NURBS-based free-form deformation

ArticleinIEEE Computer Graphics and Applications 14(6)(6):59 - 65 · December 1994with 94 Reads
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Abstract
Since the advent of computer-based geometric modeling, designers have tried to develop modeling and deformation tools that allow users to emulate the ease with which sculptors work with clay. T.W. Sederberg and S.R. Parry (1986) demonstrated the application of free-form deformations. FFDs let the user conceptually embed an object in a clear pliable solid and apply deformations to the solid, which then carry through to the encased object. We describe a technique that logically extends current FFDs by basing them on nonuniform rational B-splines. The resulting NURBS-based FFDs (NFFDs) offer flexibility and control not achieved in prior implementations. We conclude by describing a straightforward combination of this technique with global and local deformations of solid primitives used to animate a lifelike surface model of the human leg.< >

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    With the continuous increase of the running speed, the head shape of a high-speed train turns out to be the critical factor to boost the speed further. In order to reduce the time required to design the head of a high-speed train and to improve the modelling efficiency, various parametric modelling methods have been widely applied in the optimization design of the head of a high-speed train to obtain an optimal head shape so that the aerodynamic effect acting on the head of a high-speed train can be reduced and more energy can be saved. This paper reviews these parametric modelling methods and classifies them into four categories: two-dimensional, three-dimensional, CATIA-based, and mesh deformation-based parametric modelling methods. Each of the methods is introduced, and the advantages and disadvantages of these methods are identified. The simulation results are presented to demonstrate that the aerodynamic performance of the optimal models constructed by these parametric modelling methods has been improved when compared with the numerical calculation results of the original models or the prototype models of running trains. Since different parametric modelling methods used different original models and optimization methods, few publications could be found which compare the simulation results of the aerodynamic performance among different parametric modelling methods. In spite of this, these parametric modelling methods indicate that more local shape details will lead to more accurate simulation results, and fewer design variables will result in higher computational efficiency. Therefore, the ability of describing more local shape details with fewer design variables could serve as a main specification to assess the performance of various parametric modelling methods. The future research directions may concentrate on how to improve such ability.
  • Article
    In this work, we propose both a theoretical framework and a numerical method to tackle shape optimization problems related with fluid dynamics applications in presence of fluid-structure interactions. We present a general framework relying on the solution to a suitable adjoint problem and the characterization of the shape gradient of the cost functional to be minimized. We show how to derive a system of (first-order) optimality conditions combining several tools from shape analysis and how to exploit them in order to set a numerical iterative procedure to approximate the optimal solution. We also show how to deal efficiently with shape deformations (resulting from both the fluid-structure interaction and the optimization process). As benchmark case, we consider an unsteady Stokes flow in an elastic channel with compliant walls, whose motion under the effect of the flow is described through a linear Koiter shell model. Potential applications are related e.g.To design of cardiovascular prostheses in physiological flows or design of components in aerodynamics.
  • Chapter
    Full-text available
    Virtual Reality applications strive to simulate real or imaginary scenes with which users can interact and perceive the effects of their actions in real time. Adding haptic information such as vibration, tactile array, and force feedback enhances the sense of presence in virtual environments. Haptics interfaces present new challenges in the situation where it is crucial for the operators to touch, grasp and manipulate rigid/soft objects in the immersive virtual worlds. Soft-touch haptics modeling is the core component in feeling and manipulating dynamic objects within the virtual environments. For adding the haptic sensations with interactive soft objects, the authors first present multiple force-reflecting dynamics in Loop subdivision surfaces, and further the haptic freeform deformation of soft objects through mass-spring Bezier volume lattice. The haptic constraint modeling based on metaballs is experimented to intuitively control the interactive force distribution within the dynamically constructed constraint, making the soft-touch simulation of objects simple to manipulate with enhanced realism.
