In this paper, we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method. The linear relations between control points are firstly derived for different energy-minimization problems, then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system. The existence and uniqueness of the solution for the linear system are also proved. Experimental results show the efficiency of the proposed approach, and its application in G1 blending curve construction is also presented.

Generalized B-splines have been employed as geometric modeling and numerical simulation tools for isogeometric analysis (IGA for short). However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by { α ( t ), β ( t ), ξ ( t ), η ( t ), 1, t , · · ·, t n –4 } is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometric heat conduction problems are presented to show the effectiveness of the proposed methods.

We present an approach to accelerate spherical range-search (SRS) for dynamic points that employs the computational power of many-core GPUs. Unlike finding k approximate nearest neighbours (ANNs), exact SRS is needed in geometry processing and physical simulation to avoid missing small features. The spatial coherence of query points and the temporal coherence of dynamic points are exploited in our approach to achieve very efficient range-search on AABB-trees. We test our coherent SRS in several applications including point-point-set geometry processing, distance-field generation and particle-based simulation, which are best scenarios to present the spatial and the temporal coherence of spherical queries on dynamic points. On a PC with NVIDIA GTX 660 Ti GPUs, our approach can take 1M queries on 1M dynamic points at a rate of 1600 queries/ms, where 49 neighbours are found on average within the range of 1/100 of the bounding-box’s diagonal length. We observe an increase of up to 4x compared with conventional voxel-based GPU searching approaches in the benchmark of particle-based fluid simulation. Moreover, the speedup can be scaled up to 150x when being applied to highly non-uniform distribution of particles in the simulation.

Today's CAD modelers are very efficient in processing 3D shapes of CAD models by means of B-Rep modeling operators such as pad, pocket, shaft, groove, hole, fillet and so on.At a lower description level, those modeling operators are based on Euler operators acting directly on the faces, edges and vertices of the B-Rep models.Using such a top-down approach, the designers do not have to work on low-level geometric entities, but rather manipulate so-called structural and detail features to shape directly the CAD models.However, there is still a gap between the shapes the designers have in mind and the way they have to decompose them in a succession of modeling steps.This paper proposes a new declarative modeling approach to design industrial shapes allowing the designers to interact with a CAD software at a more conceptual level.The designers enter a high-level description of the expected shapes that is then transformed through scripts into traditional CAD operators successively called to create the shapes.Compared to the traditional feature-based approaches, our declarative modeling approach is closer to the way designers think.It saves time while keeping all the advantages of existing efficient CAD modelers.This new approach aims at quickly creating drafts rather than final shapes.Those drafts can then be modified using classical CAD software in which our new approach is fully embedded.This approach is a first step towards a declarative CAD modeler.

Isogeometric analysis attempts to unify the mathematical languages in design and analysis to realize the seamless integration of CAD and CAE. In three-dimensional isogeometric analysis, parametric volume is employed as the computational domain for a given set of boundary information. In this paper, we propose a discrete mask method for the efficient construction of multi-block volumetric parameterization based on a set of given boundary spline surfaces. Given the block-partition information of a model, the interior control points can be obtained efficiently by solving a sparse linear system. The existence and uniqueness of the solution for the linear system are also proved. After performing a pre-process on the non-compatible boundary surfaces, the discrete Coons mask is generalized to a unified form, which provides more choices for the construction of inner control points. The proposed method is not only suitable for the multi-block case with C 1 continuity, but can also be used for the case in which the boundary surfaces are of different degrees, and with different number of control points and knot vectors. Several examples are presented to illustrate the effectiveness of the proposed method.

Numerical approximation of minimal surface is an important problem in form-finding of structural membranes. In this paper, we present a novel approach to construct minimal surface from a given boundary by quasi-harmonic Bézier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bézier surface from given boundaries. The quasi-harmonic mask is also proposed to generate approximate minimal surfaces by solving a sparse linear system. We propose a framework to construct multi-patch quasi-harmonic Bézier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.

A proposed framework for remeshing polygonal models employs mesh-free techniques for processing surface sample points. It's robust to input models with problematic connectivity, and the geometric processing of points runs easily in parallel on a GPU. The framework extracts visual-perception information in the image space and maps it back to the Euclidean space. On the basis of these visual cues, the framework generates a saliency field to resample the input model. A new projection operator further optimizes the distribution of resampled points. Because the downsampled points control the number of vertices on the resulting model, this framework also works for model simplification. All the algorithms in the framework can be easily parallelized to run on GPUs. In experiments, the framework remeshed diverse polygonal models to well-shaped triangular meshes with high visual fidelity.

