Control Mesh Research Articles

Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull–Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently refined control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. This multiresolution approach provides a means for regularising the optimisation problem and prevents the appearance of sub-optimal jagged geometries with fine-scale oscillations. The finest control mesh for optimisation is chosen in accordance with the desired smallest feature size in the optimised geometry. The proposed approach is applied to three optimisation examples, namely a catenary, a roof over a rectangular domain and a freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries is investigated in detail.

Technical Note: DoseMapper: A validated GUI-based exact numerical modeling method of shielding in PET/CT facilities.

To provide a faster and more intuitive way of designing shielding for PET facilities, while still relying on the principles of the AAPM 108 Taskforce guidelines, as well as illustrating the calculation output using dose maps that are easily evaluated. A graphical user interface was developed, implementing an inverse AAPM method, wherein radiation sources and shield barriers are manually defined. Simulations are calculated using a user-defined control mesh grid. DoseMapper simulations were verified against manual calculations using the AAPM guidelines, as well as compared with in situ dose rate measurements using four different dosemeters. DoseMapper simulations were virtually identical to manual calculations using AAPM guidelines, with a maximum relative error of <0.01%. Comparison with in situ measurements showed that DoseMapper-simulated dose rates in all instances are higher than what can be measured, ensuring that no unintended hotspots can be overlooked in the shielding design. DoseMapper is an easy to use implementation of the AAPM 108 Taskforce principles that allows for a rapid iterative design process of shielding in PET facilities, and the resulting maps of dose rate and annual accumulated dose serve as clear documentation for the design.

A universal prototype design framework of the stem and stern contours of hull surface and the self-adaptive solving strategy

Ship geometry reconstruction technology is a key technique and research focus in the ship design. And the optimization algorithm used in the ship design is always a hot research area. To establish the control points’ distribution model database of characteristic curves, based on the NURBS control mesh of the hull surface, an approach to approximate the initial stem and stern contours of hull form modeling using the concept of parametric generation is proposed. The optimization model is constructed with the homogeneous coordinate component of the fitted contour’s control points as the design variables. The objective function is set to minimize the maximum relative difference among the longitudinal coordinates of the approximated contour and the original ones corresponding to the same drafts. The appropriate constraints are set according to the characteristics of the contours and the geometrical characteristic of NURBS. Considering a number of empirical knowledge existing in the process of ship design, and the conventional quantum-behaved particle swarm optimization (QPSO) algorithm depending upon good initial population, the immune quantum-behaved particle swarm optimization (IQPSO) is specifically designed and used to solve this complex nonlinear constrained optimization problem through the immune operator of the immune genetic algorithm combining with the QPSO algorithm. Meanwhile, the self-adaptive constraint evolution strategy is proposed to improve the IQPSO algorithm. The simulation results of the full-scale ship’s contours demonstrate the feasibility and effectiveness of the proposed algorithm and method.

Truncated hierarchical tricubic [formula omitted] spline construction on unstructured hexahedral meshes for isogeometric analysis applications

We present a new method for truncated hierarchical tricubic spline (TH-spline3D) construction to enable adaptive isogeometric analysis on unstructured hexahedral meshes. Taking the input unstructured hexahedral mesh as the control mesh, we first develop blending functions with the aid of tricubic Bernstein polynomials. This development is an extension of defining bicubic Bernstein polynomial blending functions over quadrilateral meshes. We further build the hierarchical structure and apply the truncation mechanism to the developed blending functions for highly localized refinement. During the refinement of TH-spline3D, high-level blending functions are added in the solution space, whereas certain low-level ones are discarded or truncated depending on the high-level subdomain. The blending functions are piecewise polynomials that form a partition of unity. Their support overlapping is also reduced due to the truncation mechanism, resulting in sparser stiffness matrices compared to the classical hierarchical refinement. TH-spline3D supports Bézier extraction such that it can be easily incorporated into existing finite element frameworks. Several examples are used to demonstrate the analysis suitability and efficiency of the proposed method.

