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Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications. In the literature, several approaches have been proposed to solve this problem. However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k), and point sample size (r) on the optimized curve reconstruction measured by a penalty function (f). The paper aims to discuss these issues.

A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed. Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored.

It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m. Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks. The authors were able to detect the presence of such spurious features with spectral analysis. Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample.

The authors have addressed important voids of previous works in this field. The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how. Also, the authors performed a characterization of the curve fitting problem from the optimization perspective. And finally, the authors devised a method to detect spurious features in the fitting curve.

This paper provides a methodology to select the important tuning parameters in a formal manner.

Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.).

When establishing a mathematical model to simulate solid mechanics, considering realistic geometries, special tools are needed to translate measured data, possibly with noise, into idealized geometrical entities. As an engineering application, wheel-rail contact interactions are fundamental in the dynamic modeling of railway vehicles. Many approaches used to solve the contact problem require a continuous parametric description of the geometries involved. However, measured wheel and rail profiles are often available as sets of discrete points. A reconstruction method is needed to transform discrete data into a continuous geometry.

The authors present an approximation method based on optimization to solve the problem of fitting a set of points with an arc spline. It consists of an initial guess based on a curvature function estimated from the data, followed by a least-squares optimization to improve the approximation. The authors also present a segmentation scheme that allows the method to increment the number of segments of the spline, trying to keep it at a minimal value, to satisfy a given error tolerance.

The paper provides a better understanding of arc splines and how they can be deformed. Examples with parametric curves and slightly noisy data from realistic wheel and rail profiles show that the approach is successful.

The developed methods have theoretical value. Furthermore, they have practical value since the approximation approach is better suited to deal with the reconstruction of wheel/rail profiles than interpolation, which most methods use to some degree.

The purpose of this paper is to present a topology-based tissue scaffold design methodology to accurately represent the heterogeneous internal architecture of tissues/organs.

An image analysis technique is used that digitizes the topology information contained in medical images of tissues/organs. A weighted topology reconstruction algorithm is implemented to represent the heterogeneity with parametric functions. The parametric functions are then used to map the spatial material distribution following voxelization. The generated chronological information yields hierarchical tool-path points which are directly transferred to the three-dimensional (3D) bio-printer through a proposed generic platform called Application Program Interface (API). This seamless data corridor between design (virtual) and fabrication (physical) ensures the manufacturability of personalized heterogeneous porous scaffold structure without any CAD/STL file.

The proposed methodology is implemented to verify the effectiveness of the approach and the designed example structures are bio-fabricated with a deposition-based bio-additive manufacturing system. The designed and fabricated heterogeneous structures are evaluated which shows conforming porosity distribution compared to uniform method.

In bio-fabrication process, the generated bio-models with boundary representation (B-rep) or surface tessellation (mesh) do not capture the internal architectural information. This paper provides a design methodology for scaffold structure mimicking the native tissue/organ architecture and direct fabricating the structure without reconstructing the CAD model. Therefore, designing and direct bio-printing the heterogeneous topology of tissue scaffolds from medical images minimize the disparity between the internal architecture of target tissue and its scaffold.

For over three decades, vector autoregressions have played a central role in empirical macroeconomics. These models are general, can capture sophisticated dynamic behavior, and can be extended to include features such as structural instability, time-varying parameters, dynamic factors, threshold-crossing behavior, and discrete outcomes. Building upon growing evidence that the assumption of linearity may be undesirable in modeling certain macroeconomic relationships, this article seeks to add to recent advances in VAR modeling by proposing a nonparametric dynamic model for multivariate time series. In this model, the problems of modeling and estimation are approached from a hierarchical Bayesian perspective. The article considers the issues of identification, estimation, and model comparison, enabling nonparametric VAR (or NPVAR) models to be fit efficiently by Markov chain Monte Carlo (MCMC) algorithms and compared to parametric and semiparametric alternatives by marginal likelihoods and Bayes factors. Among other benefits, the methodology allows for a more careful study of structural instability while guarding against the possibility of unaccounted nonlinearity in otherwise stable economic relationships. Extensions of the proposed nonparametric model to settings with heteroskedasticity and other important modeling features are also considered. The techniques are employed to study the postwar U.S. economy, confirming the presence of distinct volatility regimes and supporting the contention that certain nonlinear relationships in the data can remain undetected by standard models.

This paper identifies the “idiosyncratic basis”, the residual premia computed from stripping away the hypothetical cross-currency basis (CCB) from the cross-currency credit spread (CCCS) of eligible senior corporate dollar-denominated bonds relative to their hypothetical euro-denominated comparator of identical seniority, duration, credit risk and issuer. The adherence of the idiosyncratic basis to the no-arbitrage condition is subsequently evaluated through the application of an indicative market-neutral credit strategy that is designed to harvest the apparent static arbitrage opportunities. The success of the strategy, which systematically captures the idiosyncratic basis as it adheres to the no-arbitrage conditions, is validated retrospectively to frame the basis as an additional class of alternative risk premia (ARP), which investors can seek to optimise exposure to in a long-only context.

