is applied, which converts the nonlinear intersection computation into solving a sequence of linear algebra problems using the singular value decomposition (SVD). Finally, the lattice-skin geometry is generated by projecting selected lattice nodes to the nearest intersection points intersected by the lattice edges. The Stanford bunny example demonstrates the efficiency and accuracy of the developed algorithm. The structural analysis of lattice-skin structures follows the isogeometric approach, in which the thin-shell is discretised with spline basis functions and the lattice structure is modelled with pin-jointed truss elements. In order to consider the lattice-skin coupling, a Lagrange multiplier approach is implemented to enforce the displacement compatibility between the coupled lattice nodes and the thin-shell. More importantly, the parametric coordinates of the coupled lattice nodes on the thin-shell surface are obtained directly from the lattice-skin geometry generation, which integrates the design and analysis process of lattice-skin structures. A sandwich plate example is analysed to verify the implementation and the accuracy of the lattice-skin coupling computation. In addition, a SIMP-like lattice topology optimisation method is proposed. The topology optimisation results of lattice structures are analysed and compared with several examples adapted from the benchmark examples commonly used in continuum topology optimisation. The SIMP-like lattice topology optimisation proposed is further applied to optimise the lattice in lattice-skin structures. The lattice-skin topology optimisation is fully integrated with the lattice-skin geometry design since the sensitivity analysis in the proposed method is based on lattice unit cells which are inherited from the geometry design stage. Finally, shape optimisation of lattice-skin structures using the free-form deformation (FFD) technique is studied. The corresponding shape sensitivity of lattice-skin structures is derived. The geometry update of the lattice-skin structure is determined by the deformation of the FFD control volume, and in this process the coupling between lattice nodes and the thin-shell is guaranteed by keeping the parametric coordinates of coupled lattice nodes which are obtained in the lattice-skin geometry design stage. A pentagon roof example is used to explore the combination of lattice topology optimisation and shape optimisation of lattice-skin structures

Accurate Real-Time Framework for Complex Pre-defined Cuts in Finite Element Modeling

PhD ThesisAchieving detailed pre-defined cuts on deformable materials is vitally pivotal for many commercial applications, such as cutting scenes in games and vandalism effects in virtual movies. In these types of applications, the majority of resources are allocated to achieve high-fidelity representations of materials and the virtual environments. In the case of limited computing resources, it is challenging to achieve a convincing cutting effect. On the premise of sacrificing realism effects or computational cost, a considerable amount of research work has been carried out, but the best solution that can be compatible with both cases has not yet been identified. This doctoral dissertation is dedicated to developing a unique framework for representing pre-defined cuts of deformable surface models, which can achieve real-time, detailed cutting while maintaining the realistic physical behaviours. In order to achieve this goal, we have made in-depth explorations from geometric and numerical perspectives. From a geometric perspective, we propose a robust subdivision mechanism that allows users to make arbitrary predetermined cuts on elastic surface models based on the finite element method (FEM). Specifically, after the user separates the elements in an arbitrary manner (i.e., linear or non-linear) on the topological mesh, we then optimise the resulting mesh by regenerating the triangulation within the element based on the Delaunay triangulation principle. The optimisation of regenerated triangles, as a process of refining the ill-shaped elements that have small Aspect Ratio, greatly improves the realism of physical behaviours and guarantees that the refinement process is balanced with real-time requirements. The above subdivision mechanism can improve the visual effect of cutting, but it neglects the fact that elements cannot be perfectly cut through any pre-defined trajectories. The number of ill-shaped elements generated yield a significant impact on the optimisation time: a large number of ill-shaped elements will render the cutting slow or even collapse, and vice versa. Our idea is based on the core observation that the producing of ill-shaped elements is largely attributed to the condition number of the global stiffness matrix. Practically, for a stiffness matrix, a large condition number means that it is almost singular, and the calculation of its inverse or the solution of a system of linear equations are prone to large numerical errors and time-consuming. It motivates us to alleviate the impact of condition number of the global stiffness matrix from the numerical aspects. Specifically, we address this issue in a novel manner by converting the global stiffness matrix into the form of a covariance matrix, in which the number of conditions of the matrix can be reduced by exploiting appropriate matrix normalisation to the eigenvalues. Furthermore, we investigated the efficiency of two different scenarios: an exact square-root normalisation and its approximation based on the Newton-Schulz iteration. Experimental tests of the proposed framework demonstrate that it can successfully reproduce competitive visuals of detailed pre-defined cuts compared with the state-of-the-art method (Manteaux et al. 2015) while obtaining a significant improvement on the FPS, increasing up to 46.49 FPS and 21.93 FPS during and after the cuts, respectively. Also, the new refinement method can stably maintain the average Aspect Ratio of the model mesh after the cuts at less than 3 and the average Area Ratio around 3%. Besides, the proposed two matrix normalisation strategies, including ES-CGM and AS-CGM, have shown the superiority of time efficiency compared with the baseline method (Xin et al. 2018). Specifically, the ES-CGM and AS-CGM methods obtained 5 FPS and 10 FPS higher than the baseline method, respectively. These experimental results strongly support our conclusion which is that this new framework would provide significant benefits when implemented for achieving detailed pre-defined cuts at a real-time rate

