When Deterministic Design Optimization (DDO) methods are used, deterministic optimum designs are frequently pushed to the design constraint boundary, leaving little or no room for tolerances (or uncertainties) in design, manufacture, and operating processes. In the Reliability-Based Design Optimization (RBDO) model for robust system design, the mean values of uncertain system variables are usually used as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide an improved design but also a higher level of confidence in the design. In this work, we seek to improve the quality of RBDO processes using efficient optimization techniques with object of improving the resulting objective function and satisfying the required constraints. Our recent RBDO developments show its efficiency and applicability in this context. So we present some recent structural engineering applications demonstrate the efficiency of these developed RBDO methods.

For several years, researchers have focused on improving the integration of the CAD, CAM and Analysis through a better communication between the various analysis tools. This tendency to integrate the CAD/Analysis and automation of the corresponding processes requires data sharing between the various tasks using an integrated product model. We are interested in this research orientation to CAD/CAM/Analysis integration by rebuilding the CAD model (BREP), starting from the Analysis results (deformed mesh). Because this problem is complex, it requires to be split into several complementary parts. This paper presents an original interoperability process between the CAD and CAE. This approach is based on a new technique of rebuilding the CAD surface model (Nurbs, Bezier, etc.) starting from triangulation (meshed surface) as a main step of the BREP solid model. In our work, the advantages of this approach are identified using a centrifugal pump example.

Let $S_n^r(\Omega)$ be the spline space of degree n and smoothness r with respect to $\Omega$ where $\Omega$ is a triangulation of a planner polygonal domain. Dimensions of $S_n^r(\Omega)$ over the so-called unconstricted triangulation were given by Farin in [J. Comput. Appl. Math. 192(2006), 320-327]. In this paper, a counter example is given to show that the condition used in the main result in Farins paper is not correct, and then an improved necessary and sufficient condition is presented.

3D point data acquired from laser scan or stereo vision can be quite noisy. A preprocessing step is often needed before a surface reconstruction algorithm can be applied. In this paper, we propose a nonparametric approach for noisy point data preprocessing. In particular, we proposed an anisotropic kernel based nonparametric density estimation method for outlier removal, and a hill-climbing line search approach for projecting data points onto the real surface boundary. Our approach is simple, robust and efficient. We demonstrate our method on both real and synthetic point datasets.

Existing methods for the registration of blurred images are efficient for the artificially blurred images or a planar registration, but not suitable for the naturally blurred images existing in the real image mosaic process. In this paper, we attempt to resolve this problem and propose a method for a distortion-free stitching of naturally blurred images for image mosaic. It adopts a multi-resolution and robust feature based inter-layer mosaic together. In each layer, Harris corner detector is chosen to effectively detect features and RANSAC is used to find reliable matches for further calibration as well as an initial homography as the initial motion of next layer. Simplex and subspace trust region methods are used consequently to estimate the stable focal length and rotation matrix through the transformation property of feature matches. In order to stitch multiple images together, an iterative registration strategy is also adopted to estimate the focal length of each image. Experimental results demonstrate the performance of the proposed method.

In this paper we propose a new type of splines-biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.

Quadratic B$\acute{e}$zier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic B$\acute{e}$zier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing $G^1$ quadratic B$\acute{e}$zier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the $G^1$ quadratic B$\acute{e}$zier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

Based on the equivalence principles of physical properties, geometric properties and externally applied forces between a surface and the corresponding curves, we present a fast physics and example based skin deformation method for character animation in this paper. The main idea is to represent the skin surface and its deformations with a group of curves whose computation incurs much less computing overheads than the direct surface-based approach. The geometric and physical properties together with externally applied forces of the curves are determined from those of the surface defined by these curves according to the equivalence principles between the surface and the curves. This ensures the curve-based approach is equivalent to the original problem. A fourth order ordinary differential equation is introduced to describe the deformations of the curves between two example skin shapes which relates geometric and physical properties and externally applied forces to shape changes of the curves. The skin deformation is determined from these deformed curves. Several examples are given in this paper to demonstrate the application of the method.

