Visual spatio-temporal function-based querying

Visual interfaces are very important for human interactions in cyberworlds. Visual spatio-temporal querying should be one of the basic tools for data mining and retrieval in cyberworlds. In this paper, we propose a novel function-based query model for arbitrary shape spatio-temporal querying. The queries are defined as geometric shapes changing over time. In our model, data are interpreted geometrically as multidimensional points with time dimension or as moving points. The queries are formulated with geometric objects and operations over them to form the query solid changing over time. The proposed query model allows us to pose arbitrary shape spatio-temporal range queries. With the uniform geometric model we integrate visual mining and querying of time-dependent data employing 3D visualization tools. It allows for creating an intuitive visual interface using 2D projections of 3D query shapes. Our approach combines visualization of spatio-temporal data with visualization of the range query formulation employing very compact function-based query model. The implemented visual query system and its visual interface are proposed and described. An example of application of the system in analysis of simulation results in molecular dynamics is considered.     

Globally optimal surface mapping for surfaces with arbitrary topology

Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angular distortions among different shapes. This paper proposes and develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The existing state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via boundary cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We design and articulate an automatic variational algorithm that can reach the global distortion minimum for surface mapping between shapes of arbitrary topology, and our algorithm is sorely founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps. Consequently, our mapping framework offers a powerful computational tool for graphics and visualization tasks such as data and texture transfer, shape morphing, and shape matching.     

Parallel computational methods for 3D simulation of a parafoil with prescribed shape changes

In this paper we describe parallel computational methods for 3D simulation of the dynamics and fluid dynamics of a parafoil with prescribed, time-dependent shape changes. The mathematical model is based on the time-dependent, 3D Navier-Stokes equations governing the incompressible flow around the parafoil and Newton's law of motion governing the dynamics of the parafoil, with the aerodynamic forces acting on the parafoil calculated from the flow field. The computational methods developed for these 3D simulations include a stabilized space-time finite element formulation to accommodate for the shape changes, special mesh generation and mesh moving strategies developed for this purpose, iterative solution techniques for the large, coupled nonlinear equation systems involved, and parallel implementation of all these methods on scalable computing systems such as the Thinking Machines CM-5. As an example, we report 3D simulation of a flare maneuver in which the parafoil velocity is reduced by pulling down the flaps. This simulation requires solution of over 3.6 million coupled, nonlinear equations at every time step of the simulation.     

Optimal cross-sectional area distribution of a high-speed train nose to minimize the tunnel micro-pressure wave

Optimization of the cross-sectional area distribution of a high-speed train nose is conducted for various nose lengths in order to minimize the micro-pressure wave intensity at a tunnel exit. To this end, an inviscid compressible flow solver is adopted with an axi-symmetric patched grid system. To improve the shape of the train nose, multi-step design optimization is performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with a response surface model. The optimization reveals that the optimal nose shapes differ for different nose lengths. For a short nose, the shape has an extremely blunt front end, and the cross-sectional area decreases in the middle section. As the nose length increases, the nose shape flattens around the middle section. These optimal shapes divide one large compression wave into two small waves by causing a strong expansion effect between the front and rear ends. As a result, through the nose shape optimization, the intensity of the micro-pressure wave is reduced by 18–27% compared to a parabolic nose, which has a minimum variation of the cross-sectional area change. The optimized distribution of the cross-sectional area can be used as a guideline for the design of three-dimensional nose shapes of high-speed trains, further improving their aerodynamic performance.     

Using evolutionary design to interactively sketch car silhouettes and stimulate designer's creativity

An Interactive Genetic Algorithm is proposed to progressively sketch the desired side-view of a car profile. It adopts a Fourier decomposition of a 2D profile as the genotype, and proposes a cross-over mechanism. In addition, a formula function of two genes' discrepancies is fitted to the perceived dissimilarity between two car profiles. This similarity index is intensively used, throughout a series of user tests, to highlight the added value of the IGA compared to a systematic car shape exploration, to prove its ability to create superior satisfactory designs and to stimulate designer's creativity. These tests have involved six designers with a design goal defined by a semantic attribute. The results reveal that if “friendly” is diversely interpreted in terms of car shapes, “sportive” denotes a very conventional representation which may be a limitation for shape renewal.     

Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization

Gradient-based aerodynamic shape optimization using computational fluid dynamics (CFD), and time dependent problems in aeroelasticity, that is, coupled calculations between computational structural mechanics (CSM) and CFD, require repeated deformations of the CFD mesh.An interpolation scheme, based on radial basis functions (RBF), is devised in order to propagate the deformations from the boundaries to the interior of the CFD mesh. This method can lower the computational costs due to the deformation of the mesh, in comparison with the usual Laplace smoothing. Moreover, the algorithm is independent of the mesh connectivities. Therefore, structured and unstructured meshes are equally treated as well as hybrid meshes.The application of this interpolation scheme in problems of aerodynamic shape optimization is also carefully investigated. When the optimization is executed by a gradient-based algorithm the cost function is differentiated with respect to the design parameters in order to obtain the gradient. The gradient is most efficiently and accurately calculated by solving a certain adjoint equation derived from the discretized flow equations. The calculation of the gradient, which is detailed in this presentation, involves the Jacobian matrix of the mesh deformation.Finally, we present the results of an optimization of the ONERA M6 wing at transonic speed using the interpolation algorithm. The results are used for comparison with another technique of mesh deformation. The quality of the mesh obtained by the new algorithm, and the interpolation error, are analyzed with respect to the parameters of the interpolation scheme: the type of RBF, the RBF’s shape parameter, and the sets of control points.     

Autonomous experimental design optimization of a flapping wing

Applying evolutionary computation to the optimization of aerodynamic properties of shapes and structures usually involves computational fluid dynamics simulations. The simulation of the physical properties of a possible solution has various advantages. However, like in all simulations various restrictions and simplifications exist even for the most advanced simulation methods. Furthermore, the high computational demand very often does not allow high fidelity simulations together with numerical optimization methods. In this paper, we present an approach to combine evolutionary algorithms with physical measurements in order to allow an experiment-based evaluation of solutions. In this way, we can overcome the limitations connected to simulations of physical environments. We present the approach for a set-up in which the geometry of a flapping wing is optimized in order to find optimal configurations for various quality criteria.     

Generation of Smooth Surfaces by Controlling Curvature Variation

To satisfy a designer's intention for constructing aesthetic shapes such as automotive bodies, we propose a surface generation method. In the surface design process, designers determine shapes according to their great concern for the reflected images of vehicle surroundings, shade lines and highlight lines. Since reflection and shading are affected by changes of surface normal, the curvature variation of the surface, which represents the change of the surface normal, should be smooth and distributed as designers want. The proposed method controls curvature distribution directly by determining a surface shape from an evolute, which is a locus of the curvature center of the generatrix and moves along directrices to form the surface. It first generates evolutes of boundary curves to be generatrices as rational Bezier curves, then interpolates their shapes with the Bezier polygons, and locates the interpolated shape to the corresponding position of the directrices. By applying this method, we have confirmed that a smooth shape is generated from four boundary curves.     

Kano integrated robust design approach for aesthetical product design: a case study of a car profile

Visual shape parameters and aesthetic aspects of a product are one of the crucial factors for the success of a product in the market. The type and the value of the shape parameters plays an important role in visual appearance of a product and designers tends to be critical while deciding these parameters. The aesthetic aspect of a product has been matter of concern for researchers with its electromechanical design. The Kano model has been found to be a useful tool to establish the relationship between performance criteria and customer satisfaction. To achieve the desired customer satisfaction weight of each product criteria is determined by using Kano model. This study presents an integrative design approach combining the Kano model, Taguchi method and grey relation analysis to obtain the optimal combination of shape parameters and aesthetic aspects. Prioritized criteria of aesthetic attributes have been abstracted through proposed methodology. A case study has been presented to evolve a profile of a car.     

Robust aerodynamic shape design based on an adaptive stochastic optimization framework

Optimization techniques combined with uncertainty quantification are computationally expensive for robust aerodynamic optimization due to expensive CFD costs. Surrogate model technology can be used to improve the efficiency of robust optimization. In this paper, non-intrusive polynomial chaos method and Kriging model are used to construct a surrogate model that associate stochastic aerodynamic statistics with airfoil shapes. Then, global search algorithm is used to optimize the model to obtain optimal airfoil fast. However, optimization results always depend on the approximation accuracy of the surrogate model. Actually, it is difficult to achieve a high accuracy of the model in the whole design space. Therefore, we introduce the idea of adaptive strategy to robust aerodynamic optimization and propose an adaptive stochastic optimization framework. The surrogate model is updated adaptively by increasing training airfoils according to historical optimization results to guarantee the accuracy near the optimal design point, which can greatly reduce the number of training airfoils. The proposed method is applied to a robust aerodynamic shape optimization for drag minimization considering uncertainty of Mach number in transonic region. It can be concluded that the proposed method can obtain better optimal results more efficiently than the traditional robust optimization method and global surrogate model method.     