Variational reconstruction using subdivision surfaces with continuous sharpness control

We present a variational method for subdivision surface reconstruction from a noisy dense mesh. A new set of subdivision rules with continuous sharpness control is introduced into Loop subdivision for better modeling subdivision surface features such as semi-sharp creases, creases, and corners. The key idea is to assign a sharpness value to each edge of the control mesh to continuously control the surface features. Based on the new subdivision rules, a variational model with L1 norm is formulated to find the control mesh and the corresponding sharpness values of the subdivision surface that best fits the input mesh. An iterative solver based on the augmented Lagrangian method and particle swarm optimization is used to solve the resulting non-linear, non-differentiable optimization problem. Our experimental results show that our method can handle meshes well with sharp/semi-sharp features and noise.

Interactive modeling of smooth manifold meshes with arbitrary topology: G1 stitched bi-cubic Bézier patches

In this paper, we present a new piecewise parametric approach to obtain smooth surfaces from any given orientable 2-manifold polynomial control mesh. Our approach provides C2 continuous Bi-Cubic Bézier patches that are guaranteed to be stitched with G1 continuity regardless of the underlying mesh topology. A high level summary of the approach can be given as a two-step process: (1) Starting from an orientable 2-manifold mesh we apply vertex-insertion, which is remeshing algorithm of Catmull–Clark subdivision, to break that surface into a set of all quadrilateral patches. (2) for each such quadrilateral patch, we construct a Bi-Cubic Bézier patch, where the positions of the 16 control points are obtained from the limit surface of the Doo–Sabin subdivision scheme.This approach, when combined with topological modeling, provides a framework for real-time interactive modeling of smooth manifold meshes with arbitrary topology. Based on this approach, we have developed an interactive modeling system that allows users to work with smooth surfaces in real-time by opening or closing holes, creating handles, and combining and disconnecting surfaces. The paper has three main contributions: (1) We guarantee that our method will produce only smooth manifold meshes with C2 continuous Bi-Cubic Bézier patches. (2) We guarantee visual smoothness for any arbitrary topological structure by providing geometric G1 continuity in boundaries of patches. (3) We demonstrate that smooth surfaces with arbitrary topology can be created interactively in real-time using parametric patches.

Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision

In this paper, we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended Loop surface subdivision approach. The exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure, which is thought of as the initial control mesh of Loop subdivision. By performing extended Loop subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of quartic box-spline while maintaining its original exactness. The limit function representation of extended Loop subdivision forms our finite element space, which possesses C1 smoothness and the flexibility of mesh topology. We establish its inverse inequalities which resemble the ones of general finite element spaces. We develop the approximation estimate with the aid of H1 convergence property of the corresponding linear models. It enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models. Numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results.

Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow

We develop an algorithm for the three dimensional simulation of the dynamics of soft objects (drops, capsules, vesicles) under creeping flow conditions. Loop elements are used to describe the shape of the soft objects. This surface representation is used both for membrane solver based on finite element method (FEM) and for the fluid solver based on the boundary element method (BEM). This isogeometric analysis of the low Reynolds fluid–structure interaction problem is then coupled to high-order explicit time stepping or second-order implicit time stepping algorithm. For vesicles simulation, a preconditioner is designed for the resolution of the surface velocity incompressibility constraint, which is treated by the use of a local Lagrange multiplier. A mesh quality preserving algorithm is introduced to improve the control mesh quality over long simulation times. We test the proposed algorithm on capsule and vesicle dynamics in various flows, and study its convergence properties, showing a second-order convergence O(N−2) with mesh number of elements.

Smooth interpolation of key frames in a Riemannian shell space

Splines and subdivision curves are flexible tools in the design and manipulation of curves in Euclidean space. In this paper we study generalizations of interpolating splines and subdivision schemes to the Riemannian manifold of shell surfaces in which the associated metric measures both bending and membrane distortion. The shells under consideration are assumed to be represented by Loop subdivision surfaces. This enables the animation of shells via the smooth interpolation of a given set of key frame control meshes. Using a variational time discretization of geodesics efficient numerical implementations can be derived. These are based on discrete geodesic interpolation, a discrete geometric logarithm, a discrete exponential map, and discrete parallel transport. With these building blocks at hand discrete Riemannian cardinal splines and three different types of discrete, interpolatory subdivision schemes are defined. Numerical results for two different subdivision shell models underline the potential of this approach in key frame animation.

Video Vectorization via Tetrahedral Remeshing.