We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation,and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation, rotation, and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.

The use of 3D CAD in mechanical product design has become a standard practice.Consequently, methods and tools are continually being developed to improve designers' efficiency in the creation, modification and analysis of 3D CAD models.Recent software developments had led to the emergence of multiple tools capable of comparing 3D CAD models to locate shape similarities or differences, leading to benefits in various CAD-and PLM-related application domains such as design reuse, data exchange and engineering change management.This paper describes evaluation trials that were performed on sets of commercially available 3D CAD model comparison tools.The goal was to evaluate their capacity to efficiently calculate, represent and display 3D CAD model differences in shape change transposition scenarios where shape modifications must be precisely located and elaborated in order to be consistently propagated between application-specific models of a product.First, some basic concepts of 3D CAD model comparison are presented.Then, simulated shape change assessment scenarios are defined to pilot two series of evaluation trials intended for existing software tools capable of comparing 3D CAD procedural and explicit models, respectively.The results are summarized and conclusions are drawn.

Curve-pair based deformation is an extension of axial deformation for providing more intuitive and convenient control of object deformation. In this paper, we investigate the problem of the direct manipulation of curve-pair based deformation with geometric constraints. With different objective functions, two kinds of constrained optimization problems are derived from the direct manipulation problem, the first one is based on the minimization of the changes in the control polygon of the curve pair, and the second one is based on the minimization of the length change of the object to be deformed. The corresponding nonlinear constrained optimization problems are solved by using the Uzawa method. In order to preserve geometric detail in a deformation, we propose a detail-preserving direct manipulation approach by using Laplacian coordinates. Users are only required to specify some constraint points to control the deformation. Experimental results and comparisons with other approaches are presented to demonstrate the effectiveness and stability of the proposed methods.

CAD tools are becoming increasingly powerful today.They provide users with more efficiency and improve the overall performance of design activities.CAD software publishers include specific tools that are dedicated to knowledge management in order to achieve this design performance and significant savings.The use of these tools and certain functions is nevertheless context-oriented.A decisional model for the use of knowledgeware has therefore been developed here, and the application of knowledgeware in different industrial cases is discussed.

Comfort test of footwear is mainly based on subjective perception of the wearer and a large number of subjects are required to obtain a reliable result. Therefore, the subjective comfort test is expensive and time consuming. Although the foot size and shape of a subject can be obtained by using a three-dimensional (3D) foot scanner, it is still difficult to create foot motion animations of each subject suitable for computer simulation. In this paper, we propose a fast approach to model foot deformation and present its application in simulating interaction with footwear towards footwear design. The simulation determines deformation of foot and footwear models. It can also determine stress distribution in the footwear. Given an initial foot model and a captured foot motion, human foot animation is created first. Then, the footwear model is fitted to the foot to compute the deformation and stress in the footwear. In this article, the boundary element method (BEM) is adopted. We demonstrate the results by conducting simulation of a captured gait motion. Experimental results showed that the method can be used to simulate human gait motion, and can determine deformation of footwear.

In this paper, we present an automatic approach to match correspondences on 3-D human bodies in various postures so that feature points can be automatically extracted. The feature points are very important to the establishment of volumetric parameterization around human bodies for the human-centered customization of soft-products (Trans. Autom. Sci. Eng., vol. 4, issue no. 1, pp. 11-21, 2007). For a given template human model with a set of predefined feature points, we first down-sample the input model into a set of sample points. Then, the corresponding points of these samples on the human model are identified by minimizing the distortion with the help of a series of transformations regardless of their differences in postures, scales or positions. The basic idea of our algorithm is to transform the template human body to the shape of the input model iteratively. To generate a bending invariant mapping, the initial correspondence/transformation is computed in a multidimensional scaling (MDS) embedding domain of 3-D human models, where the Euclidean distance between two samples on a 3-D model in the MDS domain corresponds to the geodesic distance between them in ℜ3 . As the posture change (i.e., the body bending) of a human model can be considered as approximately isometric in the intrinsic 3-D shape, the initial correspondences established in the MDS domain can greatly enhance the robustness of our approach in body bending. Once the correspondences between the surface samples on the template model and the input model are determined after iterative transformations, we have essentially found the corresponding feature points on the input model. Finally, the locations of the based local matching step.