  • Article
    This review paper presents an overview of simulation-based hydrodynamic design optimization of ship hull forms. A computational tool that is aimed to accomplishing early-stage simulation-based design in terms of hydrodynamic performance is discussed in detail. The main components of this computational tool consist of a hydrodynamic module, a hull surface modeling module, and an optimization module. The hydrodynamic module includes both design-oriented simple CFD tools and high-fidelity CFD tools. These integrated CFD tools are used for evaluating hydrodynamic performances at different design stages. The hull surface modeling module includes various techniques for ship hull surface representation and modification. This module is used to automatically produce hull forms or modify existing hull forms in terms of hydrodynamic performance and design constraints. The optimization module includes various optimization algorithms and surrogate models, which are used to determine optimal designs in terms of given hydrodynamic performance. As an illustration of the computational tool, a Series 60 hull is optimized for reduced drag using three different modification strategies to outline the specific procedure for conducting simulation-based hydrodynamic design of ship hull forms using the present tool. Numerical results show that the present tool is well suited for the hull form design optimization at early design stage because it can produce effective optimal designs within a short period of time.
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    In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offline–online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.
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    In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field.
  • Article
    Free-form deformation (FFD) is a method first introduced within the graphics industry to enable flexible deformation of geometric models. FFD uses an R3 to R3 mapping of a deformable space to the global Cartesian space to produce the geometry deformation. This method has been extensively used within the design optimisation field as a shape parameterisation technique. Typically it has been used to parameterise analysis meshes, where new design geometries are produced by deforming the original mesh. This method allows a concise set of design variables to be used while maintaining a flexible shape representation. However, if a computer aided design (CAD) model of the resulting geometry is required, reverse engineering techniques would need to be utilised to recreate the model from the deformed mesh. This paper extends the use of FFD within an optimisation routine by using FFD to directly parameterise a CAD geometry. Two methods of linking the FFD methods with the CATIA V5 CAD package are presented. Each CAD integration technique is then critiqued with respect to shape optimisation. Finally the set-up and initialisation of a case study is illustrated. The case study chosen is the aerodynamic optimisation of the wingfuselage junction of a typical passenger aircraft.
  • Conference Paper
    Deformation mechanics in combination with artistic control allows the creation of remarkably fluid and life-like 3-dimensional models. Slightly deforming and distorting a graphical mesh injects vibrant harmonious characteristics that would otherwise be lacking. Having said that, the deformation of high poly complex shapes is a challenging and important problem (e.g., a solution that is computationally fast, exploits parallel architecture, such as, the graphical processing unit, is controllable, and produces aesthetically pleasing results). We present a solution that addresses these problems by combining a tetrahedron interpolation method with an automated tetrahedronization partitioning algorithm. For this paper, we focus on 3-dimensional tetrahedron meshes, while our technique is applicable to both 3-dimensional (tetrahedron) and 2-dimensional (triangulated planar) meshes. With this in mind, we compare and review free-form deformation techniques over the past few years. We also show experimental results to demonstrate our algorithm’s advantages and simplicity compared to other more esoteric approaches.
  • Article
    A free-form deformation parameterization (FFD) method is established based on non-uniform rational B-spline (NURBS) basis function. Furthermore, by coupling the transfinite interpolation (TFI) grid deformation technology and computational fluid dynamics (CFD) method with improved particle swarm optimization (PSO) arithmetic, a general aerodynamic optimization design system is constructed. Then, the aerodynamic optimization design system is applied to designing a large upswept afterbody of transport aircraft C17 on the restrictions of nondecreasing maximum structure height, width and upswept angle. The optimized afterbody decreases the total drag by 2.6% and pressure drag by 19.8% respectively. A comparison analysis of the aerodynamic shape and flow pattern reveals that the key factors for the optimized afterbody to decrease the pressure drag greatly are the increased near-roundness of the afterbody cross-section and decreased near-roundness change ratio along the fuselage axis. The two factors enable the adverse pressure gradient along the circumferential direction to become smaller, which can suspend aferbody separation and weaken afterbody vortex strength. The aerodynamic optimization design system constructed in this paper has good practicability and engineering application prospect.