We present a video vectorization method that generates a video in vector representation from an input video in raster representation. A vector-based video representation offers the benefits of vector graphics, such as compactness and scalability. The vector video we generate is represented by a simplified tetrahedral control mesh over the spatial-temporal video volume, with color attributes defined at the mesh vertices. We present novel techniques for simplification and subdivision of a tetrahedral mesh to achieve high simplification ratio while preserving features and ensuring color fidelity. From an input raster video, our method is capable of generating a compact video in vector representation that allows a faithful reconstruction with low reconstruction errors.

细分曲面奇异点处的光滑过渡

首先通过引入形状调节参数c(0≤c≤1)给出了一种形状可调的C-C细分方法，基于该理论，针对细分曲面中的奇异点，本文以奇异点处的2-环作为控制网格，采用循环映射的方法，提出了一种形状可调的G2曲面造型方法，得到Bezier控制点的显式解。与以往的方法相比，生成的曲面不仅在奇异点处达到G2连续，而且解决了曲面设计的可调性问题。本文给出了算法流程和相关数据结构，也给出了相应的实例进行验证。 This paper discusses G2 smooth connection near singular points on subdivision surfaces. A shape adjustable Catmull-Clark subdivision algorithm is present by introducing subdivision shape ad-justment parameter c(0≤c≤1). Based on this, aimed at the singular points in subdivision surface, based on the 2-ring of the singular points as control mesh, adopting the method of cyclic mapping, this paper proposes a G2 surface modeling method which is shape-adjustable. Then we can get the explicit solution of the Bezier control points. Compared with existing methods, the generated surface not only achieves the G2 continuous at singular points, but solves the problem of the curved surface design to be adjustable. The algorithm process and data structure are present. Corresponding examples are also given in this paper.

Plug-In Hybrid Electric Bus Energy Management Based on Dynamic Programming

Abstract An energy management strategy based on dynamic programming for a plug-in serial-parallel hybrid electric bus is proposed. The sets of comprehensive cost function, five control variables and mesh accuracies are illustrated. Then the fuel economy is discussed, followed by the sensitivity analysis of this strategy on different lengths of driving cycle input and dissimilar control variable settings. It can be concluded that scaling the length of driving cycle and battery capacity have little effect on control laws output while optimum control variable settings should combine exact characters of driving cycles and driving components of the bus.

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.

Isogeometric Reissner‐Mindlin shell analysis ‐ employing different control meshes for displacements and rotations

AbstractThe main purpose of this paper is the development and implementation of a method for the reduction of the so‐called locking effect in the isogeometric Reissner‐Mindlin shell formulation. In [1] an isogeometric Reissner‐Mindlin shell formulation with an exact interpolation of the director vector based on continuum mechanics was introduced. The numerical examples showed that the accuracy and efficiency increased. However, there are only few effective concepts for the prevention of locking effects for low polynomial degrees. In the work of Beirão da Veiga [2], shear locking is prevented for a Reissner‐Mindlin plate formulation by using suitable solution spaces. Here, the method is extended to the Reissner‐Mindlin shell formulation. Different control meshes are used for displacements and rotations. Furthermore, the basis functions in the direction of the relevant rotation are one degree less than the ones which are chosen for the displacements. That leads to control meshes with different number and location of the control points. The aim is to avoid shear locking due to the coupling of shear strains and curvature since the compatibility requirement for pure bending is then fulfilled. The accuracy and efficiency of this method are investigated for different examples. In addition, the results are compared to the analytical solutions. (© 2016 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

In vitro assessment of an antibacterial quaternary ammonium-based polymer loaded with chlorhexidine for the coating of polypropylene prosthetic meshes.