This paper presents a technique for creating 3D fractal art forms automatically. Using this approach, designers can get access to a large number of 3D art shapes that can be modified interactively. This is based on a modified evolutionary algorithm using Fractal Transform (FT) and Iterated Function System (IFS), which provides tunable geometric parameters. Fitness function for measuring the aesthetics of a fractal shape is formulated based on characteristic parameters in fractal theory, including capacity dimension, correlation dimension, and largest Lyapunov exponent. The productivity of visually appealing fractal can be enhanced by using the proposed technique. Experiments demonstrated the effectiveness of the proposed method, which can be applied to the design of jewelry, light fixture, and decorative patterns.

This paper presents optimization of rolling mill housing design for rigidity to have better gage control of the material being rolled.The stress distribution of housing is analyzed using Computer-Aided Engineering (CAE) by calculating maximum static stress at critical areas.Comparing the stress distribution before and after the optimization, the stresses of housing after optimization has considerably been reduced under the given boundary conditions and is within the recommended value.To calculate the stresses in actual conditions, a prototype of optimized housing design is generated in 1:10 scale.The results of the CAE analysis are compared with the experimental results getting from the prototype of optimized design and a good correlation between the results has been observed.

In this paper, a traction superimposition method for simulating the deformation of multicomponent elastic models with different interfacial mesh densities is introduced. By applying linear interpolation method, the displacement data can be transferred between nonconforming interfaces. With the application of energy conservation principle, a relationship between the forces on different surfaces is constructed. By considering the displacement compatibility conditions together with force equilibrium conditions over the common interfaces, a relation between different components of a system is established. However, this interpolation method is only applicable to object components with the same or similar mesh densities. For models with different mesh densities between neighboring components, abnormities arise in the deformation. The causes of these abnormities are parsed by experiments and theoretical analysis. To eliminate the abnormal deformation, a traction superimposition method is proposed to enforce the force constraints on the interfaces. Experimental results are provided to verify this approach.

In this paper, we investigate the direct manipulation problem of free form deformation with rational DMS spline volume (RDMS-FFD). For the weights based direct manipulation method, the solution of the weights can be achieved by solving a linear system; for the control points based method, the explicit solution of displacements of the control points can be obtained, and some properties are also derived from the results. For the constraint points inside the control lattices, we use the weights based methods; for the constraint points outside the control lattices, the control points based method is adopted. Several examples are presented to show the effectiveness of the proposed methods.

Sculpting deformation is a powerful tool to modify the shape of objects intuitively. However, the detail preserving problem has not been considered in sculpting deformation. In the deformation of a source object by pressing a primitive object against it, the source object is deformed while geometric details of the object should be maintained. In order to address this problem, we present a detail preserving sculpting deformation algorithm by using Laplacian coordinates. Based on the property of Laplacian coordinate, we propose two feature invariants to encode the Laplacian coordinate. Instead of mapping the source mesh to the primitive mesh, we map the smooth version of source mesh to the primitive mesh and use the Laplacian coordinates to encode the geometric details. When the smooth version of the source mesh is deformed, the Laplacian coordinates of the deformed mesh are computed for each vertex firstly and then the deformed mesh is reconstructed by solving a linear system that satisfies the reconstruction of the local details in least squares sense. Several examples are presented to show the effectiveness of the proposed approach.

Traditional axial deformation is simple and intuitive for users to modify the shape of objects. However, unexpected twist of the object may be obtained. The use of a curve-pair allows the local coordinate frame to be controlled intuitively. However, some important geometric details may be lost and changed in the deformation process. In this paper, we present a detail-preserving axial deformation algorithm based on Laplacian coordinates. Instead of embedding the absolute coordinates into deformation space in traditional axial deformation, we transform the Laplacian coordinates at each vertex according to the transformation of local frames at the closest points on the axial curve. Then the deformed mesh is reconstructed by solving a linear system that describes the reconstruction of the local details in least squares sense. By associating a complex 3D object to a curve-pair, the object can be stretched, bend, twisted intuitively through manipulating the curve-pair, and can also be edited by means of view-dependent sketching. This method combines the advantages of axial deformation and Laplacian mesh editing. Experimental results are presented to show the effectiveness of the proposed method.