Boundary shape design by using PDE filtered design variables

This paper deals with a design method for boundary shapes using filtering techniques based on a partial differential equation (PDE). In shape optimization, it is known that oscillatory boundaries appear when design variables are directly assigned to the design boundaries. In addition, during the optimization process, discretized elements in a computational domain are distorted due to extremely large shape changes along the design boundaries. The distorted elements may cause accuracy deterioration or numerical instability in a forward problem. In this paper, we propose a shape optimization method by using the PDE as a low pass filter which prevents the oscillatory boundaries of the optimized design. For restricting the shape distortion of the discretized elements, the shear deformation of the elements is constrained in the optimization problem. Mathematical programming is used to find the boundary shapes under the KKT conditions. The effectiveness of the proposed method is demonstrated through numerical examples in solid and fluid mechanics.     

Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. A high fidelity computational fluid dynamics (CFD) algorithm modelling the Euler equations is used to calculate the aerodynamic properties of complex three-dimensional aircraft configurations. The design process is greatly accelerated through the use of both control theory and parallel computing. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented in parallel using a domain decomposition approach, an optimized communication schedule, and the Message Passing Interface (MPI) Standard for portability and efficiency. In our earlier studies, the serial implementation of this design method, was shown to be effective for the optimization of airfoils, wings, wing–bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In this work, our concern will be to extend the methodologies such that the combined capabilities of these new technologies can be used routinely and efficiently in an industrial design environment. The aerodynamic optimization of a supersonic transport configuration is presented as a demonstration test case of the capability. A particular difficulty of this test case is posed by the close coupling of the propulsion/airframe integration.     

Physics-inspired controllable flame animation

We propose a novel method conceptualized from the properties of physics where in particular the shape of a flame is determined by temperature that enables a control mechanism for the intuitive shaping of a flame. We focused on a trade-off issue from computer graphics whereby the turbulent flow that expresses the characteristics of the flame has a tendency to shift continuously, whereas the velocity constraints that contain a fluid within a target shape have a tendency to force movement in a particular direction. Trade-off made it difficult for animation designers to maintain a flame within the intended target shape. This paper resolves the issue by enabling the flame to be controlled without any velocity constraints by using the following two techniques: First, we model the temperature and force of the explosion generated by the combustion of explosive gaseous fuel and apply it to certain regions. Second, we expand the space of the interface between the fuel and the burned products, classifying that space into four regions and controlling the target shape of the flame by delicate adjustments to the temperature in each region. Experiments show that the flame maintains the appearance of dynamic movement while preserving the detailed 3D shapes specified by the scene designers.     

Adaptive Surface Visualization of Vessels with Animated Blood Flow

The investigation of hemodynamic information for the assessment of cardiovascular diseases (CVDs) gained importance in recent years. Improved flow measuring modalities and computational fluid dynamics (CFD) simulations yield in reliable blood flow information. For a visual exploration of the flow information, domain experts are used to investigate the flow information combined with its enclosed vessel anatomy. Since the flow is spatially embedded in the surrounding vessel surface, occlusion problems have to be resolved. A visual reduction of the vessel surface that still provides important anatomical features is required. We accomplish this by applying an adaptive surface visualization inspired by the suggestive contour measure. Furthermore, an illustration is employed to highlight the animated pathlines and to emphasize nearby surface regions. Our approach combines several visualization techniques to improve the perception of surface shape and depth. Thereby, we ensure appropriate visibility of the embedded flow information, which can be depicted with established or advanced flow visualization techniques. We apply our approach to cerebral aneurysms and aortas with simulated and measured blood flow. An informal user feedback with nine domain experts, we confirm the advantages of our approach compared with existing methods, e.g. semi‐transparent surface rendering. Additionally, we assessed the applicability and usefulness of the pathline animation with highlighting nearby surface regions.     

Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.     