This study assesses the use of an absorbable polymer loaded with chlorhexidine (CHX) as an antibacterial coating for polypropylene (PP) meshes employed in hernia repair. The polymer N,N-dimethyl-N-benzyl-N-(2-methacryloyloxyethyl) ammonium bromide was loaded with CHX (1% w/w). Fragments (1cm2) of Optilene® Mesh Elastic were coated either with the unloaded (POL) or CHX-loaded polymer (POL-CHX). Uncoated fragments (PP) served as controls. The release kinetics of the POL-CHX coating was monitored by HPLC. Sterile fragments were placed on agar plates previously contaminated with 106CFU of Staphylococcus aureus (Sa) ATCC25923, Staphylococcus epidermidis (Se) ATCC12228, or Escherichia coli (Ec) ATCC25922 and incubated at 37°C for 1/2/7days. At each time point, inhibition halos were measured and bacterial adhesion to the meshes quantified by sonication and scanning electron microscopy. Coating cytotoxic effects were examined on cultured fibroblasts. The polymer coating gradually released CHX over 3days. Inhibition halos were produced only around the POL-CHX-coated meshes and these were significantly smaller for Ec than Sa or Se (p<0.01). While POL-CHX prevented bacterial adhesion to the mesh, the reduced bacterial yields over time were observed for the POL-coated versus control PP meshes (p<0.001). By day 7, only Ec remained attached to the surface of control meshes. The POL coating was not cytotoxic, yet POL-CHX reduced the viability of cultured fibroblasts. When loaded with the antiseptic CHX, this quaternary ammonium-based polymer coating released its contents in a controlled manner indicating its potential prophylactic use to reduce the risk of infection following PP mesh implantation.

Isogeometric analysis using manifold-based smooth basis functions

We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of variants exist. Common to most is the concept of constructing a smooth surface by blending together overlapping patches (or, charts), as in differential geometry description of manifolds. Each patch on the surface has a corresponding planar patch with a smooth one-to-one mapping onto the surface. In our implementation, manifold techniques are combined with conformal parameterisations and the partition-of-unity method for deriving smooth basis functions on unstructured quadrilateral meshes. Each vertex and its adjacent elements on the surface control mesh have a corresponding planar patch of elements. The star-shaped planar patch with congruent wedge-shaped elements is smoothly parameterised with copies of a conformally mapped unit square. The conformal maps can be easily inverted in order to compute the transition functions between the different planar patches that have an overlap on the surface. On the collection of star-shaped planar patches the partition of unity method is used for approximation. The smooth partition of unity, or blending functions, are assembled from tensor-product b-spline segments defined on a unit square. On each patch a polynomial with a prescribed degree is used as a local approximant. In order to obtain a mesh-based approximation scheme the coefficients of the local approximants are expressed in dependence of vertex coefficients. This yields a basis function for each vertex of the mesh which is smooth and non-zero over a vertex and its adjacent elements. Our numerical simulations indicate the optimal convergence of the resulting approximation scheme for Poisson problems and near optimal convergence for thin-plate and thin-shell problems discretised with structured and unstructured quadrilateral meshes.

Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three optimisation examples, namely a catenary, a roof over a rectangular domain, and free-form architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.

G 1 non-uniform Catmull-Clark surfaces

This paper develops new refinement rules for non-uniform Catmull-Clark surfaces that produce G 1 extraordinary points whose blending functions have a single local maximum. The method consists of designing an "eigen polyhedron" in R 2 for each extraordinary point, and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules, when applied to a non-uniform Catmull-Clark control mesh in R 3 , yield a G 1 extraordinary point.

An algorithm for multi-resolution analysis of NURBS surfaces

A new algorithm is proposed for the multi-resolution representation of NURBS (Non-Uniform Rational B-Spline) surfaces with boundary consistency constraints. The kernel idea is to employ T-meshes (T-spline control meshes) to construct the multi-resolution representation for surfaces. To this end, the original B-mesh (B-spline control mesh) is first divided into a boundary part and an inner one; then, the multi-resolution representation of the inner part is achieved by wavelet transform; at last, the topology of the boundary part is added onto the obtained multi-resolution meshes to construct the final T-spline based multi-resolution representation result. The boundary shapes keep unchanged in the whole process of the treatment, because the boundary consistency constraints are always contained in the boundary part. This advantage of the new algorithm is demonstrated by three examples.

Procedural mesh features applied to subdivision surfaces using graph grammars

A typical industrial design modelling scenario involves defining the overall shape of a product followed by adding detail features. Procedural features are well-established in computer aided design (CAD) involving regular forms, but are less applicable to free-form modelling involving subdivision surfaces. Current approaches do not generate sparse subdivision control meshes as output, which is why free-form features are manually modelled into subdivision control meshes by domain experts. Domain experts change the local topology of the subdivision control mesh to incorporate features into the surface, without increasing the mesh density unnecessarily and carefully avoiding the appearance of artefacts.In this paper we show how to translate this expert knowledge to grammar rules. The rules may then be invoked in an interactive system to automatically apply features to subdivision surfaces.