Various applications, such as mesh composition and model repair, ask for a natural stitching for polygonal surfaces. Unlike the existing algorithms, we make full use of the information from the two feature lines to be stitched up, and present an accurate stitching method for polygonal surfaces, which minimizes the error between the feature lines. Given two directional polylines as the feature lines on polygonal surfaces, we modify the general placement method for points matching and arrive at a closed-form solution for optimal rotation and translation between the polylines. Following calculating out the stitching line, a local surface optimization method is designed and employed for postprocess in order to gain a natural blending of the stitching region.

Tidal bore is a peculiar nature phenomenon which is caused by the lunar and solar gravitation. Based on the physical characters of tidal bores, in this paper we propose a novel method to model and render this phenomenon, especially the tidal waves in Qiantang estuary. According to Boltzmann equation for tidal waves, we solve it with the novel triangle mesh of Kinectic Flux Vector Splitting (KFVS) mode. Then a method combining a curve forecasting wave and particles model is proposed to render the dynamic scenes of overturning tidal waves. Finally, with some rendering technologies, various realistic tidal waves under diversified conditions is rendered in real time.

In this paper, we demonstrate an autonomous design of motion control of virtual creatures (called animated robots in this paper) and develop modeling software for animated robots. An animated robot can behave autonomously by using its own sensors and controllers on three-dimensional physically modeled environment. The developed software can enable us to execute the simulation of animated robots on physical environment at any time during the modeling process. In order to simulate more realistic world, an approximate fluid environment model with low computational costs is presented. It is shown that a combinatorial use of neural network implementation for controllers and the genetic algorithm (GA) or the particle swarm optimization (PSO) is effective for emerging more realistic autonomous behaviours of animated robots.

Shaping realistic hairstyles for digital characters is a difficult, long and tedious task. The lack of appropriate interaction metaphors enabling efficient and simple, yet accurate hair modeling further aggravates the situation. This paper presents 3D interaction metaphors for modeling virtual hair using haptic interfaces. We discuss user tasks, ergonomic aspects, as well as haptics-based styling and fine-tuning tools on an experimental prototype. In order to achieve faster haptic rates with respect to the hair simulation and obtain a transparent rendering, we adapt our simulation models to comply with the specific requirements of haptic hairstyling actions and decouple the simulation of the hair strand dynamics from the haptic rendering while relying on the same physiochemical hair constants. Besides the direct use of the discussed interaction metaphors in the 3D modeling area, the presented results have further application potential in hair modeling facilities for the entertainment industry and the cosmetic sciences.

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

In this paper, we propose a volume rendering method using grid computing for large-scale volume data. Grid computing is attractive because medical institutions and research facilities often have a large number of idle computers. A large-scale volume data is divided into sub-volumes and the sub-volumes are rendered using grid computing. When using grid computing, different computers rarely have the same processor speeds. Thus the return order of results rarely matches the sending order. However order is vital when combining results to create a final image. Job-Scheduling is important in grid computing for volume rendering, so we use an obstacle-flag which changes priorities dynamically to manage sub-volume results. Obstacle-Flags manage visibility of each sub-volume when line of sight from the view point is obscured by other subvolumes. The proposed Dynamic Job-Scheduling based on visibility substantially increases efficiency. Our Dynamic Job-Scheduling method was implemented on our university's campus grid and we conducted comparative experiments, which showed that the proposed method provides significant improvements in efficiency for large-scale volume rendering.

The purpose of this study is to clarify the mechanical behavior of human lumbar vertebrae (L3/L4) with and without fusion bone under physiological axial compression. The author has developed the program code to build the patient specific three-dimensional geometric model from the computed tomography (CT) images. The developed three-dimensional model provides the necessary information to the physicians and surgeons to visually interact with the model and if needed, plan the way of surgery in advance. The processed data of the model is versatile and compatible with the commercial computer aided design (CAD), finite element analysis (FEA) software and rapid prototyping technology. The actual physical model is manufactured using rapid prototyping technique to confirm the executable competence of the processed data from the developed program code. The patient specific model of L3/L4 vertebrae is analyzed under compressive loading condition by the FEA approach. By varying the spacer position and fusion bone with and without pedicle instrumentation, simulations were carried out to find the increasing axial stiffness so as to ensure the success of fusion technique. The finding was helpful in positioning the fusion bone graft and to predict the mechanical stress and deformation of body organ indicating the critical section.