  • Article
    The adjoint method is now employed more and more widely for aerodynamic shape optimization. But when used for reducing the drag of a complex aircraft, it still requires a large amount of time-consuming calculation. Based on an unstructured mesh, this paper proposes a parallel multigrid algorithm to solve the discrete adjoint equation for a 3D Reynolds-averaged Navier-Stokes solver, so as to improve the optimization system efficiency. The prolongation operator and the restriction operator are described for the multigrid adjoint solver. By using the V-cycle, the accelerating effect of different layers is compared, and the influence of coarse grid residuals computing methods on the gradient of the objective function is analyzed. Combined with Metis partitioning technology, a simplified parallel-data transfer approach is implemented for the adjoint solver, so that the parallel speedup of the adjoint equation is only 13% lower than the ideal speedup in 300 parallel partitions. The optimization system is successfully demonstrated for a DLR F6 wing-body transonic shape optimization design, in which 112 design variables are selected with the purpose of reducing drag. Shock structure change is presented before and after the optimization, and drag reduction is nine counts. It shows that the efficient optimization system established in this paper has a bright application prospect for three-dimensional complex shape optimization.
  • Article
    Because solving adjoint equation does not depend on the number of design variables, there is no relationship between the calculation amount of iterative optimization and the number of design variables. Based on the unstructured grid, a discrete adjoint solver is developed for a 3D Reynolds-averaged Navier-Stokes solver. Free-form deformation (FFD) technology is implemented to modify the mesh. Discrete adjoint equation can be acquired directly by formula derivation method and solved through LU-SGS iteration. The adjoint code is verified by comparing flux Jacobian and objective function gradient with finite differences. The design system is successfully applied to ONERA M6 wing transonic shape optimization design with the purpose of reducing drag, and the influence of volume constraint is also studied in this paper. It shows that the optimization method established is effective with a better application prospect.
  • Article
    Based on the deformation principle of rigid frame under force in FEM, a novel surface modeling method is proposed. A rigid frame is created according to topological relation of mesh, so the mesh surface deformation can be driven by rigid frame deformation. Two ways are introduced to get loads that urge rigid frame to deform, that is, directly exerting loads on nodes of rigid frame and adding geometric constraint interactively to get the inverse calculation of load. Aiming at geometric constrain deformation, a constrained optimization problem is established with minimization of external load and node displacement. In deformation process, the elastic modulus of elements associating with features of mesh is increased to preserve form feature. Compared with traditional method, sophisticate equations describing geometric feature information are avoided. Experimental results show that the method is straightforward and can generate desired deformation results.
  • Article
    Using the deformation principle of rigid frame under force for reference, linear elastic FEM is applied to realize deformation design of mesh model. Combining skeleton-driven biological motion with linear elastic FEM, an efficient deformation algorithm is proposed based on finite element shape function interpolating. Firstly, the rigid frame is constructed by building low-solution skeleton of the original mesh. Secondly, the map between mesh vertices and beam is established to realize skeleton-driven mesh deformation. Thirdly, through adding boundary conditions and exerting external load interactively, node displacement could be calculated by solving global stiffness matrix equation. Lastly, displacement vector of mesh vertices are computed out by interpolating node displacements with shape function. Owing to the limitation of linear FEM in large deformation problem, a rotating field is established to modify this drawback and the cubic Hermite interpolation is introduced to interpolate two ends of deflection curves at common node to realize smooth deformation results. Experimental results show this algorithm is effective and can be applied to model deformation such as expanding, bending, rotating and other operations.