Multidisciplinary and multiple operating points shape optimization of three-dimensional compressor blades

The recent progress in simulation technologies in several fields such as computational fluid dynamics, structures, thermal analysis, and unsteady flow combined with the emergence of improved optimization algorithms makes it now possible to develop and use automatic optimization software and methodologies to perform complex multidisciplinary shape optimization process. In the present applications, the MAX optimization software developed at CENAERO is used to perform the optimization. This software allows performing derivative free optimization with very few calls to the computer intensive simulation software. The method employed in this paper combines the use of a genetic algorithm (with real coding of the variables) to an approximate (or meta) model to accelerate significantly the optimization process. The performance of this optimization methodology is illustrated on the optimization of three-dimensional turbomachinery blades for multiple operating points and multidisciplinary objectives and constraints. The NASA rotor 67 geometry is used to demonstrate the capabilities of the method. The aim is to find the optimal shape for three different operating conditions: one at a near peak efficiency point, one at choked mass flow, and one near the stall flow. The three points are analyzed at the same blade rotational speed but with different mass flows. A finite element structural mechanics software is used to compute the static and dynamic mechanical responses of the blade. A Navier–Stokes solver is used to calculate the aerodynamic performance. High performance computers (HPC) are used in this application. Cenaero’s HPC infrastructure contains a Linux cluster with 170 3.06 GHz Xeon processors. The optimization algorithm is parallelized using MPI.     

ArchiDNA: An interactive system for creating 2D and 3D conceptual drawings in architectural design

We present an interactive system called ArchiDNA for creating 2D and 3D conceptual drawings in architectural design. We developed a novel principle of shape generation called match-and-attach by analyzing drawing styles of a contemporary architect, Peter Eisenman. The process consists of user interaction techniques and a set of rules that decide how one or more shapes attach to another shape. One key ingredient of our process is a unique concept for the interactive semi-automatic shape generation that uses the combination of algorithmic rules of a computer and designers’ manual inputs. These techniques enable designers to use CAD software in the early stages of architectural designs to explore conceptual building forms. ArchiDNA dynamically responds to drawing inputs, configures 2D shapes, and converts them to 3D shapes in a similar style. We intend to complement existing CAD software and computational drawing pipelines for intuitive 2D and 3D conceptual drawing creation.     

Aerodynamic characteristics of carriage arm equipped on hard magnetic disks

In order to study aerodynamic characteristics of a carriage arm equipped on hard disk drives, water tunnel tests with ten times enlarged models of an actual arm were conducted based on Reynolds number similitude, which allows the time scale of the phenomena about 1,300 times slower than that compared with the phenomena under actual operation condition in the air. In the tests, flow visualization around the arm model with fluorescent dye injection and laser-light sheet technique was carried out. Fluid dynamic drag, lift and torque on the model were also measured. The effects of the oncoming flow velocity and profile, the installation angle and position of the arm and the configuration of the trailing edge of the arm on the power spectral density of the fluid dynamic force were investigated. As a result, predominant spectrum peak, the Strouhal number of which is about 0.24, is found in the power spectral density of dynamic lift force on the arm. The flow visualization confirmed that the dynamic lift with the spectral peak originates from the alternating vortex shedding from the trailing edge of the arm. The peak rapidly decreases as the installation angle increases while the velocity profile of oncoming flow and the position of the arm in the gap direction have little effect on the peak component. Furthermore, it was demonstrated that the dynamic lift can be reduced by modification of trailing edge shape of the arm.     

A computational technology for constructing the optimal shape of a power plant blade assembly taking into account structural constraints

A computational technology for constructing the optimal shape of a power plant three-dimensional blade assembly is presented. The shape of the blade assembly is optimized to improve the power characteristics of the blade assembly taking into account structural constraints. The computational technology is a unified chain of algorithms beginning with constructing a CAD model of the assembly, generation of a computational grid, simulation of the flow around the assembly using OpenFoam, and finally the animated stereo visualization of the power plant operation. The visual representation of the results in all phases is required for debugging, verification, and control. The proposed technology provides a basis for finding the optimal shape of the blade assembly by varying its key geometric parameters. Practical results of the simulation are discussed.     

Formation of recirculation zones in a sudden expansion microchannel with a rectangular block structure over a wide Reynolds number range

This article involves computational and experimental investigations into the flow of a Newtonian fluid through a sudden expansion microchannel consisting of a rectangular block. The results elucidate that the Reynolds number and aspect ratio has a significant impact on the sequence of vortex growth downstream of the expansion channel. The experimental flow visualization results are found to be in good agreement with the numerical predictions of the local fluid dynamics. The simulation results also draw the Re—γ (Reynolds number—aspect ratio) flow pattern map to classify how the flow structures vary with Reynolds number, for example, the resulting flow structures can be classified as five types progressively. The findings in this study provide designers with valuable guidelines for improving the design and operation of the proposed microfluidic rectifier.