Automated CAD Model Generation for Structural Optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this translation either can be performed semi-manually or fails to reserve the structural optimality found by the structural optimisation due to the intrinsic difference in geometric representation between finite element mesh and CAD model. This thesis propose a fully automated and topologically accurate approach to synthesise structurally sound parametric CAD models from topology-optimised finite element models to fill the long-existing gap between structural optimisation and CAD systems. This approach successfully preserves the optimal structural performance during the mesh-CAD conversion. The solution provided in this thesis is to first convert the topology-optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology-optimised structure into an optimal spatial frame structure is accomplished in several steps. The first step is to generate a one-voxel-wide voxel chain model from the topology-optimised voxel model using a topology-preserving skeletonisation algorithm from digital topology. The undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with the proposed graph algorithms. Subsequently, the cross-sections and layout of the frame members are optimised to recover its optimality, which may have been compromised during the conversion process. At last, the obtained frame structure is generated in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces. The numerical studies in this thesis clarify that the converted spatial frame structures are with equivalent structural performance. Moreover, CAD models generated from the spatial frame structures have significantly fewer geometric degree of freedom compared to the topology-optimised structures. Though the numerical studies use topology-optimised structures as input and compact CSG models as output, this thesis also provides the way to extend the proposed generation process to taking other optimised meshes and producing outputs of various geometric representations. This offers a wide range of possible applications and brings new thoughts to industrial design and manufacturing.Chinese Scholarship Counci

A Parametrization-Based Surface Reconstruction System for Triangular Mesh Simplification with Application to Large Scale Scenes

The laser scanner is nowadays widely used to capture the geometry of art, animation maquettes, or large architectural, industrial, and land form models. It thus poses specific problems depending on the model scale. This thesis provides a solution for simplification of triangulated data and for surface reconstruction of large data sets, where feature edges provide an obvious segmentation structure. It also explores a new method for model segmentation, with the goal of applying multiresolution techniques to data sets characterized by curvy areas and the lack of clear demarcation features. The preliminary stage of surface segmentation, which takes as input single or multiple scan data files, generates surface patches which are processed independently. The surface components are mapped onto a two-dimensional domain with boundary constraints, using a novel parametrization weight coefficient. This stage generates valid parameter domain points, which can be fed as arguments to parametric modeling functions or surface approximation schemes. On this domain, our approach explores two types of remeshing. First, we generate points in a regular grid pattern, achieving multiresolution through a flexible grid step, which nevertheless is designed to produce a globally uniform resampling aspect. In this case, for reconstruction, we attempt to solve the open problem of border reconciliation across adjacent domains by retriangulating the border gap between the grid and the fixed irregular border. Alternatively, we straighten the domain borders in the parameter domain and coarsely triangulate the resulting simplified polygons, resampling the base domain triangles in a 1-4 subdivision pattern, achieving multiresolution from the number of subdivision steps. For mesh reconstruction, we use a linear interpolation method based on the original mesh triangles as control points on local planes, using a saved triangle correspondence between the original mesh and the parametric domain. We also use a region-wide approximation method, applied to the parameter grid points, which first generates data-trained control points, and then uses them to obtain the reconstruction values at the resamples. In the grid resampling scheme, due to the border constraints, the reassembly of the segmented, sequentially processed data sets is seamless. In the subdivision scheme, we align adjacent border fragments in the parameter space, and use a region-to-fragment map to achieve the same border reconstruction across two neighboring components. We successfully process data sets up to 1,000,000 points in one pass of our program, and are capable of assembling larger scenes from sequential runs. Our program consists of a single run, without intermediate storage. Where we process large input data files, we fragment the input using a nested application of our segmentation algorithm to reduce the size of the input scenes, and our pipeline reassembles the reconstruction output from multiple data files into a unique view

Domänen parallele Maschinen

A computational model is introduced, which abstracts and idealizes computers with access to fragment shaders. While the set of functions computable by this model remains the same, the running times can be drastically reduced through parallelization compared to conventional models. Some of the algorithms designed for the model can be approximated using fragment shaders. With an automatic transcompilation scheme, fragment shader programs can be generated automatically from a description in a high-level language.In dieser Arbeit wird ein Rechenmodell, das Computer mit Zugriff zu Fragment Shader abstrahiert und idealisiert, eingeführt. Zwar bleibt der Umfang der durch dieses Modell berechenbarer Funktionen gleich, jedoch können die Laufzeiten durch Parallelisierung im Vergleich zu herkömmlichen Modellen drastisch verkürzt werden. Einige der für das Modell entworfenen Algorithmen lassen sich mithilfe von Fragment Shadern approximieren. In einer Hochsprache beschriebene Algorithmen werden automatisiert in Fragment Shader Programme übersetzt