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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.).

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 paper aims to apply Buckingham Pi dimensional analysis method for assessing direct evaporative cooler performance with a cooling pad made of banana midrib and ramie fiber. The saturation efficiency acted as the indicator performance of the evaporative cooler.

The paper describes an experimental study of the direct evaporative cooler with a cooling pad made of banana midrib and rami fiber. There were six parameters in the experiment: absorbed water as a dependent variable was affected by independent parameters such as air velocity and temperature, cooling pad cross-section area and thickness. Based on these variables, we arranged three dimensionless numbers and their correlation.

The paper provides three calculated dimensionless numbers plotted on a curve with a specific correlation. The curve trends for 30 mm and 50 mm pad thickness were almost similar. The range of Reynolds number for 10 mm pad was narrower than other pad thicknesses. The thicker the cooling pad, the more extensive was the calculated Reynolds number range. A new curve exhibited the relationship between the evaporation rate with the μA/t number. The broader cooling pad cross-section, the thinner pad thickness, and the lower pad temperature were factors that increased the evaporation rate, even though the increase was less significant.

A new material in cooling pad from banana midrib fiber was tested and compared to ramie fiber and conventional cooling pad.

We present a detailed explanation of a mathematical method and numerical technique applied to solve an irregular non‐linear fitting problem that results from attempts to model the calorimetric profiles generated by the binding of phenolic ligands to the insulin hexamer. The method employed uses a non‐traditional approach to modeling data. Rather than start with a simplified model, we use a hierarchical tree of physical models with different degrees of sophistication. Starting with the model of highest dimension, we work our way to an optimum model which is of a lower dimension and is less complex. The algorithm uses two complementary techniques. First, a sensitivity analysis in the vicinity of the optimal point for each model is used to estimate errors in the parameters; that, in turn, provides the user with insight for model simplification. Second, we utilize the optimized model in the prediction of new experimental curves. The core of the method combines a strategy based on the proper split of the initial global numerical task into three locally independent subtasks, and induces a specific split in the search space. The application of three different optimization techniques (two parametric and one variational) with an alternating objective function defined in corresponding subspaces, in combination with the search along the hierarchical tree of mathematical models, enables us to overcome difficult computational problems, including over‐parametrization. We have obtained very accurate fits to a number of calorimetric curves, resulting in a quantitative description of intrinsic functional (free ligand concentration) and vector (equilibrium coefficients and enthalpies of binding) parameters. These quantitative results can now be used to improve the stability of insulin formulations. We believe that, with small modifications to the model, the method and algorithms presented in this article can be applied to other protein‐ligand systems.

Diagrams are ubiquitous in economics and are uncontestably among the most used, if not the most important workhorses of economists, though they come in many forms. This essay examines the different uses of graphs and diagrams in the pioneering work of two Victorian economists, Stanley Jevons and Alfred Marshall. We stress the difference between their use as representations and as visual reasoning tools, a difference that became obscured in the twentieth century with the rise of econometrics.

It is aimed to provide an efficient algorithm for path planning in guidance of autonomous unmanned aerial vehicle (UAV) through 3D terrain environments.

As a stochastic search method, vibrational genetic algorithm (VGA) is improved and used to accelerate the algorithm for path planning.

Using VGA, an efficient path planning algorithm for autonomous UAV was obtained under low population rate and short generation cycle conditions.

VGA decreased the required time for optimal path solution beside its simplicity. Low population rate and short generation cycle are the main benefits of VGA.

The interaction between rock mass structural planes and dynamic stress levels is important to determine the stability of rock mass structures in underground geotechnical engineering. In this work, the authors aim to focus on the degradation effects of fracture geometric parameters and unloading stress paths on rock mechanical properties.

A three-dimensional Particle Flow Code (PFC3D) was used for a systematic numerical simulation of the strength failure and cracking behavior of granite specimens containing prefabricated cracks under conventional triaxial compression and triaxial unilateral unloading. The authors demonstrated the unique mechanical response of prefabricated fractured rock under two conditions. The crack initiation, propagation, and coalescence process of pre-fissured specimens were analyzed in detail.

The authors show that the prefabricated cracks and unilateral unloading conditions not only deteriorate the mechanical strength but also have significant differences in failure modes. The degrading effect of cracks on model strength increases linearly with the decrease of the dip angle. Under the condition of true triaxial unilateral unloading, the deterioration effect of peak strength of rock is very significant, and unloading plays a role in promoting the instability failure of rock after peak, making the rock earlier instability failure. Associating with the particle vector diagram and crack coalescence process, the authors find that model failure mode under unilateral loading conditions is obviously distinct from that in triaxial loading. The peak strain in the unloading direction increases sharply, resulting in a new shear slip.

This study is expected to improve the understanding of the strength failure and cracking behavior of fractured rock under unilateral unloading.

Results have shown that the actual delivery performance of a company is often significantly worse than management's own assessment of its performance.