  • Article
    Full-text available
    This paper proposes a parameterization method using cylindrical coordinates based free-form deformation(CYFFD) technique by introducing a coordinate transformation method and a virtual lattice method. The method is suitable for axisymmetric and non-axisymmetric cylindrical applications. CYFFD is able to deform radially and circumferentially and to maintain first order and curvature continuity across frame border. First, the coordinate transformation step helps capture geometrical characteristics of cylindrical objects to conduct radial and circumferential deformation. Due to the need of delicate shape design, FFD lattice need be set up closely around cylinder-like objects and this will cause the boundary of FFD frame to intersect with the objects, which lead to derivative discontinuity at the intersection. The virtual lattice method is introduced to reuse some control points as virtual ones so that first order and curvature continuity can be preserved. A cylinder deformation example compares the capability of CYFFD with that of conventional FFD for radial and circumferential deformation and keeping derivative continuity. An airplane nose example shows the possibility to use CYFFD and NFFD together for complex shape. A nacelle deformation example and fitting example show that CYFFD is valuable for non-axisymmetric cylindrical objects with complex shapes. The optimization example on cylinder nose shape indicates that CYFFD can give good optimization results and it is valuable for parameterizing cylinder-like objects. © 2018, Editorial Board of Journal of Northwestern Polytechnical University. All right reserved.
  • Chapter
    We present an in-depth analysis and benchmark of shape deformation techniques for their use in simulation-based design optimization scenarios. We first introduce classical free-form deformation, its direct manipulation variant, as well as deformations based on radial basis functions. We compare the techniques in a series of representative synthetic benchmarks, including computational performance, numerical robustness, quality of the deformation, adaptive refinement, as well as precision of constraint satisfaction. As an application-oriented benchmark we investigate the ability to adapt an existing volumetric simulation mesh according to an updated surface geometry, including unstructured tetrahedral, structured hexahedral, and arbitrary polyhedral example meshes. Finally, we provide a detailed assessment of the methods and give concrete advice on choosing a suitable technique for a given optimization scenario.
  • Chapter
    In order to have a good representation of deformable objects, is clever to have an adequate model to represent them. Since the origins of computer graphics, a large number of representation models have been presented. Not all of them are adequate to represent deformable objects. The way in which the objects can be handled, allowing local changes in their shape, or the possibility of the creation of objects matching with data gathered from one or more datasources, are some of the desirable characteristics in those models. This chapter represents a study of the way in which the deformable objects can be represented. It is possible to classify them into some categories allowing to select the most adequate depending on the use given to the model.
  • A methodology is proposed for creating and animating computer generated characters which combines recent research advances in robotics, physically based modeling and geometric modeling. The control points of geometric modeling deformations are constrained by an underlying articulated robotics skeleton. These deformations are tailored by the animator and act as a muscle layer to provide automatic squash and stretch behavior of the surface geometry. A hierarchy of composite deformations provides the animator with a multi-layered approach to defining both local and global transition of the character's shape. The muscle deformations determine the resulting geometric surface of the character. This approach provides independent representation of articulation from surface geometry, supports higher level motion control based on various computational models, as well as a consistent, uniform character representation which can be tuned and tweaked by the animator to meet very precise expressive qualities. A prototype system (Critter) currently under development demonstrates research results towards layered construction of deformable animated characters.
  • Deformation of Solids with Trivariate B-Splines Elsevi-er Science Publishers, North-Holland, 1989, pp. 137.148. 21-30
    • J Griessmair
    • W Purgathofer
    J. Griessmair and W. Purgathofer, " Deformation of Solids with Trivariate B-Splines, " Proc. Eurographics 89, Elsevi-er Science Publishers, North-Holland, 1989, pp. 137.148. 21-30. Past President: Martha Sloan Secretary: Luis T. Gandia Treasurer: V. Thomas Rhyne VP, Educational Activities: Kenneth R. Laker VP, Professional Activities: Charles K. Alexander VP, Publication Activities: Lloyd A. Morley VP, Regional Activities: Vijay K.Bhargava VP, Standards Activities: Wallace S. Read VP, Technical Activities: Donald M. B o k IEEE Computer Graphics and Applications
  • Chapter
    New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.