The purpose of this paper is to propose an interactive 2D–3D garment parametric pattern-making and linkage editing scheme that integrates clothing design, simulation and interaction to design 3D garments and 2D patterns. The proposed scheme has the potential to satisfy the individual needs of fashion industry, such as precise fit evaluation of the garment, interactive style editing with ease allowance and constrained contour lines in fashion design.

The authors first construct a parametric pattern-making model for flat pattern design corresponding to the body dimensions. Then, the designing 2D patterns are stitched on a virtual 3D mannequin by performing a virtual try-on. If the customer is unsatisfied after the virtual try-on, the adjustable parameters (appearance parameters and fit parameters) can be adjusted using the 2D–3D linkage editing with hierarchical constrained contour lines, and the fit evaluation tool interactively provides the feedback.

The authors observed that the usability and efficiency of the existing garment pattern-making method simplifies the garment pattern-making process. The authors utilize an interactive garment parametric flat pattern-making model to generate an individualized garment flat pattern that effectively adjust and realize the local editing of the garment pattern-making. The 2D–3D linkage editing is then employed, which alters the size and shape of garment pattern for a precise human model fit of the 3D garment using hierarchical constrained contour lines. Various instances have validated the effectiveness of the proposed scheme, which can increase the reusability of the existing garment styles and improve the efficiency of fashion design.

First, the authors do not consider the garment pattern-making design of sophisticated styles. Second, the authors do not directly consider complex garment shapes such as wrinkles, folds, multi-layer models and fabric physical properties.

The authors propose a pattern adjustment scheme that uses the 3D virtual try-on technology to avoid repetitions of reality-based fit tests and garment sample making in the designing process of clothing products. The proposed scheme provides interactive selections of garment patterns and sizes and renders modification tools for 3D garment designing and 2D garment pattern-making. The authors present the 2D–3D interactive linkage editing scheme for a custom-fit garment pattern based on the hierarchical constraint contour lines. The spatial relationship among the human body, pattern pieces and 3D garment model is adequately expressed, and the final design result of the garment pattern is obtained by constraint solving. Meanwhile, the tightness tension of different parts of the 3D garment is analyzed, and the fit and comfort of the garment are quantitatively evaluated.

In this work, minimum energy based interpolation has been done for an optimal well path and effects of energy and fitting coefficients have been studied. An optimal well path also maintains the given radius of curvature and satisfies drilling requirements. Interactive incremental design concept has been used in this work which, controls length and other geometric properties of well path. In the first part of the research, whole well segment has been taken for optimization. Geometric constraints are put to satisfy the drilling requirements. In the second part of the research only the curved portion of well segment has been taken for optimization. Geometric perspective of the well has been considered in this formulation.

This paper aims to automatically derive a 2D parametric model of the main characteristic lines of a car from images, blueprints or hand-made sketches of its side view. Then this model can be used for the further computer-aided design manipulation starting from images of the side view of a car.

The method combines different image edge detection techniques and edge removal processes with optimization techniques according to local and global constraints specific of the single curves to automatically construct a precise parametric model of the main character lines of a car from images. First, process the car image to compute the most important curves and then warp a car template model to match its feature points and curves with the ones detected in the image.

The paper provides method to construct parametric model from an image using maximum cover ratio to the edge points obtained by state-of-the-art edge detection algorithms. A feature points’ organization mechanism produces quadric curves to express feature curves of a product.

The robustness of the presented method depends on the completeness of edge detection results and the accuracy of some key points’ registration result, so if the image is not good, the result cannot be trusted. Only side-view is considered in this paper. Additional limits in the process regard the side view verification: pictures of the front or rear view can be wrongly classified as lateral ones when they contain round lights.

This program enables designers to convert the image to geometric parametric model directly.

The method is applicable to shaded pictures, sketches and blue prints of the side view of a car. It can process a database of car images in a batch mode or a specific picture on user demand. The method classifies the cars to different categories: SUV/Wagon/Hatchback, sedan, city and coupe. The authors obtain good results for every category.

The growth incidence curve of Ravallion and Chen (2003) is based on the quantile function. Its distribution-free estimator behaves erratically with usual sample sizes leading to problems in the tails. The authors propose a series of parametric models in a Bayesian framework. A first solution consists in modeling the underlying income distribution using simple densities for which the quantile function has a closed analytical form. This solution is extended by considering a mixture model for the underlying income distribution. However, in this case, the quantile function is semi-explicit and has to be evaluated numerically. The last solution consists in adjusting directly a functional form for the Lorenz curve and deriving its first-order derivative to find the corresponding quantile function. The authors compare these models by Monte Carlo simulations and using UK data from the Family Expenditure Survey. The authors devote a particular attention to the analysis of subgroups.