  • Article
    A recently developed technique for manipulating geometric models, known as Free-Form Deformation, is explored in an interactive environment. Its definition and implementation are discussed. Many uses of the technique in an interactive environment are explored. These include simple sculpting techniques, control point movement and weight changes; high-level operations, such as bending, tapering, and twisting; and complex computed operations, such as applying stored Free-Form Deformation, planar movement, curve following and blending. Some additional research areas are also identified.
  • Article
    New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.
  • Animation of a B-Spline Figure," &lt;i&gt;The Visual Computer&lt;/i&gt
    • M Nahas
    • H Huitric
    • M Saintourens
  • A technique is presented for deforming solid geometric models in a free-form manner. The technique can be used with any solid modeling system, such as CSG or B-rep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces, for example. The deformation can be applied either globally or locally. Local deformations can be imposed with any desired degree of derivative continuity. It is also possible to deform a solid model in such a way that its volume is preserved.The scheme is based on trivariate Bernstein polynomials, and provides the designer with an intuitive appreciation for its effects.
  • The development of a parameterized facial muscle process, that incorporates the use of a model to create realistic facial animation is described.Existing methods of facial parameterization have the inherent problem of hard-wiring performable actions. The development of a muscle process that is controllable by a limited number of parameters and is non-specific to facial topology allows a richer vocabulary and a more general approach to the modelling of the primary facial expressions.A brief discussion of facial structure is given, from which a method for a simple modelling of a muscle process that is suitable for the animation of a number of divergent facial types is described.
  • Article
    Summary In this paper we describe how the use of B-Spline surfaces allows lissom movements of body and face. Our method is empirical, based on a parametrical animation. It can be combined with a muscles model for facial animation as we illustrated for the speech.
  • Article
    In the production of character animation that treats living things moving at will, as in the case of humans and animals, it is important to express natural action and realistic body shape. If we can express these freely and easily, we will be able to apply character animation to many fields, such as the simulation of dances and sports, and electronic stand-ins. The computer graphics technique may be one of the most effective means to achieve such goals. We have developed human skin model capable of natural shape variation. This model has a skeleton structure, and free form surfaces cover the skeleton just like skin. The model permits continuous motion of every components of the skeleton according to actions. During such movements, the skin retains smoothness and naturalness. We are verifying the human skin model by producing several short animation pieces.
  • Article
    Thesis (M.S.)--Brigham Young University. Dept. of Computer Science. Bibliography: leaf 52.
  • Article
    Current research efforts focus on providing more efficient and effective design methods for 3D modeling systems. In this paper a new deformation technique is presented. Among other things, arbitrarily shaped bump can be designed and surfaces can be bent along arbitrarily shaped curves. The purpose of this research is to define a highly interactive and intuitive modeling technique for designers and stylists. A natural way of thinking is to mimic traditional trades, such as sculpturing and moulding. Furthermore, with this deformation technique, the modeling tool paradigm is introduced. The object is deformed with a user-defined deformation tool. This method is an extension of the Free-Form Deformation (FFD) technique proposed by Sederberg and Parry.
  • Article
    Full-text available
    Free-form deformation (FFD) is a powerful modeling tool, but controlling the shape of an object under complex deformations is often difficult. The interface to FFD in most conventional systems simply represents the underlying mathematics directly; users describe deformations by manipulating control points. The difficulty in controlling shape precisely is largely due to the control points being extraneous to the object; the deformed object does not follow the control points exactly. In addition, the number of degrees of freedom presented to the user can be overwhelming. We present a method that allows a user to control a free-form deformation of an object by manipulating the object directly, leading to better control of the deformation and a more intuitive interface. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - Curve, Surface, Solid, and Object Representations; I.3.6 [Computer Graphics ]: Methodology and Techniques - Interaction Techniques. Add...